%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP148^1 : 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 : n023.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 08:55:56 AM UTC 2026
% Result : Theorem 4.18s 2.14s
% Output : Refutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 73 ( 5 ~; 0 |; 0 &; 68 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 110 ( 108 usr; 11 con; 0-3 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
complex: $tType ).
thf(type_def_7,type,
set_complex: $tType ).
thf(type_def_8,type,
a: $tType ).
thf(type_def_9,type,
set_a: $tType ).
thf(type_def_10,type,
real: $tType ).
thf(type_def_11,type,
set_real: $tType ).
thf(type_def_12,type,
set_complex_a: $tType ).
thf(type_def_13,type,
set_real_real: $tType ).
thf(type_def_14,type,
set_real_a: $tType ).
thf(type_def_15,type,
set_a_complex: $tType ).
thf(type_def_16,type,
set_a_a: $tType ).
thf(func_def_0,type,
set_real_real: $tType ).
thf(func_def_1,type,
set_a_complex: $tType ).
thf(func_def_2,type,
set_complex_a: $tType ).
thf(func_def_3,type,
set_real_a: $tType ).
thf(func_def_4,type,
set_complex: $tType ).
thf(func_def_5,type,
set_a_a: $tType ).
thf(func_def_6,type,
set_real: $tType ).
thf(func_def_7,type,
set_a: $tType ).
thf(func_def_8,type,
complex: $tType ).
thf(func_def_9,type,
real: $tType ).
thf(func_def_10,type,
a: $tType ).
thf(func_def_11,type,
bij_be209634132omplex: ( complex > complex ) > set_complex > set_complex > $o ).
thf(func_def_12,type,
bij_betw_complex_a: ( complex > a ) > set_complex > set_a > $o ).
thf(func_def_13,type,
bij_be122140626omplex: ( real > complex ) > set_real > set_complex > $o ).
thf(func_def_14,type,
bij_betw_real_real: ( real > real ) > set_real > set_real > $o ).
thf(func_def_15,type,
bij_betw_real_a: ( real > a ) > set_real > set_a > $o ).
thf(func_def_16,type,
bij_betw_a_complex: ( a > complex ) > set_a > set_complex > $o ).
thf(func_def_17,type,
bij_betw_a_a: ( a > a ) > set_a > set_a > $o ).
thf(func_def_18,type,
comp_c130555887omplex: ( complex > complex ) > ( complex > complex ) > complex > complex ).
thf(func_def_19,type,
comp_c595887981x_real: ( complex > complex ) > ( real > complex ) > real > complex ).
thf(func_def_20,type,
comp_c124850173plex_a: ( complex > complex ) > ( a > complex ) > a > complex ).
thf(func_def_21,type,
comp_c819638635l_real: ( complex > real ) > ( real > complex ) > real > real ).
thf(func_def_22,type,
comp_complex_real_a: ( complex > real ) > ( a > complex ) > a > real ).
thf(func_def_23,type,
comp_c274302683omplex: ( complex > a ) > ( complex > complex ) > complex > a ).
thf(func_def_24,type,
comp_complex_a_real: ( complex > a ) > ( real > complex ) > real > a ).
thf(func_def_25,type,
comp_complex_a_a: ( complex > a ) > ( a > complex ) > a > a ).
thf(func_def_26,type,
comp_r667767405omplex: ( real > complex ) > ( complex > real ) > complex > complex ).
thf(func_def_27,type,
comp_r701421291x_real: ( real > complex ) > ( real > real ) > real > complex ).
thf(func_def_28,type,
comp_real_complex_a: ( real > complex ) > ( a > real ) > a > complex ).
thf(func_def_29,type,
comp_r422820971omplex: ( real > real ) > ( complex > real ) > complex > real ).
thf(func_def_30,type,
comp_real_real_real: ( real > real ) > ( real > real ) > real > real ).
thf(func_def_31,type,
comp_real_real_a: ( real > real ) > ( a > real ) > a > real ).
thf(func_def_32,type,
comp_real_a_complex: ( real > a ) > ( complex > real ) > complex > a ).
thf(func_def_33,type,
comp_real_a_real: ( real > a ) > ( real > real ) > real > a ).
thf(func_def_34,type,
comp_real_a_a: ( real > a ) > ( a > real ) > a > a ).
thf(func_def_35,type,
comp_a1063143865omplex: ( a > complex ) > ( complex > a ) > complex > complex ).
thf(func_def_36,type,
comp_a_complex_real: ( a > complex ) > ( real > a ) > real > complex ).
thf(func_def_37,type,
comp_a_complex_a: ( a > complex ) > ( a > a ) > a > complex ).
thf(func_def_38,type,
comp_a_real_complex: ( a > real ) > ( complex > a ) > complex > real ).
thf(func_def_39,type,
comp_a_real_real: ( a > real ) > ( real > a ) > real > real ).
thf(func_def_40,type,
comp_a_real_a: ( a > real ) > ( a > a ) > a > real ).
thf(func_def_41,type,
comp_a_a_complex: ( a > a ) > ( complex > a ) > complex > a ).
thf(func_def_42,type,
comp_a_a_real: ( a > a ) > ( real > a ) > real > a ).
thf(func_def_43,type,
comp_a_a_a: ( a > a ) > ( a > a ) > a > a ).
thf(func_def_44,type,
id_complex_a: ( complex > a ) > complex > a ).
thf(func_def_45,type,
id_real_a: ( real > a ) > real > a ).
thf(func_def_46,type,
id_a_a: ( a > a ) > a > a ).
thf(func_def_47,type,
id_complex: complex > complex ).
thf(func_def_48,type,
id_real: real > real ).
thf(func_def_49,type,
id_a: a > a ).
thf(func_def_50,type,
inj_on893405649omplex: ( ( complex > a ) > complex > complex ) > set_complex_a > $o ).
thf(func_def_51,type,
inj_on1576005937plex_a: ( ( complex > a ) > complex > a ) > set_complex_a > $o ).
thf(func_def_52,type,
inj_on958237983real_a: ( ( real > real ) > real > a ) > set_real_real > $o ).
thf(func_def_53,type,
inj_on319905617omplex: ( ( real > a ) > real > complex ) > set_real_a > $o ).
thf(func_def_54,type,
inj_on_real_a_real_a: ( ( real > a ) > real > a ) > set_real_a > $o ).
thf(func_def_55,type,
inj_on_a_complex_a_a: ( ( a > complex ) > a > a ) > set_a_complex > $o ).
thf(func_def_56,type,
inj_on_a_a_a_complex: ( ( a > a ) > a > complex ) > set_a_a > $o ).
thf(func_def_57,type,
inj_on_a_a_a_a: ( ( a > a ) > a > a ) > set_a_a > $o ).
thf(func_def_58,type,
inj_on94911183omplex: ( complex > complex ) > set_complex > $o ).
thf(func_def_59,type,
inj_on_complex_a: ( complex > a ) > set_complex > $o ).
thf(func_def_60,type,
inj_on_real_complex: ( real > complex ) > set_real > $o ).
thf(func_def_61,type,
inj_on_real_real: ( real > real ) > set_real > $o ).
thf(func_def_62,type,
inj_on_real_a: ( real > a ) > set_real > $o ).
thf(func_def_63,type,
inj_on_a_complex: ( a > complex ) > set_a > $o ).
thf(func_def_64,type,
inj_on_a_a: ( a > a ) > set_a > $o ).
thf(func_def_65,type,
zero_zero_complex: complex ).
thf(func_def_66,type,
zero_zero_a: a ).
thf(func_def_67,type,
top_top_complex_o: complex > $o ).
thf(func_def_68,type,
top_top_a_o: a > $o ).
thf(func_def_69,type,
top_to525076535plex_a: set_complex_a ).
thf(func_def_70,type,
top_to1446257885l_real: set_real_real ).
thf(func_def_71,type,
top_top_set_real_a: set_real_a ).
thf(func_def_72,type,
top_to2109114701omplex: set_a_complex ).
thf(func_def_73,type,
top_top_set_a_a: set_a_a ).
thf(func_def_74,type,
top_top_set_complex: set_complex ).
thf(func_def_75,type,
top_top_set_real: set_real ).
thf(func_def_76,type,
top_top_set_a: set_a ).
thf(func_def_77,type,
path_arc_complex: ( real > complex ) > $o ).
thf(func_def_78,type,
path_arc_real: ( real > real ) > $o ).
thf(func_def_79,type,
path_arc_a: ( real > a ) > $o ).
thf(func_def_80,type,
path_path_complex: ( real > complex ) > $o ).
thf(func_def_81,type,
path_path_real: ( real > real ) > $o ).
thf(func_def_82,type,
path_path_a: ( real > a ) > $o ).
thf(func_def_83,type,
path_p769714271omplex: ( real > complex ) > complex ).
thf(func_def_84,type,
path_pathfinish_real: ( real > real ) > real ).
thf(func_def_85,type,
path_pathfinish_a: ( real > a ) > a ).
thf(func_def_86,type,
path_p797330068omplex: ( real > complex ) > complex ).
thf(func_def_87,type,
path_pathstart_real: ( real > real ) > real ).
thf(func_def_88,type,
path_pathstart_a: ( real > a ) > a ).
thf(func_def_89,type,
path_rectpath: complex > complex > real > complex ).
thf(func_def_90,type,
path_s36253918omplex: ( real > complex ) > $o ).
thf(func_def_91,type,
path_s1005760220h_real: ( real > real ) > $o ).
thf(func_def_92,type,
path_simple_path_a: ( real > a ) > $o ).
thf(func_def_93,type,
poinca1910941596x_of_a: a > complex ).
thf(func_def_94,type,
poinca837721858l_of_a: complex > a ).
thf(func_def_95,type,
real_V762982918plex_a: ( complex > a ) > $o ).
thf(func_def_96,type,
real_V912435428omplex: ( a > complex ) > $o ).
thf(func_def_97,type,
real_V301987619plex_a: ( complex > a ) > $o ).
thf(func_def_98,type,
real_V451440129omplex: ( a > complex ) > $o ).
thf(func_def_99,type,
real_V670066493omplex: ( complex > complex ) > $o ).
thf(func_def_100,type,
real_V1327653935plex_a: ( complex > a ) > $o ).
thf(func_def_101,type,
real_V1948715323omplex: ( real > complex ) > $o ).
thf(func_def_102,type,
real_V1354572473l_real: ( real > real ) > $o ).
thf(func_def_103,type,
real_V779700657real_a: ( real > a ) > $o ).
thf(func_def_104,type,
real_V1477106445omplex: ( a > complex ) > $o ).
thf(func_def_105,type,
real_V202220639ar_a_a: ( a > a ) > $o ).
thf(func_def_106,type,
collect_complex: ( complex > $o ) > set_complex ).
thf(func_def_107,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_108,type,
member_complex: complex > set_complex > $o ).
thf(func_def_109,type,
member_a: a > set_a > $o ).
thf(func_def_110,type,
c: real > a ).
thf(func_def_126,type,
sK0: complex > ( a > complex ) > a ).
thf(func_def_127,type,
sK1: ( complex > a ) > a > complex ).
thf(func_def_128,type,
sK2: ( a > complex ) > a ).
thf(func_def_129,type,
sK3: ( a > complex ) > a ).
thf(func_def_130,type,
sK4: ( a > complex ) > complex > a ).
thf(func_def_131,type,
sK5: ( a > complex ) > a ).
thf(func_def_132,type,
sK6: ( a > complex ) > a ).
thf(func_def_134,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f883,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f882,f844]) ).
thf(f844,plain,
! [X0: a > complex,X1: real > a] :
( ( path_p769714271omplex @ ( comp_a_complex_real @ X0 @ X1 ) )
= ( X0 @ ( path_pathfinish_a @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f751]) ).
thf(f751,plain,
! [X0: a > complex,X1: real > a] :
( ( path_p769714271omplex @ ( comp_a_complex_real @ X0 @ X1 ) )
= ( X0 @ ( path_pathfinish_a @ X1 ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
! [X3: a > complex,X4: real > a] :
( ( path_p769714271omplex @ ( comp_a_complex_real @ X3 @ X4 ) )
= ( X3 @ ( path_pathfinish_a @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.I8HVgnaxTf/DTF2THF_21628.p',fact_13_pathfinish__compose) ).
thf(f882,plain,
( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
!= ( poinca1910941596x_of_a @ ( path_pathfinish_a @ c ) ) ),
inference(forward_demodulation,[status(thm)],[f881,f872]) ).
thf(f872,plain,
( ( path_pathfinish_a @ c )
= ( path_pathstart_a @ c ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( path_pathfinish_a @ c )
= ( path_pathstart_a @ c ) ),
file('/export/starexec/sandbox/tmp/tmp.I8HVgnaxTf/DTF2THF_21628.p',fact_0_assms_I2_J) ).
thf(f881,plain,
( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
!= ( poinca1910941596x_of_a @ ( path_pathstart_a @ c ) ) ),
inference(forward_demodulation,[status(thm)],[f821,f845]) ).
thf(f845,plain,
! [X0: a > complex,X1: real > a] :
( ( path_p797330068omplex @ ( comp_a_complex_real @ X0 @ X1 ) )
= ( X0 @ ( path_pathstart_a @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f754]) ).
thf(f754,plain,
! [X0: a > complex,X1: real > a] :
( ( path_p797330068omplex @ ( comp_a_complex_real @ X0 @ X1 ) )
= ( X0 @ ( path_pathstart_a @ X1 ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,axiom,
! [X3: a > complex,X4: real > a] :
( ( path_p797330068omplex @ ( comp_a_complex_real @ X3 @ X4 ) )
= ( X3 @ ( path_pathstart_a @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.I8HVgnaxTf/DTF2THF_21628.p',fact_18_pathstart__compose) ).
thf(f821,plain,
( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
!= ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ),
inference(cnf_transformation,[status(thm)],[f746]) ).
thf(f746,plain,
( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
!= ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ),
inference(flattening,[status(thm)],[f356]) ).
thf(f356,negated_conjecture,
( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
!= ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ),
inference(negated_conjecture,[status(cth)],[f355]) ).
thf(f355,conjecture,
( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
= ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ),
file('/export/starexec/sandbox/tmp/tmp.I8HVgnaxTf/DTF2THF_21628.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP148^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n023.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 08:28:34 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.43 ---- Original DTF file ---
% 0.18/0.43 thf(spec,logic,$$dhol).
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 % File : ITP148^1 : TPTP v9.2.1. Released v7.5.0.
% 0.18/0.43 % Domain : Interactive Theorem Proving
% 0.18/0.43 % Problem : Sledgehammer Poincare_Bendixson problem prob_301__19573322_1
% 0.18/0.43 % Version : Especial.
% 0.18/0.43 % English :
% 0.18/0.43
% 0.18/0.43 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.18/0.43 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.18/0.43 % Source : [Des21]
% 0.18/0.43 % Names : Poincare_Bendixson/prob_301__19573322_1 [Des21]
% 0.18/0.43
% 0.18/0.43 % Status : Theorem
% 0.18/0.43 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.50 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0
% 0.18/0.43 % Syntax : Number of formulae : 466 ( 110 unt; 111 typ; 0 def)
% 0.18/0.43 % Number of atoms : 864 ( 450 equ; 0 cnn)
% 0.18/0.43 % Maximal formula atoms : 5 ( 2 avg)
% 0.18/0.43 % Number of connectives : 2663 ( 20 ~; 2 |; 17 &;2246 @)
% 0.18/0.43 % ( 0 <=>; 378 =>; 0 <=; 0 <~>)
% 0.18/0.43 % Maximal formula depth : 13 ( 6 avg)
% 0.18/0.43 % Number of types : 12 ( 11 usr)
% 0.18/0.43 % Number of type conns : 1090 (1090 >; 0 *; 0 +; 0 <<)
% 0.18/0.43 % Number of symbols : 101 ( 100 usr; 10 con; 0-3 aty)
% 0.18/0.43 % Number of variables : 1087 ( 74 ^;1002 !; 11 ?;1087 :)
% 0.18/0.43 % SPC : TH0_THM_EQU_NAR
% 0.18/0.43
% 0.18/0.43 % Comments : This file was generated by Sledgehammer 2021-02-23 15:42:34.421
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 % Could-be-implicit typings (11)
% 0.18/0.43 thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 0.18/0.43 set_real_real: $tType ).
% 0.18/0.43
% 0.18/0.43 thf(ty_n_t__Set__Oset_I_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
% 0.18/0.43 set_a_complex: $tType ).
% 0.18/0.43
% 0.18/0.43 thf(ty_n_t__Set__Oset_I_062_It__Complex__Ocomplex_Mtf__a_J_J,type,
% 0.18/0.43 set_complex_a: $tType ).
% 0.18/0.43
% 0.18/0.43 thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mtf__a_J_J,type,
% 0.18/0.43 set_real_a: $tType ).
% 0.18/0.43
% 0.18/0.43 thf(ty_n_t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.18/0.43 set_complex: $tType ).
% 0.18/0.43
% 0.18/0.43 thf(ty_n_t__Set__Oset_I_062_Itf__a_Mtf__a_J_J,type,
% 0.18/0.43 set_a_a: $tType ).
% 0.18/0.43
% 0.18/0.43 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 0.18/0.43 set_real: $tType ).
% 0.18/0.43
% 0.18/0.43 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.18/0.43 set_a: $tType ).
% 0.18/0.43
% 0.18/0.43 thf(ty_n_t__Complex__Ocomplex,type,
% 0.18/0.43 complex: $tType ).
% 0.18/0.43
% 0.18/0.43 thf(ty_n_t__Real__Oreal,type,
% 0.18/0.43 real: $tType ).
% 0.18/0.43
% 0.18/0.43 thf(ty_n_tf__a,type,
% 0.18/0.43 a: $tType ).
% 0.18/0.43
% 0.18/0.43 % Explicit typings (100)
% 0.18/0.43 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 0.18/0.43 bij_be209634132omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001tf__a,type,
% 0.18/0.43 bij_betw_complex_a: ( complex > a ) > set_complex > set_a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Obij__betw_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 0.18/0.43 bij_be122140626omplex: ( real > complex ) > set_real > set_complex > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Obij__betw_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.18/0.43 bij_betw_real_real: ( real > real ) > set_real > set_real > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Obij__betw_001t__Real__Oreal_001tf__a,type,
% 0.18/0.43 bij_betw_real_a: ( real > a ) > set_real > set_a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Obij__betw_001tf__a_001t__Complex__Ocomplex,type,
% 0.18/0.43 bij_betw_a_complex: ( a > complex ) > set_a > set_complex > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Obij__betw_001tf__a_001tf__a,type,
% 0.18/0.43 bij_betw_a_a: ( a > a ) > set_a > set_a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 0.18/0.43 comp_c130555887omplex: ( complex > complex ) > ( complex > complex ) > complex > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 0.18/0.43 comp_c595887981x_real: ( complex > complex ) > ( real > complex ) > real > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001tf__a,type,
% 0.18/0.43 comp_c124850173plex_a: ( complex > complex ) > ( a > complex ) > a > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.18/0.43 comp_c819638635l_real: ( complex > real ) > ( real > complex ) > real > real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Real__Oreal_001tf__a,type,
% 0.18/0.43 comp_complex_real_a: ( complex > real ) > ( a > complex ) > a > real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001tf__a_001t__Complex__Ocomplex,type,
% 0.18/0.43 comp_c274302683omplex: ( complex > a ) > ( complex > complex ) > complex > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001tf__a_001t__Real__Oreal,type,
% 0.18/0.43 comp_complex_a_real: ( complex > a ) > ( real > complex ) > real > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001tf__a_001tf__a,type,
% 0.18/0.43 comp_complex_a_a: ( complex > a ) > ( a > complex ) > a > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 0.18/0.43 comp_r667767405omplex: ( real > complex ) > ( complex > real ) > complex > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 0.18/0.43 comp_r701421291x_real: ( real > complex ) > ( real > real ) > real > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Complex__Ocomplex_001tf__a,type,
% 0.18/0.43 comp_real_complex_a: ( real > complex ) > ( a > real ) > a > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 0.18/0.43 comp_r422820971omplex: ( real > real ) > ( complex > real ) > complex > real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.18/0.43 comp_real_real_real: ( real > real ) > ( real > real ) > real > real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Real__Oreal_001tf__a,type,
% 0.18/0.43 comp_real_real_a: ( real > real ) > ( a > real ) > a > real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001tf__a_001t__Complex__Ocomplex,type,
% 0.18/0.43 comp_real_a_complex: ( real > a ) > ( complex > real ) > complex > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001tf__a_001t__Real__Oreal,type,
% 0.18/0.43 comp_real_a_real: ( real > a ) > ( real > real ) > real > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001tf__a_001tf__a,type,
% 0.18/0.43 comp_real_a_a: ( real > a ) > ( a > real ) > a > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001tf__a_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 0.18/0.43 comp_a1063143865omplex: ( a > complex ) > ( complex > a ) > complex > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001tf__a_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 0.18/0.43 comp_a_complex_real: ( a > complex ) > ( real > a ) > real > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001tf__a_001t__Complex__Ocomplex_001tf__a,type,
% 0.18/0.43 comp_a_complex_a: ( a > complex ) > ( a > a ) > a > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001tf__a_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 0.18/0.43 comp_a_real_complex: ( a > real ) > ( complex > a ) > complex > real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001tf__a_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.18/0.43 comp_a_real_real: ( a > real ) > ( real > a ) > real > real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001tf__a_001t__Real__Oreal_001tf__a,type,
% 0.18/0.43 comp_a_real_a: ( a > real ) > ( a > a ) > a > real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001t__Complex__Ocomplex,type,
% 0.18/0.43 comp_a_a_complex: ( a > a ) > ( complex > a ) > complex > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001t__Real__Oreal,type,
% 0.18/0.43 comp_a_a_real: ( a > a ) > ( real > a ) > real > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001tf__a,type,
% 0.18/0.43 comp_a_a_a: ( a > a ) > ( a > a ) > a > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oid_001_062_It__Complex__Ocomplex_Mtf__a_J,type,
% 0.18/0.43 id_complex_a: ( complex > a ) > complex > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oid_001_062_It__Real__Oreal_Mtf__a_J,type,
% 0.18/0.43 id_real_a: ( real > a ) > real > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oid_001_062_Itf__a_Mtf__a_J,type,
% 0.18/0.43 id_a_a: ( a > a ) > a > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oid_001t__Complex__Ocomplex,type,
% 0.18/0.43 id_complex: complex > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oid_001t__Real__Oreal,type,
% 0.18/0.43 id_real: real > real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oid_001tf__a,type,
% 0.18/0.43 id_a: a > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001_062_It__Complex__Ocomplex_Mtf__a_J_001_062_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 0.18/0.43 inj_on893405649omplex: ( ( complex > a ) > complex > complex ) > set_complex_a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001_062_It__Complex__Ocomplex_Mtf__a_J_001_062_It__Complex__Ocomplex_Mtf__a_J,type,
% 0.18/0.43 inj_on1576005937plex_a: ( ( complex > a ) > complex > a ) > set_complex_a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001_062_It__Real__Oreal_Mt__Real__Oreal_J_001_062_It__Real__Oreal_Mtf__a_J,type,
% 0.18/0.43 inj_on958237983real_a: ( ( real > real ) > real > a ) > set_real_real > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001_062_It__Real__Oreal_Mtf__a_J_001_062_It__Real__Oreal_Mt__Complex__Ocomplex_J,type,
% 0.18/0.43 inj_on319905617omplex: ( ( real > a ) > real > complex ) > set_real_a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001_062_It__Real__Oreal_Mtf__a_J_001_062_It__Real__Oreal_Mtf__a_J,type,
% 0.18/0.43 inj_on_real_a_real_a: ( ( real > a ) > real > a ) > set_real_a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001_062_Itf__a_Mt__Complex__Ocomplex_J_001_062_Itf__a_Mtf__a_J,type,
% 0.18/0.43 inj_on_a_complex_a_a: ( ( a > complex ) > a > a ) > set_a_complex > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mt__Complex__Ocomplex_J,type,
% 0.18/0.43 inj_on_a_a_a_complex: ( ( a > a ) > a > complex ) > set_a_a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J,type,
% 0.18/0.43 inj_on_a_a_a_a: ( ( a > a ) > a > a ) > set_a_a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 0.18/0.43 inj_on94911183omplex: ( complex > complex ) > set_complex > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001t__Complex__Ocomplex_001tf__a,type,
% 0.18/0.43 inj_on_complex_a: ( complex > a ) > set_complex > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 0.18/0.43 inj_on_real_complex: ( real > complex ) > set_real > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.18/0.43 inj_on_real_real: ( real > real ) > set_real > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001tf__a,type,
% 0.18/0.43 inj_on_real_a: ( real > a ) > set_real > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001tf__a_001t__Complex__Ocomplex,type,
% 0.18/0.43 inj_on_a_complex: ( a > complex ) > set_a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Fun_Oinj__on_001tf__a_001tf__a,type,
% 0.18/0.43 inj_on_a_a: ( a > a ) > set_a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex,type,
% 0.18/0.43 zero_zero_complex: complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Groups_Ozero__class_Ozero_001tf__a,type,
% 0.18/0.43 zero_zero_a: a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 0.18/0.43 top_top_complex_o: complex > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Orderings_Otop__class_Otop_001_062_Itf__a_M_Eo_J,type,
% 0.18/0.43 top_top_a_o: a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Complex__Ocomplex_Mtf__a_J_J,type,
% 0.18/0.43 top_to525076535plex_a: set_complex_a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 0.18/0.43 top_to1446257885l_real: set_real_real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Real__Oreal_Mtf__a_J_J,type,
% 0.18/0.43 top_top_set_real_a: set_real_a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
% 0.18/0.43 top_to2109114701omplex: set_a_complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_Itf__a_Mtf__a_J_J,type,
% 0.18/0.43 top_top_set_a_a: set_a_a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.18/0.43 top_top_set_complex: set_complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.18/0.43 top_top_set_real: set_real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
% 0.18/0.43 top_top_set_a: set_a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Oarc_001t__Complex__Ocomplex,type,
% 0.18/0.43 path_arc_complex: ( real > complex ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Oarc_001t__Real__Oreal,type,
% 0.18/0.43 path_arc_real: ( real > real ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Oarc_001tf__a,type,
% 0.18/0.43 path_arc_a: ( real > a ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Opath_001t__Complex__Ocomplex,type,
% 0.18/0.43 path_path_complex: ( real > complex ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Opath_001t__Real__Oreal,type,
% 0.18/0.43 path_path_real: ( real > real ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Opath_001tf__a,type,
% 0.18/0.43 path_path_a: ( real > a ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Opathfinish_001t__Complex__Ocomplex,type,
% 0.18/0.43 path_p769714271omplex: ( real > complex ) > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Opathfinish_001t__Real__Oreal,type,
% 0.18/0.43 path_pathfinish_real: ( real > real ) > real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Opathfinish_001tf__a,type,
% 0.18/0.43 path_pathfinish_a: ( real > a ) > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Opathstart_001t__Complex__Ocomplex,type,
% 0.18/0.43 path_p797330068omplex: ( real > complex ) > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Opathstart_001t__Real__Oreal,type,
% 0.18/0.43 path_pathstart_real: ( real > real ) > real ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Opathstart_001tf__a,type,
% 0.18/0.43 path_pathstart_a: ( real > a ) > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Orectpath,type,
% 0.18/0.43 path_rectpath: complex > complex > real > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Osimple__path_001t__Complex__Ocomplex,type,
% 0.18/0.43 path_s36253918omplex: ( real > complex ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Osimple__path_001t__Real__Oreal,type,
% 0.18/0.43 path_s1005760220h_real: ( real > real ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Path__Connected_Osimple__path_001tf__a,type,
% 0.18/0.43 path_simple_path_a: ( real > a ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Poincare__Bendixson__Mirabelle__pwkwpzhsyu_Oc1__on__open__R2_Ocomplex__of_001tf__a,type,
% 0.18/0.43 poinca1910941596x_of_a: a > complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Poincare__Bendixson__Mirabelle__pwkwpzhsyu_Oc1__on__open__R2_Oreal__of_001tf__a,type,
% 0.18/0.43 poinca837721858l_of_a: complex > a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Complex__Ocomplex_001tf__a,type,
% 0.18/0.43 real_V762982918plex_a: ( complex > a ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001tf__a_001t__Complex__Ocomplex,type,
% 0.18/0.43 real_V912435428omplex: ( a > complex ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Real__Vector__Spaces_Obounded__linear__axioms_001t__Complex__Ocomplex_001tf__a,type,
% 0.18/0.43 real_V301987619plex_a: ( complex > a ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Real__Vector__Spaces_Obounded__linear__axioms_001tf__a_001t__Complex__Ocomplex,type,
% 0.18/0.43 real_V451440129omplex: ( a > complex ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Real__Vector__Spaces_Olinear_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 0.18/0.43 real_V670066493omplex: ( complex > complex ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Real__Vector__Spaces_Olinear_001t__Complex__Ocomplex_001tf__a,type,
% 0.18/0.43 real_V1327653935plex_a: ( complex > a ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Real__Vector__Spaces_Olinear_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 0.18/0.43 real_V1948715323omplex: ( real > complex ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Real__Vector__Spaces_Olinear_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.18/0.43 real_V1354572473l_real: ( real > real ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Real__Vector__Spaces_Olinear_001t__Real__Oreal_001tf__a,type,
% 0.18/0.43 real_V779700657real_a: ( real > a ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Real__Vector__Spaces_Olinear_001tf__a_001t__Complex__Ocomplex,type,
% 0.18/0.43 real_V1477106445omplex: ( a > complex ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Real__Vector__Spaces_Olinear_001tf__a_001tf__a,type,
% 0.18/0.43 real_V202220639ar_a_a: ( a > a ) > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 0.18/0.43 collect_complex: ( complex > $o ) > set_complex ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.18/0.43 collect_a: ( a > $o ) > set_a ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 0.18/0.43 member_complex: complex > set_complex > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_c_member_001tf__a,type,
% 0.18/0.43 member_a: a > set_a > $o ).
% 0.18/0.43
% 0.18/0.43 thf(sy_v_c,type,
% 0.18/0.43 c: real > a ).
% 0.18/0.43
% 0.18/0.43 % Relevant facts (354)
% 0.18/0.43 thf(fact_0_assms_I2_J,axiom,
% 0.18/0.43 ( ( path_pathfinish_a @ c )
% 0.18/0.43 = ( path_pathstart_a @ c ) ) ).
% 0.18/0.43
% 0.18/0.43 % assms(2)
% 0.18/0.43 thf(fact_1_assms_I1_J,axiom,
% 0.18/0.43 path_simple_path_a @ c ).
% 0.18/0.43
% 0.18/0.43 % assms(1)
% 0.18/0.43 thf(fact_2_a1,axiom,
% 0.18/0.43 path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ).
% 0.18/0.43
% 0.18/0.43 % a1
% 0.18/0.43 thf(fact_3_comp__apply,axiom,
% 0.18/0.43 ( comp_real_a_real
% 0.18/0.43 = ( ^ [F: real > a,G: real > real,X: real] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_apply
% 0.18/0.43 thf(fact_4_comp__apply,axiom,
% 0.18/0.43 ( comp_a_complex_a
% 0.18/0.43 = ( ^ [F: a > complex,G: a > a,X: a] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_apply
% 0.18/0.43 thf(fact_5_comp__apply,axiom,
% 0.18/0.43 ( comp_a_a_complex
% 0.18/0.43 = ( ^ [F: a > a,G: complex > a,X: complex] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_apply
% 0.18/0.43 thf(fact_6_comp__apply,axiom,
% 0.18/0.43 ( comp_a_a_real
% 0.18/0.43 = ( ^ [F: a > a,G: real > a,X: real] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_apply
% 0.18/0.43 thf(fact_7_comp__apply,axiom,
% 0.18/0.43 ( comp_a_a_a
% 0.18/0.43 = ( ^ [F: a > a,G: a > a,X: a] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_apply
% 0.18/0.43 thf(fact_8_comp__apply,axiom,
% 0.18/0.43 ( comp_a_complex_real
% 0.18/0.43 = ( ^ [F: a > complex,G: real > a,X: real] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_apply
% 0.18/0.43 thf(fact_9_comp__apply,axiom,
% 0.18/0.43 ( comp_a1063143865omplex
% 0.18/0.43 = ( ^ [F: a > complex,G: complex > a,X: complex] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_apply
% 0.18/0.43 thf(fact_10_comp__apply,axiom,
% 0.18/0.43 ( comp_complex_a_a
% 0.18/0.43 = ( ^ [F: complex > a,G: a > complex,X: a] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_apply
% 0.18/0.43 thf(fact_11_pathfinish__compose,axiom,
% 0.18/0.43 ! [F2: real > a,P: real > real] :
% 0.18/0.43 ( ( path_pathfinish_a @ ( comp_real_a_real @ F2 @ P ) )
% 0.18/0.43 = ( F2 @ ( path_pathfinish_real @ P ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathfinish_compose
% 0.18/0.43 thf(fact_12_pathfinish__compose,axiom,
% 0.18/0.43 ! [F2: complex > complex,P: real > complex] :
% 0.18/0.43 ( ( path_p769714271omplex @ ( comp_c595887981x_real @ F2 @ P ) )
% 0.18/0.43 = ( F2 @ ( path_p769714271omplex @ P ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathfinish_compose
% 0.18/0.43 thf(fact_13_pathfinish__compose,axiom,
% 0.18/0.43 ! [F2: a > complex,P: real > a] :
% 0.18/0.43 ( ( path_p769714271omplex @ ( comp_a_complex_real @ F2 @ P ) )
% 0.18/0.43 = ( F2 @ ( path_pathfinish_a @ P ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathfinish_compose
% 0.18/0.43 thf(fact_14_pathfinish__compose,axiom,
% 0.18/0.43 ! [F2: complex > a,P: real > complex] :
% 0.18/0.43 ( ( path_pathfinish_a @ ( comp_complex_a_real @ F2 @ P ) )
% 0.18/0.43 = ( F2 @ ( path_p769714271omplex @ P ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathfinish_compose
% 0.18/0.43 thf(fact_15_pathfinish__compose,axiom,
% 0.18/0.43 ! [F2: a > a,P: real > a] :
% 0.18/0.43 ( ( path_pathfinish_a @ ( comp_a_a_real @ F2 @ P ) )
% 0.18/0.43 = ( F2 @ ( path_pathfinish_a @ P ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathfinish_compose
% 0.18/0.43 thf(fact_16_pathstart__compose,axiom,
% 0.18/0.43 ! [F2: real > a,P: real > real] :
% 0.18/0.43 ( ( path_pathstart_a @ ( comp_real_a_real @ F2 @ P ) )
% 0.18/0.43 = ( F2 @ ( path_pathstart_real @ P ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathstart_compose
% 0.18/0.43 thf(fact_17_pathstart__compose,axiom,
% 0.18/0.43 ! [F2: complex > complex,P: real > complex] :
% 0.18/0.43 ( ( path_p797330068omplex @ ( comp_c595887981x_real @ F2 @ P ) )
% 0.18/0.43 = ( F2 @ ( path_p797330068omplex @ P ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathstart_compose
% 0.18/0.43 thf(fact_18_pathstart__compose,axiom,
% 0.18/0.43 ! [F2: a > complex,P: real > a] :
% 0.18/0.43 ( ( path_p797330068omplex @ ( comp_a_complex_real @ F2 @ P ) )
% 0.18/0.43 = ( F2 @ ( path_pathstart_a @ P ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathstart_compose
% 0.18/0.43 thf(fact_19_pathstart__compose,axiom,
% 0.18/0.43 ! [F2: complex > a,P: real > complex] :
% 0.18/0.43 ( ( path_pathstart_a @ ( comp_complex_a_real @ F2 @ P ) )
% 0.18/0.43 = ( F2 @ ( path_p797330068omplex @ P ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathstart_compose
% 0.18/0.43 thf(fact_20_pathstart__compose,axiom,
% 0.18/0.43 ! [F2: a > a,P: real > a] :
% 0.18/0.43 ( ( path_pathstart_a @ ( comp_a_a_real @ F2 @ P ) )
% 0.18/0.43 = ( F2 @ ( path_pathstart_a @ P ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathstart_compose
% 0.18/0.43 thf(fact_21_complex__of__bounded__linear,axiom,
% 0.18/0.43 real_V912435428omplex @ poinca1910941596x_of_a ).
% 0.18/0.43
% 0.18/0.43 % complex_of_bounded_linear
% 0.18/0.43 thf(fact_22_complex__of__linear,axiom,
% 0.18/0.43 real_V1477106445omplex @ poinca1910941596x_of_a ).
% 0.18/0.43
% 0.18/0.43 % complex_of_linear
% 0.18/0.43 thf(fact_23_comp__def,axiom,
% 0.18/0.43 ( comp_real_a_real
% 0.18/0.43 = ( ^ [F: real > a,G: real > real,X: real] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_def
% 0.18/0.43 thf(fact_24_comp__def,axiom,
% 0.18/0.43 ( comp_a_complex_a
% 0.18/0.43 = ( ^ [F: a > complex,G: a > a,X: a] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_def
% 0.18/0.43 thf(fact_25_comp__def,axiom,
% 0.18/0.43 ( comp_a_a_complex
% 0.18/0.43 = ( ^ [F: a > a,G: complex > a,X: complex] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_def
% 0.18/0.43 thf(fact_26_comp__def,axiom,
% 0.18/0.43 ( comp_a_a_real
% 0.18/0.43 = ( ^ [F: a > a,G: real > a,X: real] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_def
% 0.18/0.43 thf(fact_27_comp__def,axiom,
% 0.18/0.43 ( comp_a_a_a
% 0.18/0.43 = ( ^ [F: a > a,G: a > a,X: a] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_def
% 0.18/0.43 thf(fact_28_comp__def,axiom,
% 0.18/0.43 ( comp_a_complex_real
% 0.18/0.43 = ( ^ [F: a > complex,G: real > a,X: real] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_def
% 0.18/0.43 thf(fact_29_comp__def,axiom,
% 0.18/0.43 ( comp_a1063143865omplex
% 0.18/0.43 = ( ^ [F: a > complex,G: complex > a,X: complex] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_def
% 0.18/0.43 thf(fact_30_comp__def,axiom,
% 0.18/0.43 ( comp_complex_a_a
% 0.18/0.43 = ( ^ [F: complex > a,G: a > complex,X: a] : ( F @ ( G @ X ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_def
% 0.18/0.43 thf(fact_31_comp__assoc,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: real > a,H: real > real] :
% 0.18/0.43 ( ( comp_r701421291x_real @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_complex_real @ F2 @ ( comp_real_a_real @ G2 @ H ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_assoc
% 0.18/0.43 thf(fact_32_comp__assoc,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: real > a,H: complex > real] :
% 0.18/0.43 ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_assoc
% 0.18/0.43 thf(fact_33_comp__assoc,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: complex > a,H: a > complex] :
% 0.18/0.43 ( ( comp_c124850173plex_a @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_complex_a @ F2 @ ( comp_complex_a_a @ G2 @ H ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_assoc
% 0.18/0.43 thf(fact_34_comp__assoc,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: complex > a,H: real > complex] :
% 0.18/0.43 ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_complex_real @ F2 @ ( comp_complex_a_real @ G2 @ H ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_assoc
% 0.18/0.43 thf(fact_35_comp__assoc,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: complex > a,H: complex > complex] :
% 0.18/0.43 ( ( comp_c130555887omplex @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a1063143865omplex @ F2 @ ( comp_c274302683omplex @ G2 @ H ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_assoc
% 0.18/0.43 thf(fact_36_comp__assoc,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: a > complex,H: real > a] :
% 0.18/0.43 ( ( comp_a_a_real @ ( comp_complex_a_a @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_complex_a_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_assoc
% 0.18/0.43 thf(fact_37_comp__assoc,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: a > complex,H: complex > a] :
% 0.18/0.43 ( ( comp_a_a_complex @ ( comp_complex_a_a @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_c274302683omplex @ F2 @ ( comp_a1063143865omplex @ G2 @ H ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_assoc
% 0.18/0.43 thf(fact_38_comp__assoc,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: a > complex,H: a > a] :
% 0.18/0.43 ( ( comp_a_a_a @ ( comp_complex_a_a @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_complex_a_a @ F2 @ ( comp_a_complex_a @ G2 @ H ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_assoc
% 0.18/0.43 thf(fact_39_comp__assoc,axiom,
% 0.18/0.43 ! [F2: complex > complex,G2: a > complex,H: real > a] :
% 0.18/0.43 ( ( comp_a_complex_real @ ( comp_c124850173plex_a @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_c595887981x_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_assoc
% 0.18/0.43 thf(fact_40_comp__assoc,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: a > a,H: real > a] :
% 0.18/0.43 ( ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_complex_real @ F2 @ ( comp_a_a_real @ G2 @ H ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_assoc
% 0.18/0.43 thf(fact_41_comp__eq__dest,axiom,
% 0.18/0.43 ! [A: a > complex,B: real > a,C: a > complex,D: real > a,V: real] :
% 0.18/0.43 ( ( ( comp_a_complex_real @ A @ B )
% 0.18/0.43 = ( comp_a_complex_real @ C @ D ) )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ ( D @ V ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest
% 0.18/0.43 thf(fact_42_comp__eq__dest,axiom,
% 0.18/0.43 ! [A: a > complex,B: complex > a,C: a > complex,D: complex > a,V: complex] :
% 0.18/0.43 ( ( ( comp_a1063143865omplex @ A @ B )
% 0.18/0.43 = ( comp_a1063143865omplex @ C @ D ) )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ ( D @ V ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest
% 0.18/0.43 thf(fact_43_comp__eq__dest,axiom,
% 0.18/0.43 ! [A: complex > a,B: a > complex,C: complex > a,D: a > complex,V: a] :
% 0.18/0.43 ( ( ( comp_complex_a_a @ A @ B )
% 0.18/0.43 = ( comp_complex_a_a @ C @ D ) )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ ( D @ V ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest
% 0.18/0.43 thf(fact_44_comp__eq__dest,axiom,
% 0.18/0.43 ! [A: complex > a,B: a > complex,C: a > a,D: a > a,V: a] :
% 0.18/0.43 ( ( ( comp_complex_a_a @ A @ B )
% 0.18/0.43 = ( comp_a_a_a @ C @ D ) )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ ( D @ V ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest
% 0.18/0.43 thf(fact_45_comp__eq__dest,axiom,
% 0.18/0.43 ! [A: real > a,B: real > real,C: real > a,D: real > real,V: real] :
% 0.18/0.43 ( ( ( comp_real_a_real @ A @ B )
% 0.18/0.43 = ( comp_real_a_real @ C @ D ) )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ ( D @ V ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest
% 0.18/0.43 thf(fact_46_comp__eq__dest,axiom,
% 0.18/0.43 ! [A: real > a,B: real > real,C: a > a,D: real > a,V: real] :
% 0.18/0.43 ( ( ( comp_real_a_real @ A @ B )
% 0.18/0.43 = ( comp_a_a_real @ C @ D ) )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ ( D @ V ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest
% 0.18/0.43 thf(fact_47_comp__eq__dest,axiom,
% 0.18/0.43 ! [A: a > complex,B: a > a,C: a > complex,D: a > a,V: a] :
% 0.18/0.43 ( ( ( comp_a_complex_a @ A @ B )
% 0.18/0.43 = ( comp_a_complex_a @ C @ D ) )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ ( D @ V ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest
% 0.18/0.43 thf(fact_48_comp__eq__dest,axiom,
% 0.18/0.43 ! [A: a > a,B: complex > a,C: a > a,D: complex > a,V: complex] :
% 0.18/0.43 ( ( ( comp_a_a_complex @ A @ B )
% 0.18/0.43 = ( comp_a_a_complex @ C @ D ) )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ ( D @ V ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest
% 0.18/0.43 thf(fact_49_comp__eq__dest,axiom,
% 0.18/0.43 ! [A: a > a,B: real > a,C: real > a,D: real > real,V: real] :
% 0.18/0.43 ( ( ( comp_a_a_real @ A @ B )
% 0.18/0.43 = ( comp_real_a_real @ C @ D ) )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ ( D @ V ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest
% 0.18/0.43 thf(fact_50_comp__eq__dest,axiom,
% 0.18/0.43 ! [A: a > a,B: real > a,C: a > a,D: real > a,V: real] :
% 0.18/0.43 ( ( ( comp_a_a_real @ A @ B )
% 0.18/0.43 = ( comp_a_a_real @ C @ D ) )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ ( D @ V ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest
% 0.18/0.43 thf(fact_51_comp__eq__elim,axiom,
% 0.18/0.43 ! [A: a > complex,B: real > a,C: a > complex,D: real > a] :
% 0.18/0.43 ( ( ( comp_a_complex_real @ A @ B )
% 0.18/0.43 = ( comp_a_complex_real @ C @ D ) )
% 0.18/0.43 => ! [V2: real] :
% 0.18/0.43 ( ( A @ ( B @ V2 ) )
% 0.18/0.43 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_elim
% 0.18/0.43 thf(fact_52_comp__eq__elim,axiom,
% 0.18/0.43 ! [A: a > complex,B: complex > a,C: a > complex,D: complex > a] :
% 0.18/0.43 ( ( ( comp_a1063143865omplex @ A @ B )
% 0.18/0.43 = ( comp_a1063143865omplex @ C @ D ) )
% 0.18/0.43 => ! [V2: complex] :
% 0.18/0.43 ( ( A @ ( B @ V2 ) )
% 0.18/0.43 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_elim
% 0.18/0.43 thf(fact_53_comp__eq__elim,axiom,
% 0.18/0.43 ! [A: complex > a,B: a > complex,C: complex > a,D: a > complex] :
% 0.18/0.43 ( ( ( comp_complex_a_a @ A @ B )
% 0.18/0.43 = ( comp_complex_a_a @ C @ D ) )
% 0.18/0.43 => ! [V2: a] :
% 0.18/0.43 ( ( A @ ( B @ V2 ) )
% 0.18/0.43 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_elim
% 0.18/0.43 thf(fact_54_comp__eq__elim,axiom,
% 0.18/0.43 ! [A: complex > a,B: a > complex,C: a > a,D: a > a] :
% 0.18/0.43 ( ( ( comp_complex_a_a @ A @ B )
% 0.18/0.43 = ( comp_a_a_a @ C @ D ) )
% 0.18/0.43 => ! [V2: a] :
% 0.18/0.43 ( ( A @ ( B @ V2 ) )
% 0.18/0.43 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_elim
% 0.18/0.43 thf(fact_55_comp__eq__elim,axiom,
% 0.18/0.43 ! [A: real > a,B: real > real,C: real > a,D: real > real] :
% 0.18/0.43 ( ( ( comp_real_a_real @ A @ B )
% 0.18/0.43 = ( comp_real_a_real @ C @ D ) )
% 0.18/0.43 => ! [V2: real] :
% 0.18/0.43 ( ( A @ ( B @ V2 ) )
% 0.18/0.43 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_elim
% 0.18/0.43 thf(fact_56_comp__eq__elim,axiom,
% 0.18/0.43 ! [A: real > a,B: real > real,C: a > a,D: real > a] :
% 0.18/0.43 ( ( ( comp_real_a_real @ A @ B )
% 0.18/0.43 = ( comp_a_a_real @ C @ D ) )
% 0.18/0.43 => ! [V2: real] :
% 0.18/0.43 ( ( A @ ( B @ V2 ) )
% 0.18/0.43 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_elim
% 0.18/0.43 thf(fact_57_comp__eq__elim,axiom,
% 0.18/0.43 ! [A: a > complex,B: a > a,C: a > complex,D: a > a] :
% 0.18/0.43 ( ( ( comp_a_complex_a @ A @ B )
% 0.18/0.43 = ( comp_a_complex_a @ C @ D ) )
% 0.18/0.43 => ! [V2: a] :
% 0.18/0.43 ( ( A @ ( B @ V2 ) )
% 0.18/0.43 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_elim
% 0.18/0.43 thf(fact_58_comp__eq__elim,axiom,
% 0.18/0.43 ! [A: a > a,B: complex > a,C: a > a,D: complex > a] :
% 0.18/0.43 ( ( ( comp_a_a_complex @ A @ B )
% 0.18/0.43 = ( comp_a_a_complex @ C @ D ) )
% 0.18/0.43 => ! [V2: complex] :
% 0.18/0.43 ( ( A @ ( B @ V2 ) )
% 0.18/0.43 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_elim
% 0.18/0.43 thf(fact_59_comp__eq__elim,axiom,
% 0.18/0.43 ! [A: a > a,B: real > a,C: real > a,D: real > real] :
% 0.18/0.43 ( ( ( comp_a_a_real @ A @ B )
% 0.18/0.43 = ( comp_real_a_real @ C @ D ) )
% 0.18/0.43 => ! [V2: real] :
% 0.18/0.43 ( ( A @ ( B @ V2 ) )
% 0.18/0.43 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_elim
% 0.18/0.43 thf(fact_60_comp__eq__elim,axiom,
% 0.18/0.43 ! [A: a > a,B: real > a,C: a > a,D: real > a] :
% 0.18/0.43 ( ( ( comp_a_a_real @ A @ B )
% 0.18/0.43 = ( comp_a_a_real @ C @ D ) )
% 0.18/0.43 => ! [V2: real] :
% 0.18/0.43 ( ( A @ ( B @ V2 ) )
% 0.18/0.43 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_elim
% 0.18/0.43 thf(fact_61_comp__cong,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: real > a,X3: real] :
% 0.18/0.43 ( ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.43 = ( F3 @ ( G3 @ X3 ) ) )
% 0.18/0.43 => ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
% 0.18/0.43 = ( comp_a_complex_real @ F3 @ G3 @ X3 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_cong
% 0.18/0.43 thf(fact_62_comp__cong,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: complex > a,X3: complex] :
% 0.18/0.43 ( ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.43 = ( F3 @ ( G3 @ X3 ) ) )
% 0.18/0.43 => ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
% 0.18/0.43 = ( comp_a1063143865omplex @ F3 @ G3 @ X3 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_cong
% 0.18/0.43 thf(fact_63_comp__cong,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: a > a,X3: a] :
% 0.18/0.43 ( ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.43 = ( F3 @ ( G3 @ X3 ) ) )
% 0.18/0.43 => ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
% 0.18/0.43 = ( comp_a_complex_a @ F3 @ G3 @ X3 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_cong
% 0.18/0.43 thf(fact_64_comp__cong,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: complex > a,X2: complex,F3: a > complex,G3: real > a,X3: real] :
% 0.18/0.43 ( ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.43 = ( F3 @ ( G3 @ X3 ) ) )
% 0.18/0.43 => ( ( comp_a1063143865omplex @ F2 @ G2 @ X2 )
% 0.18/0.43 = ( comp_a_complex_real @ F3 @ G3 @ X3 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_cong
% 0.18/0.43 thf(fact_65_comp__cong,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: complex > a,X2: complex,F3: a > complex,G3: complex > a,X3: complex] :
% 0.18/0.43 ( ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.43 = ( F3 @ ( G3 @ X3 ) ) )
% 0.18/0.43 => ( ( comp_a1063143865omplex @ F2 @ G2 @ X2 )
% 0.18/0.43 = ( comp_a1063143865omplex @ F3 @ G3 @ X3 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_cong
% 0.18/0.43 thf(fact_66_comp__cong,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: complex > a,X2: complex,F3: a > complex,G3: a > a,X3: a] :
% 0.18/0.43 ( ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.43 = ( F3 @ ( G3 @ X3 ) ) )
% 0.18/0.43 => ( ( comp_a1063143865omplex @ F2 @ G2 @ X2 )
% 0.18/0.43 = ( comp_a_complex_a @ F3 @ G3 @ X3 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_cong
% 0.18/0.43 thf(fact_67_comp__cong,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: a > complex,X2: a,F3: complex > a,G3: a > complex,X3: a] :
% 0.18/0.43 ( ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.43 = ( F3 @ ( G3 @ X3 ) ) )
% 0.18/0.43 => ( ( comp_complex_a_a @ F2 @ G2 @ X2 )
% 0.18/0.43 = ( comp_complex_a_a @ F3 @ G3 @ X3 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_cong
% 0.18/0.43 thf(fact_68_comp__cong,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: a > complex,X2: a,F3: real > a,G3: real > real,X3: real] :
% 0.18/0.43 ( ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.43 = ( F3 @ ( G3 @ X3 ) ) )
% 0.18/0.43 => ( ( comp_complex_a_a @ F2 @ G2 @ X2 )
% 0.18/0.43 = ( comp_real_a_real @ F3 @ G3 @ X3 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_cong
% 0.18/0.43 thf(fact_69_comp__cong,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: a > complex,X2: a,F3: a > a,G3: complex > a,X3: complex] :
% 0.18/0.43 ( ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.43 = ( F3 @ ( G3 @ X3 ) ) )
% 0.18/0.43 => ( ( comp_complex_a_a @ F2 @ G2 @ X2 )
% 0.18/0.43 = ( comp_a_a_complex @ F3 @ G3 @ X3 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_cong
% 0.18/0.43 thf(fact_70_comp__cong,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: a > complex,X2: a,F3: a > a,G3: real > a,X3: real] :
% 0.18/0.43 ( ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.43 = ( F3 @ ( G3 @ X3 ) ) )
% 0.18/0.43 => ( ( comp_complex_a_a @ F2 @ G2 @ X2 )
% 0.18/0.43 = ( comp_a_a_real @ F3 @ G3 @ X3 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_cong
% 0.18/0.43 thf(fact_71_comp__eq__dest__lhs,axiom,
% 0.18/0.43 ! [A: a > complex,B: real > a,C: real > complex,V: real] :
% 0.18/0.43 ( ( ( comp_a_complex_real @ A @ B )
% 0.18/0.43 = C )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ V ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest_lhs
% 0.18/0.43 thf(fact_72_comp__eq__dest__lhs,axiom,
% 0.18/0.43 ! [A: a > complex,B: complex > a,C: complex > complex,V: complex] :
% 0.18/0.43 ( ( ( comp_a1063143865omplex @ A @ B )
% 0.18/0.43 = C )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ V ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest_lhs
% 0.18/0.43 thf(fact_73_comp__eq__dest__lhs,axiom,
% 0.18/0.43 ! [A: complex > a,B: a > complex,C: a > a,V: a] :
% 0.18/0.43 ( ( ( comp_complex_a_a @ A @ B )
% 0.18/0.43 = C )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ V ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest_lhs
% 0.18/0.43 thf(fact_74_comp__eq__dest__lhs,axiom,
% 0.18/0.43 ! [A: real > a,B: real > real,C: real > a,V: real] :
% 0.18/0.43 ( ( ( comp_real_a_real @ A @ B )
% 0.18/0.43 = C )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ V ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest_lhs
% 0.18/0.43 thf(fact_75_comp__eq__dest__lhs,axiom,
% 0.18/0.43 ! [A: a > complex,B: a > a,C: a > complex,V: a] :
% 0.18/0.43 ( ( ( comp_a_complex_a @ A @ B )
% 0.18/0.43 = C )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ V ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest_lhs
% 0.18/0.43 thf(fact_76_comp__eq__dest__lhs,axiom,
% 0.18/0.43 ! [A: a > a,B: complex > a,C: complex > a,V: complex] :
% 0.18/0.43 ( ( ( comp_a_a_complex @ A @ B )
% 0.18/0.43 = C )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ V ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest_lhs
% 0.18/0.43 thf(fact_77_comp__eq__dest__lhs,axiom,
% 0.18/0.43 ! [A: a > a,B: real > a,C: real > a,V: real] :
% 0.18/0.43 ( ( ( comp_a_a_real @ A @ B )
% 0.18/0.43 = C )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ V ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest_lhs
% 0.18/0.43 thf(fact_78_comp__eq__dest__lhs,axiom,
% 0.18/0.43 ! [A: a > a,B: a > a,C: a > a,V: a] :
% 0.18/0.43 ( ( ( comp_a_a_a @ A @ B )
% 0.18/0.43 = C )
% 0.18/0.43 => ( ( A @ ( B @ V ) )
% 0.18/0.43 = ( C @ V ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % comp_eq_dest_lhs
% 0.18/0.43 thf(fact_79_pathstart__linear__image__eq,axiom,
% 0.18/0.43 ! [F2: complex > complex,G2: real > complex] :
% 0.18/0.43 ( ( real_V670066493omplex @ F2 )
% 0.18/0.43 => ( ( path_p797330068omplex @ ( comp_c595887981x_real @ F2 @ G2 ) )
% 0.18/0.43 = ( F2 @ ( path_p797330068omplex @ G2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathstart_linear_image_eq
% 0.18/0.43 thf(fact_80_pathstart__linear__image__eq,axiom,
% 0.18/0.43 ! [F2: real > a,G2: real > real] :
% 0.18/0.43 ( ( real_V779700657real_a @ F2 )
% 0.18/0.43 => ( ( path_pathstart_a @ ( comp_real_a_real @ F2 @ G2 ) )
% 0.18/0.43 = ( F2 @ ( path_pathstart_real @ G2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathstart_linear_image_eq
% 0.18/0.43 thf(fact_81_pathstart__linear__image__eq,axiom,
% 0.18/0.43 ! [F2: a > a,G2: real > a] :
% 0.18/0.43 ( ( real_V202220639ar_a_a @ F2 )
% 0.18/0.43 => ( ( path_pathstart_a @ ( comp_a_a_real @ F2 @ G2 ) )
% 0.18/0.43 = ( F2 @ ( path_pathstart_a @ G2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathstart_linear_image_eq
% 0.18/0.43 thf(fact_82_pathstart__linear__image__eq,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: real > a] :
% 0.18/0.43 ( ( real_V1477106445omplex @ F2 )
% 0.18/0.43 => ( ( path_p797330068omplex @ ( comp_a_complex_real @ F2 @ G2 ) )
% 0.18/0.43 = ( F2 @ ( path_pathstart_a @ G2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathstart_linear_image_eq
% 0.18/0.43 thf(fact_83_pathstart__linear__image__eq,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: real > complex] :
% 0.18/0.43 ( ( real_V1327653935plex_a @ F2 )
% 0.18/0.43 => ( ( path_pathstart_a @ ( comp_complex_a_real @ F2 @ G2 ) )
% 0.18/0.43 = ( F2 @ ( path_p797330068omplex @ G2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathstart_linear_image_eq
% 0.18/0.43 thf(fact_84_pathfinish__linear__image,axiom,
% 0.18/0.43 ! [F2: complex > complex,G2: real > complex] :
% 0.18/0.43 ( ( real_V670066493omplex @ F2 )
% 0.18/0.43 => ( ( path_p769714271omplex @ ( comp_c595887981x_real @ F2 @ G2 ) )
% 0.18/0.43 = ( F2 @ ( path_p769714271omplex @ G2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathfinish_linear_image
% 0.18/0.43 thf(fact_85_pathfinish__linear__image,axiom,
% 0.18/0.43 ! [F2: real > a,G2: real > real] :
% 0.18/0.43 ( ( real_V779700657real_a @ F2 )
% 0.18/0.43 => ( ( path_pathfinish_a @ ( comp_real_a_real @ F2 @ G2 ) )
% 0.18/0.43 = ( F2 @ ( path_pathfinish_real @ G2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathfinish_linear_image
% 0.18/0.43 thf(fact_86_pathfinish__linear__image,axiom,
% 0.18/0.43 ! [F2: a > a,G2: real > a] :
% 0.18/0.43 ( ( real_V202220639ar_a_a @ F2 )
% 0.18/0.43 => ( ( path_pathfinish_a @ ( comp_a_a_real @ F2 @ G2 ) )
% 0.18/0.43 = ( F2 @ ( path_pathfinish_a @ G2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathfinish_linear_image
% 0.18/0.43 thf(fact_87_pathfinish__linear__image,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: real > a] :
% 0.18/0.43 ( ( real_V1477106445omplex @ F2 )
% 0.18/0.43 => ( ( path_p769714271omplex @ ( comp_a_complex_real @ F2 @ G2 ) )
% 0.18/0.43 = ( F2 @ ( path_pathfinish_a @ G2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathfinish_linear_image
% 0.18/0.43 thf(fact_88_pathfinish__linear__image,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: real > complex] :
% 0.18/0.43 ( ( real_V1327653935plex_a @ F2 )
% 0.18/0.43 => ( ( path_pathfinish_a @ ( comp_complex_a_real @ F2 @ G2 ) )
% 0.18/0.43 = ( F2 @ ( path_p769714271omplex @ G2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % pathfinish_linear_image
% 0.18/0.43 thf(fact_89_bounded__linear_Olinear,axiom,
% 0.18/0.43 ! [F2: a > complex] :
% 0.18/0.43 ( ( real_V912435428omplex @ F2 )
% 0.18/0.43 => ( real_V1477106445omplex @ F2 ) ) ).
% 0.18/0.43
% 0.18/0.43 % bounded_linear.linear
% 0.18/0.43 thf(fact_90_bounded__linear_Olinear,axiom,
% 0.18/0.43 ! [F2: complex > a] :
% 0.18/0.43 ( ( real_V762982918plex_a @ F2 )
% 0.18/0.43 => ( real_V1327653935plex_a @ F2 ) ) ).
% 0.18/0.43
% 0.18/0.43 % bounded_linear.linear
% 0.18/0.43 thf(fact_91_linear__conv__bounded__linear,axiom,
% 0.18/0.43 real_V1477106445omplex = real_V912435428omplex ).
% 0.18/0.43
% 0.18/0.43 % linear_conv_bounded_linear
% 0.18/0.43 thf(fact_92_linear__conv__bounded__linear,axiom,
% 0.18/0.43 real_V1327653935plex_a = real_V762982918plex_a ).
% 0.18/0.43
% 0.18/0.43 % linear_conv_bounded_linear
% 0.18/0.43 thf(fact_93_linear__compose,axiom,
% 0.18/0.43 ! [F2: real > real,G2: real > a] :
% 0.18/0.43 ( ( real_V1354572473l_real @ F2 )
% 0.18/0.43 => ( ( real_V779700657real_a @ G2 )
% 0.18/0.43 => ( real_V779700657real_a @ ( comp_real_a_real @ G2 @ F2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % linear_compose
% 0.18/0.43 thf(fact_94_linear__compose,axiom,
% 0.18/0.43 ! [F2: real > a,G2: a > a] :
% 0.18/0.43 ( ( real_V779700657real_a @ F2 )
% 0.18/0.43 => ( ( real_V202220639ar_a_a @ G2 )
% 0.18/0.43 => ( real_V779700657real_a @ ( comp_a_a_real @ G2 @ F2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % linear_compose
% 0.18/0.43 thf(fact_95_linear__compose,axiom,
% 0.18/0.43 ! [F2: a > a,G2: a > a] :
% 0.18/0.43 ( ( real_V202220639ar_a_a @ F2 )
% 0.18/0.43 => ( ( real_V202220639ar_a_a @ G2 )
% 0.18/0.43 => ( real_V202220639ar_a_a @ ( comp_a_a_a @ G2 @ F2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % linear_compose
% 0.18/0.43 thf(fact_96_linear__compose,axiom,
% 0.18/0.43 ! [F2: real > a,G2: a > complex] :
% 0.18/0.43 ( ( real_V779700657real_a @ F2 )
% 0.18/0.43 => ( ( real_V1477106445omplex @ G2 )
% 0.18/0.43 => ( real_V1948715323omplex @ ( comp_a_complex_real @ G2 @ F2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % linear_compose
% 0.18/0.43 thf(fact_97_linear__compose,axiom,
% 0.18/0.43 ! [F2: a > a,G2: a > complex] :
% 0.18/0.43 ( ( real_V202220639ar_a_a @ F2 )
% 0.18/0.43 => ( ( real_V1477106445omplex @ G2 )
% 0.18/0.43 => ( real_V1477106445omplex @ ( comp_a_complex_a @ G2 @ F2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % linear_compose
% 0.18/0.43 thf(fact_98_linear__compose,axiom,
% 0.18/0.43 ! [F2: complex > complex,G2: complex > a] :
% 0.18/0.43 ( ( real_V670066493omplex @ F2 )
% 0.18/0.43 => ( ( real_V1327653935plex_a @ G2 )
% 0.18/0.43 => ( real_V1327653935plex_a @ ( comp_c274302683omplex @ G2 @ F2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % linear_compose
% 0.18/0.43 thf(fact_99_linear__compose,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: complex > complex] :
% 0.18/0.43 ( ( real_V1477106445omplex @ F2 )
% 0.18/0.43 => ( ( real_V670066493omplex @ G2 )
% 0.18/0.43 => ( real_V1477106445omplex @ ( comp_c124850173plex_a @ G2 @ F2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % linear_compose
% 0.18/0.43 thf(fact_100_linear__compose,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: complex > a] :
% 0.18/0.43 ( ( real_V1477106445omplex @ F2 )
% 0.18/0.43 => ( ( real_V1327653935plex_a @ G2 )
% 0.18/0.43 => ( real_V202220639ar_a_a @ ( comp_complex_a_a @ G2 @ F2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % linear_compose
% 0.18/0.43 thf(fact_101_linear__compose,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: a > a] :
% 0.18/0.43 ( ( real_V1327653935plex_a @ F2 )
% 0.18/0.43 => ( ( real_V202220639ar_a_a @ G2 )
% 0.18/0.43 => ( real_V1327653935plex_a @ ( comp_a_a_complex @ G2 @ F2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % linear_compose
% 0.18/0.43 thf(fact_102_linear__compose,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: a > complex] :
% 0.18/0.43 ( ( real_V1327653935plex_a @ F2 )
% 0.18/0.43 => ( ( real_V1477106445omplex @ G2 )
% 0.18/0.43 => ( real_V670066493omplex @ ( comp_a1063143865omplex @ G2 @ F2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % linear_compose
% 0.18/0.43 thf(fact_103__092_060open_062_092_060And_062g_O_Ainj_Acomplex__of_A_092_060Longrightarrow_062_Asimple__path_A_Icomplex__of_A_092_060circ_062_Ag_J_A_061_Asimple__path_Ag_092_060close_062,axiom,
% 0.18/0.43 ! [G2: real > a] :
% 0.18/0.43 ( ( inj_on_a_complex @ poinca1910941596x_of_a @ top_top_set_a )
% 0.18/0.43 => ( ( path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ G2 ) )
% 0.18/0.43 = ( path_simple_path_a @ G2 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % \<open>\<And>g. inj complex_of \<Longrightarrow> simple_path (complex_of \<circ> g) = simple_path g\<close>
% 0.18/0.43 thf(fact_104_pathfinish__rectpath,axiom,
% 0.18/0.43 ! [A1: complex,A3: complex] :
% 0.18/0.43 ( ( path_p769714271omplex @ ( path_rectpath @ A1 @ A3 ) )
% 0.18/0.43 = A1 ) ).
% 0.18/0.43
% 0.18/0.43 % pathfinish_rectpath
% 0.18/0.43 thf(fact_105_pathstart__rectpath,axiom,
% 0.18/0.43 ! [A1: complex,A3: complex] :
% 0.18/0.43 ( ( path_p797330068omplex @ ( path_rectpath @ A1 @ A3 ) )
% 0.18/0.43 = A1 ) ).
% 0.18/0.43
% 0.18/0.43 % pathstart_rectpath
% 0.18/0.43 thf(fact_106_bounded__linear_Obounded__linear,axiom,
% 0.18/0.43 ! [F2: a > complex] :
% 0.18/0.43 ( ( real_V912435428omplex @ F2 )
% 0.18/0.43 => ( real_V912435428omplex @ F2 ) ) ).
% 0.18/0.43
% 0.18/0.43 % bounded_linear.bounded_linear
% 0.18/0.43 thf(fact_107_bounded__linear_Obounded__linear,axiom,
% 0.18/0.43 ! [F2: complex > a] :
% 0.18/0.43 ( ( real_V762982918plex_a @ F2 )
% 0.18/0.43 => ( real_V762982918plex_a @ F2 ) ) ).
% 0.18/0.43
% 0.18/0.43 % bounded_linear.bounded_linear
% 0.18/0.43 thf(fact_108_rewriteR__comp__comp2,axiom,
% 0.18/0.43 ! [G2: real > real,H: a > real,R1: complex > real,R2: a > complex,F2: real > a,L: complex > a] :
% 0.18/0.43 ( ( ( comp_real_real_a @ G2 @ H )
% 0.18/0.43 = ( comp_complex_real_a @ R1 @ R2 ) )
% 0.18/0.43 => ( ( ( comp_real_a_complex @ F2 @ R1 )
% 0.18/0.43 = L )
% 0.18/0.43 => ( ( comp_real_a_a @ ( comp_real_a_real @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_complex_a_a @ L @ R2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp2
% 0.18/0.43 thf(fact_109_rewriteR__comp__comp2,axiom,
% 0.18/0.43 ! [G2: real > real,H: complex > real,R1: a > real,R2: complex > a,F2: real > a,L: a > a] :
% 0.18/0.43 ( ( ( comp_r422820971omplex @ G2 @ H )
% 0.18/0.43 = ( comp_a_real_complex @ R1 @ R2 ) )
% 0.18/0.43 => ( ( ( comp_real_a_a @ F2 @ R1 )
% 0.18/0.43 = L )
% 0.18/0.43 => ( ( comp_real_a_complex @ ( comp_real_a_real @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_a_complex @ L @ R2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp2
% 0.18/0.43 thf(fact_110_rewriteR__comp__comp2,axiom,
% 0.18/0.43 ! [G2: real > real,H: a > real,R1: a > real,R2: a > a,F2: real > a,L: a > a] :
% 0.18/0.43 ( ( ( comp_real_real_a @ G2 @ H )
% 0.18/0.43 = ( comp_a_real_a @ R1 @ R2 ) )
% 0.18/0.43 => ( ( ( comp_real_a_a @ F2 @ R1 )
% 0.18/0.43 = L )
% 0.18/0.43 => ( ( comp_real_a_a @ ( comp_real_a_real @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_a_a @ L @ R2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp2
% 0.18/0.43 thf(fact_111_rewriteR__comp__comp2,axiom,
% 0.18/0.43 ! [G2: real > real,H: real > real,R1: a > real,R2: real > a,F2: real > a,L: a > a] :
% 0.18/0.43 ( ( ( comp_real_real_real @ G2 @ H )
% 0.18/0.43 = ( comp_a_real_real @ R1 @ R2 ) )
% 0.18/0.43 => ( ( ( comp_real_a_a @ F2 @ R1 )
% 0.18/0.43 = L )
% 0.18/0.43 => ( ( comp_real_a_real @ ( comp_real_a_real @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_a_real @ L @ R2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp2
% 0.18/0.43 thf(fact_112_rewriteR__comp__comp2,axiom,
% 0.18/0.43 ! [G2: complex > real,H: a > complex,R1: real > real,R2: a > real,F2: real > a,L: real > a] :
% 0.18/0.43 ( ( ( comp_complex_real_a @ G2 @ H )
% 0.18/0.43 = ( comp_real_real_a @ R1 @ R2 ) )
% 0.18/0.43 => ( ( ( comp_real_a_real @ F2 @ R1 )
% 0.18/0.43 = L )
% 0.18/0.43 => ( ( comp_complex_a_a @ ( comp_real_a_complex @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_real_a_a @ L @ R2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp2
% 0.18/0.43 thf(fact_113_rewriteR__comp__comp2,axiom,
% 0.18/0.43 ! [G2: real > real,H: real > real,R1: real > real,R2: real > real,F2: real > a,L: real > a] :
% 0.18/0.43 ( ( ( comp_real_real_real @ G2 @ H )
% 0.18/0.43 = ( comp_real_real_real @ R1 @ R2 ) )
% 0.18/0.43 => ( ( ( comp_real_a_real @ F2 @ R1 )
% 0.18/0.43 = L )
% 0.18/0.43 => ( ( comp_real_a_real @ ( comp_real_a_real @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_real_a_real @ L @ R2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp2
% 0.18/0.43 thf(fact_114_rewriteR__comp__comp2,axiom,
% 0.18/0.43 ! [G2: a > real,H: complex > a,R1: real > real,R2: complex > real,F2: real > a,L: real > a] :
% 0.18/0.43 ( ( ( comp_a_real_complex @ G2 @ H )
% 0.18/0.43 = ( comp_r422820971omplex @ R1 @ R2 ) )
% 0.18/0.43 => ( ( ( comp_real_a_real @ F2 @ R1 )
% 0.18/0.43 = L )
% 0.18/0.43 => ( ( comp_a_a_complex @ ( comp_real_a_a @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_real_a_complex @ L @ R2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp2
% 0.18/0.43 thf(fact_115_rewriteR__comp__comp2,axiom,
% 0.18/0.43 ! [G2: a > real,H: real > a,R1: real > real,R2: real > real,F2: real > a,L: real > a] :
% 0.18/0.43 ( ( ( comp_a_real_real @ G2 @ H )
% 0.18/0.43 = ( comp_real_real_real @ R1 @ R2 ) )
% 0.18/0.43 => ( ( ( comp_real_a_real @ F2 @ R1 )
% 0.18/0.43 = L )
% 0.18/0.43 => ( ( comp_a_a_real @ ( comp_real_a_a @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_real_a_real @ L @ R2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp2
% 0.18/0.43 thf(fact_116_rewriteR__comp__comp2,axiom,
% 0.18/0.43 ! [G2: a > real,H: a > a,R1: real > real,R2: a > real,F2: real > a,L: real > a] :
% 0.18/0.43 ( ( ( comp_a_real_a @ G2 @ H )
% 0.18/0.43 = ( comp_real_real_a @ R1 @ R2 ) )
% 0.18/0.43 => ( ( ( comp_real_a_real @ F2 @ R1 )
% 0.18/0.43 = L )
% 0.18/0.43 => ( ( comp_a_a_a @ ( comp_real_a_a @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_real_a_a @ L @ R2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp2
% 0.18/0.43 thf(fact_117_rewriteR__comp__comp2,axiom,
% 0.18/0.43 ! [G2: real > complex,H: real > real,R1: a > complex,R2: real > a,F2: complex > a,L: a > a] :
% 0.18/0.43 ( ( ( comp_r701421291x_real @ G2 @ H )
% 0.18/0.43 = ( comp_a_complex_real @ R1 @ R2 ) )
% 0.18/0.43 => ( ( ( comp_complex_a_a @ F2 @ R1 )
% 0.18/0.43 = L )
% 0.18/0.43 => ( ( comp_real_a_real @ ( comp_complex_a_real @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_a_real @ L @ R2 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp2
% 0.18/0.43 thf(fact_118_rewriteL__comp__comp2,axiom,
% 0.18/0.43 ! [F2: real > a,G2: a > real,L1: complex > a,L2: a > complex,H: real > a,R: real > complex] :
% 0.18/0.43 ( ( ( comp_real_a_a @ F2 @ G2 )
% 0.18/0.43 = ( comp_complex_a_a @ L1 @ L2 ) )
% 0.18/0.43 => ( ( ( comp_a_complex_real @ L2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_real_a_real @ F2 @ ( comp_a_real_real @ G2 @ H ) )
% 0.18/0.43 = ( comp_complex_a_real @ L1 @ R ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteL_comp_comp2
% 0.18/0.43 thf(fact_119_rewriteL__comp__comp2,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: real > complex,L1: real > a,L2: real > real,H: a > real,R: a > real] :
% 0.18/0.43 ( ( ( comp_complex_a_real @ F2 @ G2 )
% 0.18/0.43 = ( comp_real_a_real @ L1 @ L2 ) )
% 0.18/0.43 => ( ( ( comp_real_real_a @ L2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_complex_a_a @ F2 @ ( comp_real_complex_a @ G2 @ H ) )
% 0.18/0.43 = ( comp_real_a_a @ L1 @ R ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteL_comp_comp2
% 0.18/0.43 thf(fact_120_rewriteL__comp__comp2,axiom,
% 0.18/0.43 ! [F2: complex > complex,G2: a > complex,L1: a > complex,L2: a > a,H: complex > a,R: complex > a] :
% 0.18/0.43 ( ( ( comp_c124850173plex_a @ F2 @ G2 )
% 0.18/0.43 = ( comp_a_complex_a @ L1 @ L2 ) )
% 0.18/0.43 => ( ( ( comp_a_a_complex @ L2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_c130555887omplex @ F2 @ ( comp_a1063143865omplex @ G2 @ H ) )
% 0.18/0.43 = ( comp_a1063143865omplex @ L1 @ R ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteL_comp_comp2
% 0.18/0.43 thf(fact_121_rewriteL__comp__comp2,axiom,
% 0.18/0.43 ! [F2: complex > complex,G2: a > complex,L1: a > complex,L2: a > a,H: real > a,R: real > a] :
% 0.18/0.43 ( ( ( comp_c124850173plex_a @ F2 @ G2 )
% 0.18/0.43 = ( comp_a_complex_a @ L1 @ L2 ) )
% 0.18/0.43 => ( ( ( comp_a_a_real @ L2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_c595887981x_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) )
% 0.18/0.43 = ( comp_a_complex_real @ L1 @ R ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteL_comp_comp2
% 0.18/0.43 thf(fact_122_rewriteL__comp__comp2,axiom,
% 0.18/0.43 ! [F2: complex > complex,G2: a > complex,L1: a > complex,L2: a > a,H: a > a,R: a > a] :
% 0.18/0.43 ( ( ( comp_c124850173plex_a @ F2 @ G2 )
% 0.18/0.43 = ( comp_a_complex_a @ L1 @ L2 ) )
% 0.18/0.43 => ( ( ( comp_a_a_a @ L2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_c124850173plex_a @ F2 @ ( comp_a_complex_a @ G2 @ H ) )
% 0.18/0.43 = ( comp_a_complex_a @ L1 @ R ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteL_comp_comp2
% 0.18/0.43 thf(fact_123_rewriteL__comp__comp2,axiom,
% 0.18/0.43 ! [F2: real > a,G2: complex > real,L1: a > a,L2: complex > a,H: real > complex,R: real > a] :
% 0.18/0.43 ( ( ( comp_real_a_complex @ F2 @ G2 )
% 0.18/0.43 = ( comp_a_a_complex @ L1 @ L2 ) )
% 0.18/0.43 => ( ( ( comp_complex_a_real @ L2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_real_a_real @ F2 @ ( comp_c819638635l_real @ G2 @ H ) )
% 0.18/0.43 = ( comp_a_a_real @ L1 @ R ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteL_comp_comp2
% 0.18/0.43 thf(fact_124_rewriteL__comp__comp2,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: complex > complex,L1: a > a,L2: complex > a,H: a > complex,R: a > a] :
% 0.18/0.43 ( ( ( comp_c274302683omplex @ F2 @ G2 )
% 0.18/0.43 = ( comp_a_a_complex @ L1 @ L2 ) )
% 0.18/0.43 => ( ( ( comp_complex_a_a @ L2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_complex_a_a @ F2 @ ( comp_c124850173plex_a @ G2 @ H ) )
% 0.18/0.43 = ( comp_a_a_a @ L1 @ R ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteL_comp_comp2
% 0.18/0.43 thf(fact_125_rewriteL__comp__comp2,axiom,
% 0.18/0.43 ! [F2: complex > a,G2: real > complex,L1: a > a,L2: real > a,H: a > real,R: a > a] :
% 0.18/0.43 ( ( ( comp_complex_a_real @ F2 @ G2 )
% 0.18/0.43 = ( comp_a_a_real @ L1 @ L2 ) )
% 0.18/0.43 => ( ( ( comp_real_a_a @ L2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_complex_a_a @ F2 @ ( comp_real_complex_a @ G2 @ H ) )
% 0.18/0.43 = ( comp_a_a_a @ L1 @ R ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteL_comp_comp2
% 0.18/0.43 thf(fact_126_rewriteL__comp__comp2,axiom,
% 0.18/0.43 ! [F2: real > a,G2: a > real,L1: a > a,L2: a > a,H: real > a,R: real > a] :
% 0.18/0.43 ( ( ( comp_real_a_a @ F2 @ G2 )
% 0.18/0.43 = ( comp_a_a_a @ L1 @ L2 ) )
% 0.18/0.43 => ( ( ( comp_a_a_real @ L2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_real_a_real @ F2 @ ( comp_a_real_real @ G2 @ H ) )
% 0.18/0.43 = ( comp_a_a_real @ L1 @ R ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteL_comp_comp2
% 0.18/0.43 thf(fact_127_rewriteL__comp__comp2,axiom,
% 0.18/0.43 ! [F2: a > complex,G2: real > a,L1: a > complex,L2: real > a,H: complex > real,R: complex > a] :
% 0.18/0.43 ( ( ( comp_a_complex_real @ F2 @ G2 )
% 0.18/0.43 = ( comp_a_complex_real @ L1 @ L2 ) )
% 0.18/0.43 => ( ( ( comp_real_a_complex @ L2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) )
% 0.18/0.43 = ( comp_a1063143865omplex @ L1 @ R ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteL_comp_comp2
% 0.18/0.43 thf(fact_128_rewriteR__comp__comp,axiom,
% 0.18/0.43 ! [G2: real > a,H: complex > real,R: complex > a,F2: a > complex] :
% 0.18/0.43 ( ( ( comp_real_a_complex @ G2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a1063143865omplex @ F2 @ R ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp
% 0.18/0.43 thf(fact_129_rewriteR__comp__comp,axiom,
% 0.18/0.43 ! [G2: real > a,H: a > real,R: a > a,F2: a > complex] :
% 0.18/0.43 ( ( ( comp_real_a_a @ G2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_real_complex_a @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_complex_a @ F2 @ R ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp
% 0.18/0.43 thf(fact_130_rewriteR__comp__comp,axiom,
% 0.18/0.43 ! [G2: complex > a,H: real > complex,R: real > a,F2: a > complex] :
% 0.18/0.43 ( ( ( comp_complex_a_real @ G2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_complex_real @ F2 @ R ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp
% 0.18/0.43 thf(fact_131_rewriteR__comp__comp,axiom,
% 0.18/0.43 ! [G2: complex > a,H: complex > complex,R: complex > a,F2: a > complex] :
% 0.18/0.43 ( ( ( comp_c274302683omplex @ G2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_c130555887omplex @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a1063143865omplex @ F2 @ R ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp
% 0.18/0.43 thf(fact_132_rewriteR__comp__comp,axiom,
% 0.18/0.43 ! [G2: complex > a,H: complex > complex,R: complex > a,F2: a > a] :
% 0.18/0.43 ( ( ( comp_c274302683omplex @ G2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_c274302683omplex @ ( comp_a_a_complex @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_a_complex @ F2 @ R ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp
% 0.18/0.43 thf(fact_133_rewriteR__comp__comp,axiom,
% 0.18/0.43 ! [G2: complex > a,H: real > complex,R: real > a,F2: a > a] :
% 0.18/0.43 ( ( ( comp_complex_a_real @ G2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_complex_a_real @ ( comp_a_a_complex @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_a_real @ F2 @ R ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp
% 0.18/0.43 thf(fact_134_rewriteR__comp__comp,axiom,
% 0.18/0.43 ! [G2: real > a,H: complex > real,R: complex > a,F2: a > a] :
% 0.18/0.43 ( ( ( comp_real_a_complex @ G2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_real_a_complex @ ( comp_a_a_real @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_a_complex @ F2 @ R ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp
% 0.18/0.43 thf(fact_135_rewriteR__comp__comp,axiom,
% 0.18/0.43 ! [G2: real > a,H: a > real,R: a > a,F2: a > a] :
% 0.18/0.43 ( ( ( comp_real_a_a @ G2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_real_a_a @ ( comp_a_a_real @ F2 @ G2 ) @ H )
% 0.18/0.43 = ( comp_a_a_a @ F2 @ R ) ) ) ).
% 0.18/0.43
% 0.18/0.43 % rewriteR_comp_comp
% 0.18/0.43 thf(fact_136_rewriteR__comp__comp,axiom,
% 0.18/0.43 ! [G2: complex > complex,H: a > complex,R: a > complex,F2: complex > a] :
% 0.18/0.43 ( ( ( comp_c124850173plex_a @ G2 @ H )
% 0.18/0.43 = R )
% 0.18/0.43 => ( ( comp_complex_a_a @ ( comp_c274302683omplex @ F2 @ G2 ) @ H )
% 0.18/0.44 = ( comp_complex_a_a @ F2 @ R ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % rewriteR_comp_comp
% 0.18/0.44 thf(fact_137_rewriteR__comp__comp,axiom,
% 0.18/0.44 ! [G2: real > real,H: real > real,R: real > real,F2: real > a] :
% 0.18/0.44 ( ( ( comp_real_real_real @ G2 @ H )
% 0.18/0.44 = R )
% 0.18/0.44 => ( ( comp_real_a_real @ ( comp_real_a_real @ F2 @ G2 ) @ H )
% 0.18/0.44 = ( comp_real_a_real @ F2 @ R ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % rewriteR_comp_comp
% 0.18/0.44 thf(fact_138_rewriteL__comp__comp,axiom,
% 0.18/0.44 ! [F2: complex > complex,G2: a > complex,L: a > complex,H: real > a] :
% 0.18/0.44 ( ( ( comp_c124850173plex_a @ F2 @ G2 )
% 0.18/0.44 = L )
% 0.18/0.44 => ( ( comp_c595887981x_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) )
% 0.18/0.44 = ( comp_a_complex_real @ L @ H ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % rewriteL_comp_comp
% 0.18/0.44 thf(fact_139_rewriteL__comp__comp,axiom,
% 0.18/0.44 ! [F2: complex > complex,G2: a > complex,L: a > complex,H: complex > a] :
% 0.18/0.44 ( ( ( comp_c124850173plex_a @ F2 @ G2 )
% 0.18/0.44 = L )
% 0.18/0.44 => ( ( comp_c130555887omplex @ F2 @ ( comp_a1063143865omplex @ G2 @ H ) )
% 0.18/0.44 = ( comp_a1063143865omplex @ L @ H ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % rewriteL_comp_comp
% 0.18/0.44 thf(fact_140_rewriteL__comp__comp,axiom,
% 0.18/0.44 ! [F2: complex > complex,G2: a > complex,L: a > complex,H: a > a] :
% 0.18/0.44 ( ( ( comp_c124850173plex_a @ F2 @ G2 )
% 0.18/0.44 = L )
% 0.18/0.44 => ( ( comp_c124850173plex_a @ F2 @ ( comp_a_complex_a @ G2 @ H ) )
% 0.18/0.44 = ( comp_a_complex_a @ L @ H ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % rewriteL_comp_comp
% 0.18/0.44 thf(fact_141_rewriteL__comp__comp,axiom,
% 0.18/0.44 ! [F2: complex > a,G2: complex > complex,L: complex > a,H: a > complex] :
% 0.18/0.44 ( ( ( comp_c274302683omplex @ F2 @ G2 )
% 0.18/0.44 = L )
% 0.18/0.44 => ( ( comp_complex_a_a @ F2 @ ( comp_c124850173plex_a @ G2 @ H ) )
% 0.18/0.44 = ( comp_complex_a_a @ L @ H ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % rewriteL_comp_comp
% 0.18/0.44 thf(fact_142_rewriteL__comp__comp,axiom,
% 0.18/0.44 ! [F2: real > a,G2: a > real,L: a > a,H: real > a] :
% 0.18/0.44 ( ( ( comp_real_a_a @ F2 @ G2 )
% 0.18/0.44 = L )
% 0.18/0.44 => ( ( comp_real_a_real @ F2 @ ( comp_a_real_real @ G2 @ H ) )
% 0.18/0.44 = ( comp_a_a_real @ L @ H ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % rewriteL_comp_comp
% 0.18/0.44 thf(fact_143_rewriteL__comp__comp,axiom,
% 0.18/0.44 ! [F2: a > complex,G2: real > a,L: real > complex,H: real > real] :
% 0.18/0.44 ( ( ( comp_a_complex_real @ F2 @ G2 )
% 0.18/0.44 = L )
% 0.18/0.44 => ( ( comp_a_complex_real @ F2 @ ( comp_real_a_real @ G2 @ H ) )
% 0.18/0.44 = ( comp_r701421291x_real @ L @ H ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % rewriteL_comp_comp
% 0.18/0.44 thf(fact_144_rewriteL__comp__comp,axiom,
% 0.18/0.44 ! [F2: a > complex,G2: real > a,L: real > complex,H: complex > real] :
% 0.18/0.44 ( ( ( comp_a_complex_real @ F2 @ G2 )
% 0.18/0.44 = L )
% 0.18/0.44 => ( ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) )
% 0.18/0.44 = ( comp_r667767405omplex @ L @ H ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % rewriteL_comp_comp
% 0.18/0.44 thf(fact_145_rewriteL__comp__comp,axiom,
% 0.18/0.44 ! [F2: a > complex,G2: real > a,L: real > complex,H: a > real] :
% 0.18/0.44 ( ( ( comp_a_complex_real @ F2 @ G2 )
% 0.18/0.44 = L )
% 0.18/0.44 => ( ( comp_a_complex_a @ F2 @ ( comp_real_a_a @ G2 @ H ) )
% 0.18/0.44 = ( comp_real_complex_a @ L @ H ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % rewriteL_comp_comp
% 0.18/0.44 thf(fact_146_rewriteL__comp__comp,axiom,
% 0.18/0.44 ! [F2: a > complex,G2: complex > a,L: complex > complex,H: real > complex] :
% 0.18/0.44 ( ( ( comp_a1063143865omplex @ F2 @ G2 )
% 0.18/0.44 = L )
% 0.18/0.44 => ( ( comp_a_complex_real @ F2 @ ( comp_complex_a_real @ G2 @ H ) )
% 0.18/0.44 = ( comp_c595887981x_real @ L @ H ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % rewriteL_comp_comp
% 0.18/0.44 thf(fact_147_rewriteL__comp__comp,axiom,
% 0.18/0.44 ! [F2: a > complex,G2: complex > a,L: complex > complex,H: complex > complex] :
% 0.18/0.44 ( ( ( comp_a1063143865omplex @ F2 @ G2 )
% 0.18/0.44 = L )
% 0.18/0.44 => ( ( comp_a1063143865omplex @ F2 @ ( comp_c274302683omplex @ G2 @ H ) )
% 0.18/0.44 = ( comp_c130555887omplex @ L @ H ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % rewriteL_comp_comp
% 0.18/0.44 thf(fact_148_injD,axiom,
% 0.18/0.44 ! [F2: a > complex,X2: a,Y: a] :
% 0.18/0.44 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( ( F2 @ X2 )
% 0.18/0.44 = ( F2 @ Y ) )
% 0.18/0.44 => ( X2 = Y ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % injD
% 0.18/0.44 thf(fact_149_injD,axiom,
% 0.18/0.44 ! [F2: complex > a,X2: complex,Y: complex] :
% 0.18/0.44 ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 0.18/0.44 => ( ( ( F2 @ X2 )
% 0.18/0.44 = ( F2 @ Y ) )
% 0.18/0.44 => ( X2 = Y ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % injD
% 0.18/0.44 thf(fact_150_injI,axiom,
% 0.18/0.44 ! [F2: a > complex] :
% 0.18/0.44 ( ! [X4: a,Y2: a] :
% 0.18/0.44 ( ( ( F2 @ X4 )
% 0.18/0.44 = ( F2 @ Y2 ) )
% 0.18/0.44 => ( X4 = Y2 ) )
% 0.18/0.44 => ( inj_on_a_complex @ F2 @ top_top_set_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % injI
% 0.18/0.44 thf(fact_151_injI,axiom,
% 0.18/0.44 ! [F2: complex > a] :
% 0.18/0.44 ( ! [X4: complex,Y2: complex] :
% 0.18/0.44 ( ( ( F2 @ X4 )
% 0.18/0.44 = ( F2 @ Y2 ) )
% 0.18/0.44 => ( X4 = Y2 ) )
% 0.18/0.44 => ( inj_on_complex_a @ F2 @ top_top_set_complex ) ) ).
% 0.18/0.44
% 0.18/0.44 % injI
% 0.18/0.44 thf(fact_152_inj__eq,axiom,
% 0.18/0.44 ! [F2: a > complex,X2: a,Y: a] :
% 0.18/0.44 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( ( F2 @ X2 )
% 0.18/0.44 = ( F2 @ Y ) )
% 0.18/0.44 = ( X2 = Y ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_eq
% 0.18/0.44 thf(fact_153_inj__eq,axiom,
% 0.18/0.44 ! [F2: complex > a,X2: complex,Y: complex] :
% 0.18/0.44 ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 0.18/0.44 => ( ( ( F2 @ X2 )
% 0.18/0.44 = ( F2 @ Y ) )
% 0.18/0.44 = ( X2 = Y ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_eq
% 0.18/0.44 thf(fact_154_inj__def,axiom,
% 0.18/0.44 ! [F2: a > complex] :
% 0.18/0.44 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 = ( ! [X: a,Y3: a] :
% 0.18/0.44 ( ( ( F2 @ X )
% 0.18/0.44 = ( F2 @ Y3 ) )
% 0.18/0.44 => ( X = Y3 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_def
% 0.18/0.44 thf(fact_155_inj__def,axiom,
% 0.18/0.44 ! [F2: complex > a] :
% 0.18/0.44 ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 0.18/0.44 = ( ! [X: complex,Y3: complex] :
% 0.18/0.44 ( ( ( F2 @ X )
% 0.18/0.44 = ( F2 @ Y3 ) )
% 0.18/0.44 => ( X = Y3 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_def
% 0.18/0.44 thf(fact_156_inj__onD,axiom,
% 0.18/0.44 ! [F2: a > complex,A2: set_a,X2: a,Y: a] :
% 0.18/0.44 ( ( inj_on_a_complex @ F2 @ A2 )
% 0.18/0.44 => ( ( ( F2 @ X2 )
% 0.18/0.44 = ( F2 @ Y ) )
% 0.18/0.44 => ( ( member_a @ X2 @ A2 )
% 0.18/0.44 => ( ( member_a @ Y @ A2 )
% 0.18/0.44 => ( X2 = Y ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_onD
% 0.18/0.44 thf(fact_157_inj__onD,axiom,
% 0.18/0.44 ! [F2: complex > a,A2: set_complex,X2: complex,Y: complex] :
% 0.18/0.44 ( ( inj_on_complex_a @ F2 @ A2 )
% 0.18/0.44 => ( ( ( F2 @ X2 )
% 0.18/0.44 = ( F2 @ Y ) )
% 0.18/0.44 => ( ( member_complex @ X2 @ A2 )
% 0.18/0.44 => ( ( member_complex @ Y @ A2 )
% 0.18/0.44 => ( X2 = Y ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_onD
% 0.18/0.44 thf(fact_158_inj__onI,axiom,
% 0.18/0.44 ! [A2: set_a,F2: a > complex] :
% 0.18/0.44 ( ! [X4: a,Y2: a] :
% 0.18/0.44 ( ( member_a @ X4 @ A2 )
% 0.18/0.44 => ( ( member_a @ Y2 @ A2 )
% 0.18/0.44 => ( ( ( F2 @ X4 )
% 0.18/0.44 = ( F2 @ Y2 ) )
% 0.18/0.44 => ( X4 = Y2 ) ) ) )
% 0.18/0.44 => ( inj_on_a_complex @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_onI
% 0.18/0.44 thf(fact_159_inj__onI,axiom,
% 0.18/0.44 ! [A2: set_complex,F2: complex > a] :
% 0.18/0.44 ( ! [X4: complex,Y2: complex] :
% 0.18/0.44 ( ( member_complex @ X4 @ A2 )
% 0.18/0.44 => ( ( member_complex @ Y2 @ A2 )
% 0.18/0.44 => ( ( ( F2 @ X4 )
% 0.18/0.44 = ( F2 @ Y2 ) )
% 0.18/0.44 => ( X4 = Y2 ) ) ) )
% 0.18/0.44 => ( inj_on_complex_a @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_onI
% 0.18/0.44 thf(fact_160_inj__on__def,axiom,
% 0.18/0.44 ( inj_on_a_complex
% 0.18/0.44 = ( ^ [F: a > complex,A4: set_a] :
% 0.18/0.44 ! [X: a] :
% 0.18/0.44 ( ( member_a @ X @ A4 )
% 0.18/0.44 => ! [Y3: a] :
% 0.18/0.44 ( ( member_a @ Y3 @ A4 )
% 0.18/0.44 => ( ( ( F @ X )
% 0.18/0.44 = ( F @ Y3 ) )
% 0.18/0.44 => ( X = Y3 ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_def
% 0.18/0.44 thf(fact_161_inj__on__def,axiom,
% 0.18/0.44 ( inj_on_complex_a
% 0.18/0.44 = ( ^ [F: complex > a,A4: set_complex] :
% 0.18/0.44 ! [X: complex] :
% 0.18/0.44 ( ( member_complex @ X @ A4 )
% 0.18/0.44 => ! [Y3: complex] :
% 0.18/0.44 ( ( member_complex @ Y3 @ A4 )
% 0.18/0.44 => ( ( ( F @ X )
% 0.18/0.44 = ( F @ Y3 ) )
% 0.18/0.44 => ( X = Y3 ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_def
% 0.18/0.44 thf(fact_162_inj__on__cong,axiom,
% 0.18/0.44 ! [A2: set_a,F2: a > complex,G2: a > complex] :
% 0.18/0.44 ( ! [A5: a] :
% 0.18/0.44 ( ( member_a @ A5 @ A2 )
% 0.18/0.44 => ( ( F2 @ A5 )
% 0.18/0.44 = ( G2 @ A5 ) ) )
% 0.18/0.44 => ( ( inj_on_a_complex @ F2 @ A2 )
% 0.18/0.44 = ( inj_on_a_complex @ G2 @ A2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_cong
% 0.18/0.44 thf(fact_163_inj__on__cong,axiom,
% 0.18/0.44 ! [A2: set_complex,F2: complex > a,G2: complex > a] :
% 0.18/0.44 ( ! [A5: complex] :
% 0.18/0.44 ( ( member_complex @ A5 @ A2 )
% 0.18/0.44 => ( ( F2 @ A5 )
% 0.18/0.44 = ( G2 @ A5 ) ) )
% 0.18/0.44 => ( ( inj_on_complex_a @ F2 @ A2 )
% 0.18/0.44 = ( inj_on_complex_a @ G2 @ A2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_cong
% 0.18/0.44 thf(fact_164_inj__on__eq__iff,axiom,
% 0.18/0.44 ! [F2: a > complex,A2: set_a,X2: a,Y: a] :
% 0.18/0.44 ( ( inj_on_a_complex @ F2 @ A2 )
% 0.18/0.44 => ( ( member_a @ X2 @ A2 )
% 0.18/0.44 => ( ( member_a @ Y @ A2 )
% 0.18/0.44 => ( ( ( F2 @ X2 )
% 0.18/0.44 = ( F2 @ Y ) )
% 0.18/0.44 = ( X2 = Y ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_eq_iff
% 0.18/0.44 thf(fact_165_inj__on__eq__iff,axiom,
% 0.18/0.44 ! [F2: complex > a,A2: set_complex,X2: complex,Y: complex] :
% 0.18/0.44 ( ( inj_on_complex_a @ F2 @ A2 )
% 0.18/0.44 => ( ( member_complex @ X2 @ A2 )
% 0.18/0.44 => ( ( member_complex @ Y @ A2 )
% 0.18/0.44 => ( ( ( F2 @ X2 )
% 0.18/0.44 = ( F2 @ Y ) )
% 0.18/0.44 = ( X2 = Y ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_eq_iff
% 0.18/0.44 thf(fact_166_inj__on__contraD,axiom,
% 0.18/0.44 ! [F2: a > complex,A2: set_a,X2: a,Y: a] :
% 0.18/0.44 ( ( inj_on_a_complex @ F2 @ A2 )
% 0.18/0.44 => ( ( X2 != Y )
% 0.18/0.44 => ( ( member_a @ X2 @ A2 )
% 0.18/0.44 => ( ( member_a @ Y @ A2 )
% 0.18/0.44 => ( ( F2 @ X2 )
% 0.18/0.44 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_contraD
% 0.18/0.44 thf(fact_167_inj__on__contraD,axiom,
% 0.18/0.44 ! [F2: complex > a,A2: set_complex,X2: complex,Y: complex] :
% 0.18/0.44 ( ( inj_on_complex_a @ F2 @ A2 )
% 0.18/0.44 => ( ( X2 != Y )
% 0.18/0.44 => ( ( member_complex @ X2 @ A2 )
% 0.18/0.44 => ( ( member_complex @ Y @ A2 )
% 0.18/0.44 => ( ( F2 @ X2 )
% 0.18/0.44 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_contraD
% 0.18/0.44 thf(fact_168_inj__on__inverseI,axiom,
% 0.18/0.44 ! [A2: set_a,G2: complex > a,F2: a > complex] :
% 0.18/0.44 ( ! [X4: a] :
% 0.18/0.44 ( ( member_a @ X4 @ A2 )
% 0.18/0.44 => ( ( G2 @ ( F2 @ X4 ) )
% 0.18/0.44 = X4 ) )
% 0.18/0.44 => ( inj_on_a_complex @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_inverseI
% 0.18/0.44 thf(fact_169_inj__on__inverseI,axiom,
% 0.18/0.44 ! [A2: set_complex,G2: a > complex,F2: complex > a] :
% 0.18/0.44 ( ! [X4: complex] :
% 0.18/0.44 ( ( member_complex @ X4 @ A2 )
% 0.18/0.44 => ( ( G2 @ ( F2 @ X4 ) )
% 0.18/0.44 = X4 ) )
% 0.18/0.44 => ( inj_on_complex_a @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_inverseI
% 0.18/0.44 thf(fact_170_inj__compose,axiom,
% 0.18/0.44 ! [F2: real > a,G2: real > real] :
% 0.18/0.44 ( ( inj_on_real_a @ F2 @ top_top_set_real )
% 0.18/0.44 => ( ( inj_on_real_real @ G2 @ top_top_set_real )
% 0.18/0.44 => ( inj_on_real_a @ ( comp_real_a_real @ F2 @ G2 ) @ top_top_set_real ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_compose
% 0.18/0.44 thf(fact_171_inj__compose,axiom,
% 0.18/0.44 ! [F2: a > a,G2: real > a] :
% 0.18/0.44 ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( inj_on_real_a @ G2 @ top_top_set_real )
% 0.18/0.44 => ( inj_on_real_a @ ( comp_a_a_real @ F2 @ G2 ) @ top_top_set_real ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_compose
% 0.18/0.44 thf(fact_172_inj__compose,axiom,
% 0.18/0.44 ! [F2: a > complex,G2: real > a] :
% 0.18/0.44 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( inj_on_real_a @ G2 @ top_top_set_real )
% 0.18/0.44 => ( inj_on_real_complex @ ( comp_a_complex_real @ F2 @ G2 ) @ top_top_set_real ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_compose
% 0.18/0.44 thf(fact_173_inj__compose,axiom,
% 0.18/0.44 ! [F2: a > a,G2: a > a] :
% 0.18/0.44 ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( inj_on_a_a @ G2 @ top_top_set_a )
% 0.18/0.44 => ( inj_on_a_a @ ( comp_a_a_a @ F2 @ G2 ) @ top_top_set_a ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_compose
% 0.18/0.44 thf(fact_174_inj__compose,axiom,
% 0.18/0.44 ! [F2: a > complex,G2: a > a] :
% 0.18/0.44 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( inj_on_a_a @ G2 @ top_top_set_a )
% 0.18/0.44 => ( inj_on_a_complex @ ( comp_a_complex_a @ F2 @ G2 ) @ top_top_set_a ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_compose
% 0.18/0.44 thf(fact_175_inj__compose,axiom,
% 0.18/0.44 ! [F2: a > a,G2: complex > a] :
% 0.18/0.44 ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( inj_on_complex_a @ G2 @ top_top_set_complex )
% 0.18/0.44 => ( inj_on_complex_a @ ( comp_a_a_complex @ F2 @ G2 ) @ top_top_set_complex ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_compose
% 0.18/0.44 thf(fact_176_inj__compose,axiom,
% 0.18/0.44 ! [F2: a > complex,G2: complex > a] :
% 0.18/0.44 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( inj_on_complex_a @ G2 @ top_top_set_complex )
% 0.18/0.44 => ( inj_on94911183omplex @ ( comp_a1063143865omplex @ F2 @ G2 ) @ top_top_set_complex ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_compose
% 0.18/0.44 thf(fact_177_inj__compose,axiom,
% 0.18/0.44 ! [F2: complex > complex,G2: a > complex] :
% 0.18/0.44 ( ( inj_on94911183omplex @ F2 @ top_top_set_complex )
% 0.18/0.44 => ( ( inj_on_a_complex @ G2 @ top_top_set_a )
% 0.18/0.44 => ( inj_on_a_complex @ ( comp_c124850173plex_a @ F2 @ G2 ) @ top_top_set_a ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_compose
% 0.18/0.44 thf(fact_178_inj__compose,axiom,
% 0.18/0.44 ! [F2: complex > a,G2: a > complex] :
% 0.18/0.44 ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 0.18/0.44 => ( ( inj_on_a_complex @ G2 @ top_top_set_a )
% 0.18/0.44 => ( inj_on_a_a @ ( comp_complex_a_a @ F2 @ G2 ) @ top_top_set_a ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_compose
% 0.18/0.44 thf(fact_179_inj__compose,axiom,
% 0.18/0.44 ! [F2: complex > a,G2: complex > complex] :
% 0.18/0.44 ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 0.18/0.44 => ( ( inj_on94911183omplex @ G2 @ top_top_set_complex )
% 0.18/0.44 => ( inj_on_complex_a @ ( comp_c274302683omplex @ F2 @ G2 ) @ top_top_set_complex ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_compose
% 0.18/0.44 thf(fact_180_inj__on__imageI2,axiom,
% 0.18/0.44 ! [F3: a > complex,F2: real > a,A2: set_real] :
% 0.18/0.44 ( ( inj_on_real_complex @ ( comp_a_complex_real @ F3 @ F2 ) @ A2 )
% 0.18/0.44 => ( inj_on_real_a @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_imageI2
% 0.18/0.44 thf(fact_181_inj__on__imageI2,axiom,
% 0.18/0.44 ! [F3: real > a,F2: real > real,A2: set_real] :
% 0.18/0.44 ( ( inj_on_real_a @ ( comp_real_a_real @ F3 @ F2 ) @ A2 )
% 0.18/0.44 => ( inj_on_real_real @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_imageI2
% 0.18/0.44 thf(fact_182_inj__on__imageI2,axiom,
% 0.18/0.44 ! [F3: a > a,F2: real > a,A2: set_real] :
% 0.18/0.44 ( ( inj_on_real_a @ ( comp_a_a_real @ F3 @ F2 ) @ A2 )
% 0.18/0.44 => ( inj_on_real_a @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_imageI2
% 0.18/0.44 thf(fact_183_inj__on__imageI2,axiom,
% 0.18/0.44 ! [F3: a > a,F2: a > a,A2: set_a] :
% 0.18/0.44 ( ( inj_on_a_a @ ( comp_a_a_a @ F3 @ F2 ) @ A2 )
% 0.18/0.44 => ( inj_on_a_a @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_imageI2
% 0.18/0.44 thf(fact_184_inj__on__imageI2,axiom,
% 0.18/0.44 ! [F3: complex > a,F2: a > complex,A2: set_a] :
% 0.18/0.44 ( ( inj_on_a_a @ ( comp_complex_a_a @ F3 @ F2 ) @ A2 )
% 0.18/0.44 => ( inj_on_a_complex @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_imageI2
% 0.18/0.44 thf(fact_185_inj__on__imageI2,axiom,
% 0.18/0.44 ! [F3: a > complex,F2: complex > a,A2: set_complex] :
% 0.18/0.44 ( ( inj_on94911183omplex @ ( comp_a1063143865omplex @ F3 @ F2 ) @ A2 )
% 0.18/0.44 => ( inj_on_complex_a @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_imageI2
% 0.18/0.44 thf(fact_186_inj__on__imageI2,axiom,
% 0.18/0.44 ! [F3: a > complex,F2: a > a,A2: set_a] :
% 0.18/0.44 ( ( inj_on_a_complex @ ( comp_a_complex_a @ F3 @ F2 ) @ A2 )
% 0.18/0.44 => ( inj_on_a_a @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_imageI2
% 0.18/0.44 thf(fact_187_inj__on__imageI2,axiom,
% 0.18/0.44 ! [F3: complex > complex,F2: a > complex,A2: set_a] :
% 0.18/0.44 ( ( inj_on_a_complex @ ( comp_c124850173plex_a @ F3 @ F2 ) @ A2 )
% 0.18/0.44 => ( inj_on_a_complex @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_imageI2
% 0.18/0.44 thf(fact_188_inj__on__imageI2,axiom,
% 0.18/0.44 ! [F3: a > a,F2: complex > a,A2: set_complex] :
% 0.18/0.44 ( ( inj_on_complex_a @ ( comp_a_a_complex @ F3 @ F2 ) @ A2 )
% 0.18/0.44 => ( inj_on_complex_a @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_imageI2
% 0.18/0.44 thf(fact_189_simple__path__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: real > a,G2: real > real] :
% 0.18/0.44 ( ( real_V779700657real_a @ F2 )
% 0.18/0.44 => ( ( inj_on_real_a @ F2 @ top_top_set_real )
% 0.18/0.44 => ( ( path_simple_path_a @ ( comp_real_a_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_s1005760220h_real @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_linear_image_eq
% 0.18/0.44 thf(fact_190_simple__path__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: a > a,G2: real > a] :
% 0.18/0.44 ( ( real_V202220639ar_a_a @ F2 )
% 0.18/0.44 => ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( path_simple_path_a @ ( comp_a_a_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_simple_path_a @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_linear_image_eq
% 0.18/0.44 thf(fact_191_simple__path__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: complex > a,G2: real > complex] :
% 0.18/0.44 ( ( real_V1327653935plex_a @ F2 )
% 0.18/0.44 => ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 0.18/0.44 => ( ( path_simple_path_a @ ( comp_complex_a_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_s36253918omplex @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_linear_image_eq
% 0.18/0.44 thf(fact_192_simple__path__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: a > complex,G2: real > a] :
% 0.18/0.44 ( ( real_V1477106445omplex @ F2 )
% 0.18/0.44 => ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( path_s36253918omplex @ ( comp_a_complex_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_simple_path_a @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_linear_image_eq
% 0.18/0.44 thf(fact_193_simple__path__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: complex > complex,G2: real > complex] :
% 0.18/0.44 ( ( real_V670066493omplex @ F2 )
% 0.18/0.44 => ( ( inj_on94911183omplex @ F2 @ top_top_set_complex )
% 0.18/0.44 => ( ( path_s36253918omplex @ ( comp_c595887981x_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_s36253918omplex @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_linear_image_eq
% 0.18/0.44 thf(fact_194_fun_Oinj__map,axiom,
% 0.18/0.44 ! [F2: real > a] :
% 0.18/0.44 ( ( inj_on_real_a @ F2 @ top_top_set_real )
% 0.18/0.44 => ( inj_on958237983real_a @ ( comp_real_a_real @ F2 ) @ top_to1446257885l_real ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.inj_map
% 0.18/0.44 thf(fact_195_fun_Oinj__map,axiom,
% 0.18/0.44 ! [F2: a > a] :
% 0.18/0.44 ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 0.18/0.44 => ( inj_on1576005937plex_a @ ( comp_a_a_complex @ F2 ) @ top_to525076535plex_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.inj_map
% 0.18/0.44 thf(fact_196_fun_Oinj__map,axiom,
% 0.18/0.44 ! [F2: a > a] :
% 0.18/0.44 ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 0.18/0.44 => ( inj_on_real_a_real_a @ ( comp_a_a_real @ F2 ) @ top_top_set_real_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.inj_map
% 0.18/0.44 thf(fact_197_fun_Oinj__map,axiom,
% 0.18/0.44 ! [F2: a > a] :
% 0.18/0.44 ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 0.18/0.44 => ( inj_on_a_a_a_a @ ( comp_a_a_a @ F2 ) @ top_top_set_a_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.inj_map
% 0.18/0.44 thf(fact_198_fun_Oinj__map,axiom,
% 0.18/0.44 ! [F2: a > complex] :
% 0.18/0.44 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 => ( inj_on319905617omplex @ ( comp_a_complex_real @ F2 ) @ top_top_set_real_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.inj_map
% 0.18/0.44 thf(fact_199_fun_Oinj__map,axiom,
% 0.18/0.44 ! [F2: a > complex] :
% 0.18/0.44 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 => ( inj_on893405649omplex @ ( comp_a1063143865omplex @ F2 ) @ top_to525076535plex_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.inj_map
% 0.18/0.44 thf(fact_200_fun_Oinj__map,axiom,
% 0.18/0.44 ! [F2: a > complex] :
% 0.18/0.44 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 => ( inj_on_a_a_a_complex @ ( comp_a_complex_a @ F2 ) @ top_top_set_a_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.inj_map
% 0.18/0.44 thf(fact_201_fun_Oinj__map,axiom,
% 0.18/0.44 ! [F2: complex > a] :
% 0.18/0.44 ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 0.18/0.44 => ( inj_on_a_complex_a_a @ ( comp_complex_a_a @ F2 ) @ top_to2109114701omplex ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.inj_map
% 0.18/0.44 thf(fact_202_real__of__bounded__linear,axiom,
% 0.18/0.44 real_V762982918plex_a @ poinca837721858l_of_a ).
% 0.18/0.44
% 0.18/0.44 % real_of_bounded_linear
% 0.18/0.44 thf(fact_203_real__of__linear,axiom,
% 0.18/0.44 real_V1327653935plex_a @ poinca837721858l_of_a ).
% 0.18/0.44
% 0.18/0.44 % real_of_linear
% 0.18/0.44 thf(fact_204_iso__tuple__UNIV__I,axiom,
% 0.18/0.44 ! [X2: a] : ( member_a @ X2 @ top_top_set_a ) ).
% 0.18/0.44
% 0.18/0.44 % iso_tuple_UNIV_I
% 0.18/0.44 thf(fact_205_iso__tuple__UNIV__I,axiom,
% 0.18/0.44 ! [X2: complex] : ( member_complex @ X2 @ top_top_set_complex ) ).
% 0.18/0.44
% 0.18/0.44 % iso_tuple_UNIV_I
% 0.18/0.44 thf(fact_206_UNIV__I,axiom,
% 0.18/0.44 ! [X2: a] : ( member_a @ X2 @ top_top_set_a ) ).
% 0.18/0.44
% 0.18/0.44 % UNIV_I
% 0.18/0.44 thf(fact_207_UNIV__I,axiom,
% 0.18/0.44 ! [X2: complex] : ( member_complex @ X2 @ top_top_set_complex ) ).
% 0.18/0.44
% 0.18/0.44 % UNIV_I
% 0.18/0.44 thf(fact_208_bounded__linear_Ointro,axiom,
% 0.18/0.44 ! [F2: a > complex] :
% 0.18/0.44 ( ( real_V1477106445omplex @ F2 )
% 0.18/0.44 => ( ( real_V451440129omplex @ F2 )
% 0.18/0.44 => ( real_V912435428omplex @ F2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bounded_linear.intro
% 0.18/0.44 thf(fact_209_bounded__linear_Ointro,axiom,
% 0.18/0.44 ! [F2: complex > a] :
% 0.18/0.44 ( ( real_V1327653935plex_a @ F2 )
% 0.18/0.44 => ( ( real_V301987619plex_a @ F2 )
% 0.18/0.44 => ( real_V762982918plex_a @ F2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bounded_linear.intro
% 0.18/0.44 thf(fact_210_bounded__linear__def,axiom,
% 0.18/0.44 ( real_V912435428omplex
% 0.18/0.44 = ( ^ [F: a > complex] :
% 0.18/0.44 ( ( real_V1477106445omplex @ F )
% 0.18/0.44 & ( real_V451440129omplex @ F ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bounded_linear_def
% 0.18/0.44 thf(fact_211_bounded__linear__def,axiom,
% 0.18/0.44 ( real_V762982918plex_a
% 0.18/0.44 = ( ^ [F: complex > a] :
% 0.18/0.44 ( ( real_V1327653935plex_a @ F )
% 0.18/0.44 & ( real_V301987619plex_a @ F ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bounded_linear_def
% 0.18/0.44 thf(fact_212_arc__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: real > a,G2: real > real] :
% 0.18/0.44 ( ( real_V779700657real_a @ F2 )
% 0.18/0.44 => ( ( inj_on_real_a @ F2 @ top_top_set_real )
% 0.18/0.44 => ( ( path_arc_a @ ( comp_real_a_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_arc_real @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % arc_linear_image_eq
% 0.18/0.44 thf(fact_213_arc__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: a > a,G2: real > a] :
% 0.18/0.44 ( ( real_V202220639ar_a_a @ F2 )
% 0.18/0.44 => ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( path_arc_a @ ( comp_a_a_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_arc_a @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % arc_linear_image_eq
% 0.18/0.44 thf(fact_214_arc__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: a > complex,G2: real > a] :
% 0.18/0.44 ( ( real_V1477106445omplex @ F2 )
% 0.18/0.44 => ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( path_arc_complex @ ( comp_a_complex_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_arc_a @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % arc_linear_image_eq
% 0.18/0.44 thf(fact_215_arc__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: complex > a,G2: real > complex] :
% 0.18/0.44 ( ( real_V1327653935plex_a @ F2 )
% 0.18/0.44 => ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 0.18/0.44 => ( ( path_arc_a @ ( comp_complex_a_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_arc_complex @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % arc_linear_image_eq
% 0.18/0.44 thf(fact_216_real__of__inj,axiom,
% 0.18/0.44 inj_on_complex_a @ poinca837721858l_of_a @ top_top_set_complex ).
% 0.18/0.44
% 0.18/0.44 % real_of_inj
% 0.18/0.44 thf(fact_217_top__set__def,axiom,
% 0.18/0.44 ( top_top_set_a
% 0.18/0.44 = ( collect_a @ top_top_a_o ) ) ).
% 0.18/0.44
% 0.18/0.44 % top_set_def
% 0.18/0.44 thf(fact_218_top__set__def,axiom,
% 0.18/0.44 ( top_top_set_complex
% 0.18/0.44 = ( collect_complex @ top_top_complex_o ) ) ).
% 0.18/0.44
% 0.18/0.44 % top_set_def
% 0.18/0.44 thf(fact_219_arc__imp__simple__path,axiom,
% 0.18/0.44 ! [G2: real > a] :
% 0.18/0.44 ( ( path_arc_a @ G2 )
% 0.18/0.44 => ( path_simple_path_a @ G2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % arc_imp_simple_path
% 0.18/0.44 thf(fact_220_arc__imp__simple__path,axiom,
% 0.18/0.44 ! [G2: real > complex] :
% 0.18/0.44 ( ( path_arc_complex @ G2 )
% 0.18/0.44 => ( path_s36253918omplex @ G2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % arc_imp_simple_path
% 0.18/0.44 thf(fact_221_arc__distinct__ends,axiom,
% 0.18/0.44 ! [G2: real > complex] :
% 0.18/0.44 ( ( path_arc_complex @ G2 )
% 0.18/0.44 => ( ( path_p769714271omplex @ G2 )
% 0.18/0.44 != ( path_p797330068omplex @ G2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % arc_distinct_ends
% 0.18/0.44 thf(fact_222_arc__distinct__ends,axiom,
% 0.18/0.44 ! [G2: real > a] :
% 0.18/0.44 ( ( path_arc_a @ G2 )
% 0.18/0.44 => ( ( path_pathfinish_a @ G2 )
% 0.18/0.44 != ( path_pathstart_a @ G2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % arc_distinct_ends
% 0.18/0.44 thf(fact_223_bounded__linear_Oaxioms_I2_J,axiom,
% 0.18/0.44 ! [F2: a > complex] :
% 0.18/0.44 ( ( real_V912435428omplex @ F2 )
% 0.18/0.44 => ( real_V451440129omplex @ F2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % bounded_linear.axioms(2)
% 0.18/0.44 thf(fact_224_bounded__linear_Oaxioms_I2_J,axiom,
% 0.18/0.44 ! [F2: complex > a] :
% 0.18/0.44 ( ( real_V762982918plex_a @ F2 )
% 0.18/0.44 => ( real_V301987619plex_a @ F2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % bounded_linear.axioms(2)
% 0.18/0.44 thf(fact_225_UNIV__eq__I,axiom,
% 0.18/0.44 ! [A2: set_a] :
% 0.18/0.44 ( ! [X4: a] : ( member_a @ X4 @ A2 )
% 0.18/0.44 => ( top_top_set_a = A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % UNIV_eq_I
% 0.18/0.44 thf(fact_226_UNIV__eq__I,axiom,
% 0.18/0.44 ! [A2: set_complex] :
% 0.18/0.44 ( ! [X4: complex] : ( member_complex @ X4 @ A2 )
% 0.18/0.44 => ( top_top_set_complex = A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % UNIV_eq_I
% 0.18/0.44 thf(fact_227_UNIV__witness,axiom,
% 0.18/0.44 ? [X4: a] : ( member_a @ X4 @ top_top_set_a ) ).
% 0.18/0.44
% 0.18/0.44 % UNIV_witness
% 0.18/0.44 thf(fact_228_UNIV__witness,axiom,
% 0.18/0.44 ? [X4: complex] : ( member_complex @ X4 @ top_top_set_complex ) ).
% 0.18/0.44
% 0.18/0.44 % UNIV_witness
% 0.18/0.44 thf(fact_229_simple__path__imp__arc,axiom,
% 0.18/0.44 ! [G2: real > a] :
% 0.18/0.44 ( ( path_simple_path_a @ G2 )
% 0.18/0.44 => ( ( ( path_pathfinish_a @ G2 )
% 0.18/0.44 != ( path_pathstart_a @ G2 ) )
% 0.18/0.44 => ( path_arc_a @ G2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_imp_arc
% 0.18/0.44 thf(fact_230_simple__path__imp__arc,axiom,
% 0.18/0.44 ! [G2: real > complex] :
% 0.18/0.44 ( ( path_s36253918omplex @ G2 )
% 0.18/0.44 => ( ( ( path_p769714271omplex @ G2 )
% 0.18/0.44 != ( path_p797330068omplex @ G2 ) )
% 0.18/0.44 => ( path_arc_complex @ G2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_imp_arc
% 0.18/0.44 thf(fact_231_simple__path__eq__arc,axiom,
% 0.18/0.44 ! [G2: real > a] :
% 0.18/0.44 ( ( ( path_pathfinish_a @ G2 )
% 0.18/0.44 != ( path_pathstart_a @ G2 ) )
% 0.18/0.44 => ( ( path_simple_path_a @ G2 )
% 0.18/0.44 = ( path_arc_a @ G2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_eq_arc
% 0.18/0.44 thf(fact_232_simple__path__eq__arc,axiom,
% 0.18/0.44 ! [G2: real > complex] :
% 0.18/0.44 ( ( ( path_p769714271omplex @ G2 )
% 0.18/0.44 != ( path_p797330068omplex @ G2 ) )
% 0.18/0.44 => ( ( path_s36253918omplex @ G2 )
% 0.18/0.44 = ( path_arc_complex @ G2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_eq_arc
% 0.18/0.44 thf(fact_233_simple__path__cases,axiom,
% 0.18/0.44 ! [G2: real > a] :
% 0.18/0.44 ( ( path_simple_path_a @ G2 )
% 0.18/0.44 => ( ( path_arc_a @ G2 )
% 0.18/0.44 | ( ( path_pathfinish_a @ G2 )
% 0.18/0.44 = ( path_pathstart_a @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_cases
% 0.18/0.44 thf(fact_234_simple__path__cases,axiom,
% 0.18/0.44 ! [G2: real > complex] :
% 0.18/0.44 ( ( path_s36253918omplex @ G2 )
% 0.18/0.44 => ( ( path_arc_complex @ G2 )
% 0.18/0.44 | ( ( path_p769714271omplex @ G2 )
% 0.18/0.44 = ( path_p797330068omplex @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_cases
% 0.18/0.44 thf(fact_235_arc__simple__path,axiom,
% 0.18/0.44 ( path_arc_a
% 0.18/0.44 = ( ^ [G: real > a] :
% 0.18/0.44 ( ( path_simple_path_a @ G )
% 0.18/0.44 & ( ( path_pathfinish_a @ G )
% 0.18/0.44 != ( path_pathstart_a @ G ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % arc_simple_path
% 0.18/0.44 thf(fact_236_arc__simple__path,axiom,
% 0.18/0.44 ( path_arc_complex
% 0.18/0.44 = ( ^ [G: real > complex] :
% 0.18/0.44 ( ( path_s36253918omplex @ G )
% 0.18/0.44 & ( ( path_p769714271omplex @ G )
% 0.18/0.44 != ( path_p797330068omplex @ G ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % arc_simple_path
% 0.18/0.44 thf(fact_237_fun_Omap__comp,axiom,
% 0.18/0.44 ! [G2: complex > complex,F2: a > complex,V: real > a] :
% 0.18/0.44 ( ( comp_c595887981x_real @ G2 @ ( comp_a_complex_real @ F2 @ V ) )
% 0.18/0.44 = ( comp_a_complex_real @ ( comp_c124850173plex_a @ G2 @ F2 ) @ V ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_comp
% 0.18/0.44 thf(fact_238_fun_Omap__comp,axiom,
% 0.18/0.44 ! [G2: complex > a,F2: a > complex,V: real > a] :
% 0.18/0.44 ( ( comp_complex_a_real @ G2 @ ( comp_a_complex_real @ F2 @ V ) )
% 0.18/0.44 = ( comp_a_a_real @ ( comp_complex_a_a @ G2 @ F2 ) @ V ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_comp
% 0.18/0.44 thf(fact_239_fun_Omap__comp,axiom,
% 0.18/0.44 ! [G2: complex > complex,F2: a > complex,V: complex > a] :
% 0.18/0.44 ( ( comp_c130555887omplex @ G2 @ ( comp_a1063143865omplex @ F2 @ V ) )
% 0.18/0.44 = ( comp_a1063143865omplex @ ( comp_c124850173plex_a @ G2 @ F2 ) @ V ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_comp
% 0.18/0.44 thf(fact_240_fun_Omap__comp,axiom,
% 0.18/0.44 ! [G2: complex > a,F2: a > complex,V: complex > a] :
% 0.18/0.44 ( ( comp_c274302683omplex @ G2 @ ( comp_a1063143865omplex @ F2 @ V ) )
% 0.18/0.44 = ( comp_a_a_complex @ ( comp_complex_a_a @ G2 @ F2 ) @ V ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_comp
% 0.18/0.44 thf(fact_241_fun_Omap__comp,axiom,
% 0.18/0.44 ! [G2: complex > complex,F2: a > complex,V: a > a] :
% 0.18/0.44 ( ( comp_c124850173plex_a @ G2 @ ( comp_a_complex_a @ F2 @ V ) )
% 0.18/0.44 = ( comp_a_complex_a @ ( comp_c124850173plex_a @ G2 @ F2 ) @ V ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_comp
% 0.18/0.44 thf(fact_242_fun_Omap__comp,axiom,
% 0.18/0.44 ! [G2: a > complex,F2: complex > a,V: real > complex] :
% 0.18/0.44 ( ( comp_a_complex_real @ G2 @ ( comp_complex_a_real @ F2 @ V ) )
% 0.18/0.44 = ( comp_c595887981x_real @ ( comp_a1063143865omplex @ G2 @ F2 ) @ V ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_comp
% 0.18/0.44 thf(fact_243_fun_Omap__comp,axiom,
% 0.18/0.44 ! [G2: a > complex,F2: real > a,V: real > real] :
% 0.18/0.44 ( ( comp_a_complex_real @ G2 @ ( comp_real_a_real @ F2 @ V ) )
% 0.18/0.44 = ( comp_r701421291x_real @ ( comp_a_complex_real @ G2 @ F2 ) @ V ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_comp
% 0.18/0.44 thf(fact_244_fun_Omap__comp,axiom,
% 0.18/0.44 ! [G2: a > complex,F2: a > a,V: real > a] :
% 0.18/0.44 ( ( comp_a_complex_real @ G2 @ ( comp_a_a_real @ F2 @ V ) )
% 0.18/0.44 = ( comp_a_complex_real @ ( comp_a_complex_a @ G2 @ F2 ) @ V ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_comp
% 0.18/0.44 thf(fact_245_fun_Omap__comp,axiom,
% 0.18/0.44 ! [G2: a > complex,F2: real > a,V: complex > real] :
% 0.18/0.44 ( ( comp_a1063143865omplex @ G2 @ ( comp_real_a_complex @ F2 @ V ) )
% 0.18/0.44 = ( comp_r667767405omplex @ ( comp_a_complex_real @ G2 @ F2 ) @ V ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_comp
% 0.18/0.44 thf(fact_246_fun_Omap__comp,axiom,
% 0.18/0.44 ! [G2: a > complex,F2: complex > a,V: complex > complex] :
% 0.18/0.44 ( ( comp_a1063143865omplex @ G2 @ ( comp_c274302683omplex @ F2 @ V ) )
% 0.18/0.44 = ( comp_c130555887omplex @ ( comp_a1063143865omplex @ G2 @ F2 ) @ V ) ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_comp
% 0.18/0.44 thf(fact_247_complex__of__real__of,axiom,
% 0.18/0.44 ( ( comp_a1063143865omplex @ poinca1910941596x_of_a @ poinca837721858l_of_a )
% 0.18/0.44 = id_complex ) ).
% 0.18/0.44
% 0.18/0.44 % complex_of_real_of
% 0.18/0.44 thf(fact_248_real__of__complex__of,axiom,
% 0.18/0.44 ( ( comp_complex_a_a @ poinca837721858l_of_a @ poinca1910941596x_of_a )
% 0.18/0.44 = id_a ) ).
% 0.18/0.44
% 0.18/0.44 % real_of_complex_of
% 0.18/0.44 thf(fact_249_real__of__bij,axiom,
% 0.18/0.44 bij_betw_complex_a @ poinca837721858l_of_a @ top_top_set_complex @ top_top_set_a ).
% 0.18/0.44
% 0.18/0.44 % real_of_bij
% 0.18/0.44 thf(fact_250_complex__of__bij,axiom,
% 0.18/0.44 bij_betw_a_complex @ poinca1910941596x_of_a @ top_top_set_a @ top_top_set_complex ).
% 0.18/0.44
% 0.18/0.44 % complex_of_bij
% 0.18/0.44 thf(fact_251_linear__injective__left__inverse,axiom,
% 0.18/0.44 ! [F2: a > a] :
% 0.18/0.44 ( ( real_V202220639ar_a_a @ F2 )
% 0.18/0.44 => ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 0.18/0.44 => ? [G4: a > a] :
% 0.18/0.44 ( ( real_V202220639ar_a_a @ G4 )
% 0.18/0.44 & ( ( comp_a_a_a @ G4 @ F2 )
% 0.18/0.44 = id_a ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % linear_injective_left_inverse
% 0.18/0.44 thf(fact_252_linear__injective__left__inverse,axiom,
% 0.18/0.44 ! [F2: a > complex] :
% 0.18/0.44 ( ( real_V1477106445omplex @ F2 )
% 0.18/0.44 => ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 => ? [G4: complex > a] :
% 0.18/0.44 ( ( real_V1327653935plex_a @ G4 )
% 0.18/0.44 & ( ( comp_complex_a_a @ G4 @ F2 )
% 0.18/0.44 = id_a ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % linear_injective_left_inverse
% 0.18/0.44 thf(fact_253_linear__injective__left__inverse,axiom,
% 0.18/0.44 ! [F2: complex > a] :
% 0.18/0.44 ( ( real_V1327653935plex_a @ F2 )
% 0.18/0.44 => ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 0.18/0.44 => ? [G4: a > complex] :
% 0.18/0.44 ( ( real_V1477106445omplex @ G4 )
% 0.18/0.44 & ( ( comp_a1063143865omplex @ G4 @ F2 )
% 0.18/0.44 = id_complex ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % linear_injective_left_inverse
% 0.18/0.44 thf(fact_254_path__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: real > a,G2: real > real] :
% 0.18/0.44 ( ( real_V779700657real_a @ F2 )
% 0.18/0.44 => ( ( inj_on_real_a @ F2 @ top_top_set_real )
% 0.18/0.44 => ( ( path_path_a @ ( comp_real_a_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_path_real @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % path_linear_image_eq
% 0.18/0.44 thf(fact_255_path__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: a > a,G2: real > a] :
% 0.18/0.44 ( ( real_V202220639ar_a_a @ F2 )
% 0.18/0.44 => ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( path_path_a @ ( comp_a_a_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_path_a @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % path_linear_image_eq
% 0.18/0.44 thf(fact_256_path__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: complex > complex,G2: real > complex] :
% 0.18/0.44 ( ( real_V670066493omplex @ F2 )
% 0.18/0.44 => ( ( inj_on94911183omplex @ F2 @ top_top_set_complex )
% 0.18/0.44 => ( ( path_path_complex @ ( comp_c595887981x_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_path_complex @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % path_linear_image_eq
% 0.18/0.44 thf(fact_257_path__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: a > complex,G2: real > a] :
% 0.18/0.44 ( ( real_V1477106445omplex @ F2 )
% 0.18/0.44 => ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 => ( ( path_path_complex @ ( comp_a_complex_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_path_a @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % path_linear_image_eq
% 0.18/0.44 thf(fact_258_path__linear__image__eq,axiom,
% 0.18/0.44 ! [F2: complex > a,G2: real > complex] :
% 0.18/0.44 ( ( real_V1327653935plex_a @ F2 )
% 0.18/0.44 => ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 0.18/0.44 => ( ( path_path_a @ ( comp_complex_a_real @ F2 @ G2 ) )
% 0.18/0.44 = ( path_path_complex @ G2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % path_linear_image_eq
% 0.18/0.44 thf(fact_259_linear__inj__iff__eq__0,axiom,
% 0.18/0.44 ! [F2: a > complex] :
% 0.18/0.44 ( ( real_V1477106445omplex @ F2 )
% 0.18/0.44 => ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 0.18/0.44 = ( ! [X: a] :
% 0.18/0.44 ( ( ( F2 @ X )
% 0.18/0.44 = zero_zero_complex )
% 0.18/0.44 => ( X = zero_zero_a ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % linear_inj_iff_eq_0
% 0.18/0.44 thf(fact_260_linear__inj__iff__eq__0,axiom,
% 0.18/0.44 ! [F2: complex > a] :
% 0.18/0.44 ( ( real_V1327653935plex_a @ F2 )
% 0.18/0.44 => ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 0.18/0.44 = ( ! [X: complex] :
% 0.18/0.44 ( ( ( F2 @ X )
% 0.18/0.44 = zero_zero_a )
% 0.18/0.44 => ( X = zero_zero_complex ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % linear_inj_iff_eq_0
% 0.18/0.44 thf(fact_261_type__copy__map__cong0,axiom,
% 0.18/0.44 ! [M: real > a,G2: real > real,X2: real,N: a > a,H: real > a,F2: a > complex] :
% 0.18/0.44 ( ( ( M @ ( G2 @ X2 ) )
% 0.18/0.44 = ( N @ ( H @ X2 ) ) )
% 0.18/0.44 => ( ( comp_r701421291x_real @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
% 0.18/0.44 = ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % type_copy_map_cong0
% 0.18/0.44 thf(fact_262_type__copy__map__cong0,axiom,
% 0.18/0.44 ! [M: real > a,G2: complex > real,X2: complex,N: a > a,H: complex > a,F2: a > complex] :
% 0.18/0.44 ( ( ( M @ ( G2 @ X2 ) )
% 0.18/0.44 = ( N @ ( H @ X2 ) ) )
% 0.18/0.44 => ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
% 0.18/0.44 = ( comp_a1063143865omplex @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % type_copy_map_cong0
% 0.18/0.44 thf(fact_263_type__copy__map__cong0,axiom,
% 0.18/0.44 ! [M: real > a,G2: a > real,X2: a,N: a > a,H: a > a,F2: a > complex] :
% 0.18/0.44 ( ( ( M @ ( G2 @ X2 ) )
% 0.18/0.44 = ( N @ ( H @ X2 ) ) )
% 0.18/0.44 => ( ( comp_real_complex_a @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
% 0.18/0.44 = ( comp_a_complex_a @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % type_copy_map_cong0
% 0.18/0.44 thf(fact_264_type__copy__map__cong0,axiom,
% 0.18/0.44 ! [M: complex > a,G2: real > complex,X2: real,N: a > a,H: real > a,F2: a > complex] :
% 0.18/0.44 ( ( ( M @ ( G2 @ X2 ) )
% 0.18/0.44 = ( N @ ( H @ X2 ) ) )
% 0.18/0.44 => ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ M ) @ G2 @ X2 )
% 0.18/0.44 = ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % type_copy_map_cong0
% 0.18/0.44 thf(fact_265_type__copy__map__cong0,axiom,
% 0.18/0.44 ! [M: complex > a,G2: complex > complex,X2: complex,N: a > a,H: complex > a,F2: a > complex] :
% 0.18/0.44 ( ( ( M @ ( G2 @ X2 ) )
% 0.18/0.44 = ( N @ ( H @ X2 ) ) )
% 0.18/0.44 => ( ( comp_c130555887omplex @ ( comp_a1063143865omplex @ F2 @ M ) @ G2 @ X2 )
% 0.18/0.44 = ( comp_a1063143865omplex @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % type_copy_map_cong0
% 0.18/0.44 thf(fact_266_type__copy__map__cong0,axiom,
% 0.18/0.44 ! [M: complex > a,G2: a > complex,X2: a,N: a > a,H: a > a,F2: a > complex] :
% 0.18/0.44 ( ( ( M @ ( G2 @ X2 ) )
% 0.18/0.44 = ( N @ ( H @ X2 ) ) )
% 0.18/0.44 => ( ( comp_c124850173plex_a @ ( comp_a1063143865omplex @ F2 @ M ) @ G2 @ X2 )
% 0.18/0.44 = ( comp_a_complex_a @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % type_copy_map_cong0
% 0.18/0.44 thf(fact_267_type__copy__map__cong0,axiom,
% 0.18/0.44 ! [M: real > real,G2: a > real,X2: a,N: complex > real,H: a > complex,F2: real > a] :
% 0.18/0.44 ( ( ( M @ ( G2 @ X2 ) )
% 0.18/0.44 = ( N @ ( H @ X2 ) ) )
% 0.18/0.44 => ( ( comp_real_a_a @ ( comp_real_a_real @ F2 @ M ) @ G2 @ X2 )
% 0.18/0.44 = ( comp_complex_a_a @ ( comp_real_a_complex @ F2 @ N ) @ H @ X2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % type_copy_map_cong0
% 0.18/0.44 thf(fact_268_type__copy__map__cong0,axiom,
% 0.18/0.44 ! [M: real > real,G2: complex > real,X2: complex,N: a > real,H: complex > a,F2: real > a] :
% 0.18/0.44 ( ( ( M @ ( G2 @ X2 ) )
% 0.18/0.44 = ( N @ ( H @ X2 ) ) )
% 0.18/0.44 => ( ( comp_real_a_complex @ ( comp_real_a_real @ F2 @ M ) @ G2 @ X2 )
% 0.18/0.44 = ( comp_a_a_complex @ ( comp_real_a_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % type_copy_map_cong0
% 0.18/0.44 thf(fact_269_type__copy__map__cong0,axiom,
% 0.18/0.44 ! [M: real > real,G2: a > real,X2: a,N: a > real,H: a > a,F2: real > a] :
% 0.18/0.44 ( ( ( M @ ( G2 @ X2 ) )
% 0.18/0.44 = ( N @ ( H @ X2 ) ) )
% 0.18/0.44 => ( ( comp_real_a_a @ ( comp_real_a_real @ F2 @ M ) @ G2 @ X2 )
% 0.18/0.44 = ( comp_a_a_a @ ( comp_real_a_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % type_copy_map_cong0
% 0.18/0.44 thf(fact_270_type__copy__map__cong0,axiom,
% 0.18/0.44 ! [M: complex > a,G2: real > complex,X2: real,N: real > a,H: real > real,F2: a > a] :
% 0.18/0.44 ( ( ( M @ ( G2 @ X2 ) )
% 0.18/0.44 = ( N @ ( H @ X2 ) ) )
% 0.18/0.44 => ( ( comp_complex_a_real @ ( comp_a_a_complex @ F2 @ M ) @ G2 @ X2 )
% 0.18/0.44 = ( comp_real_a_real @ ( comp_a_a_real @ F2 @ N ) @ H @ X2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % type_copy_map_cong0
% 0.18/0.44 thf(fact_271_id__apply,axiom,
% 0.18/0.44 ( id_complex
% 0.18/0.44 = ( ^ [X: complex] : X ) ) ).
% 0.18/0.44
% 0.18/0.44 % id_apply
% 0.18/0.44 thf(fact_272_id__apply,axiom,
% 0.18/0.44 ( id_a
% 0.18/0.44 = ( ^ [X: a] : X ) ) ).
% 0.18/0.44
% 0.18/0.44 % id_apply
% 0.18/0.44 thf(fact_273_path__rectpath,axiom,
% 0.18/0.44 ! [A: complex,B: complex] : ( path_path_complex @ ( path_rectpath @ A @ B ) ) ).
% 0.18/0.44
% 0.18/0.44 % path_rectpath
% 0.18/0.44 thf(fact_274_comp__id,axiom,
% 0.18/0.44 ! [F2: real > a] :
% 0.18/0.44 ( ( comp_real_a_real @ F2 @ id_real )
% 0.18/0.44 = F2 ) ).
% 0.18/0.44
% 0.18/0.44 % comp_id
% 0.18/0.44 thf(fact_275_comp__id,axiom,
% 0.18/0.44 ! [F2: a > complex] :
% 0.18/0.44 ( ( comp_a_complex_a @ F2 @ id_a )
% 0.18/0.44 = F2 ) ).
% 0.18/0.44
% 0.18/0.44 % comp_id
% 0.18/0.44 thf(fact_276_comp__id,axiom,
% 0.18/0.44 ! [F2: a > a] :
% 0.18/0.44 ( ( comp_a_a_a @ F2 @ id_a )
% 0.18/0.44 = F2 ) ).
% 0.18/0.44
% 0.18/0.44 % comp_id
% 0.18/0.44 thf(fact_277_id__comp,axiom,
% 0.18/0.44 ! [G2: complex > a] :
% 0.18/0.44 ( ( comp_a_a_complex @ id_a @ G2 )
% 0.18/0.44 = G2 ) ).
% 0.18/0.44
% 0.18/0.44 % id_comp
% 0.18/0.44 thf(fact_278_id__comp,axiom,
% 0.18/0.44 ! [G2: real > a] :
% 0.18/0.44 ( ( comp_a_a_real @ id_a @ G2 )
% 0.18/0.44 = G2 ) ).
% 0.18/0.44
% 0.18/0.44 % id_comp
% 0.18/0.44 thf(fact_279_id__comp,axiom,
% 0.18/0.44 ! [G2: a > a] :
% 0.18/0.44 ( ( comp_a_a_a @ id_a @ G2 )
% 0.18/0.44 = G2 ) ).
% 0.18/0.44
% 0.18/0.44 % id_comp
% 0.18/0.44 thf(fact_280_fun_Omap__id,axiom,
% 0.18/0.44 ! [T: complex > a] :
% 0.18/0.44 ( ( comp_a_a_complex @ id_a @ T )
% 0.18/0.44 = T ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_id
% 0.18/0.44 thf(fact_281_fun_Omap__id,axiom,
% 0.18/0.44 ! [T: real > a] :
% 0.18/0.44 ( ( comp_a_a_real @ id_a @ T )
% 0.18/0.44 = T ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_id
% 0.18/0.44 thf(fact_282_fun_Omap__id,axiom,
% 0.18/0.44 ! [T: a > a] :
% 0.18/0.44 ( ( comp_a_a_a @ id_a @ T )
% 0.18/0.44 = T ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_id
% 0.18/0.44 thf(fact_283_bij__betw__id,axiom,
% 0.18/0.44 ! [A2: set_complex] : ( bij_be209634132omplex @ id_complex @ A2 @ A2 ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_id
% 0.18/0.44 thf(fact_284_bij__betw__id,axiom,
% 0.18/0.44 ! [A2: set_a] : ( bij_betw_a_a @ id_a @ A2 @ A2 ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_id
% 0.18/0.44 thf(fact_285_bij__id,axiom,
% 0.18/0.44 bij_betw_a_a @ id_a @ top_top_set_a @ top_top_set_a ).
% 0.18/0.44
% 0.18/0.44 % bij_id
% 0.18/0.44 thf(fact_286_bij__id,axiom,
% 0.18/0.44 bij_be209634132omplex @ id_complex @ top_top_set_complex @ top_top_set_complex ).
% 0.18/0.44
% 0.18/0.44 % bij_id
% 0.18/0.44 thf(fact_287_DEADID_Oin__rel,axiom,
% 0.18/0.44 ( ( ^ [Y4: a,Z: a] : ( Y4 = Z ) )
% 0.18/0.44 = ( ^ [A6: a,B2: a] :
% 0.18/0.44 ? [Z2: a] :
% 0.18/0.44 ( ( member_a @ Z2 @ top_top_set_a )
% 0.18/0.44 & ( ( id_a @ Z2 )
% 0.18/0.44 = A6 )
% 0.18/0.44 & ( ( id_a @ Z2 )
% 0.18/0.44 = B2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % DEADID.in_rel
% 0.18/0.44 thf(fact_288_DEADID_Oin__rel,axiom,
% 0.18/0.44 ( ( ^ [Y4: complex,Z: complex] : ( Y4 = Z ) )
% 0.18/0.44 = ( ^ [A6: complex,B2: complex] :
% 0.18/0.44 ? [Z2: complex] :
% 0.18/0.44 ( ( member_complex @ Z2 @ top_top_set_complex )
% 0.18/0.44 & ( ( id_complex @ Z2 )
% 0.18/0.44 = A6 )
% 0.18/0.44 & ( ( id_complex @ Z2 )
% 0.18/0.44 = B2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % DEADID.in_rel
% 0.18/0.44 thf(fact_289_fun_Omap__id0,axiom,
% 0.18/0.44 ( ( comp_a_a_complex @ id_a )
% 0.18/0.44 = id_complex_a ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_id0
% 0.18/0.44 thf(fact_290_fun_Omap__id0,axiom,
% 0.18/0.44 ( ( comp_a_a_real @ id_a )
% 0.18/0.44 = id_real_a ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_id0
% 0.18/0.44 thf(fact_291_fun_Omap__id0,axiom,
% 0.18/0.44 ( ( comp_a_a_a @ id_a )
% 0.18/0.44 = id_a_a ) ).
% 0.18/0.44
% 0.18/0.44 % fun.map_id0
% 0.18/0.44 thf(fact_292_id__def,axiom,
% 0.18/0.44 ( id_complex
% 0.18/0.44 = ( ^ [X: complex] : X ) ) ).
% 0.18/0.44
% 0.18/0.44 % id_def
% 0.18/0.44 thf(fact_293_id__def,axiom,
% 0.18/0.44 ( id_a
% 0.18/0.44 = ( ^ [X: a] : X ) ) ).
% 0.18/0.44
% 0.18/0.44 % id_def
% 0.18/0.44 thf(fact_294_bij__betwE,axiom,
% 0.18/0.44 ! [F2: complex > a,A2: set_complex,B3: set_a] :
% 0.18/0.44 ( ( bij_betw_complex_a @ F2 @ A2 @ B3 )
% 0.18/0.44 => ! [X5: complex] :
% 0.18/0.44 ( ( member_complex @ X5 @ A2 )
% 0.18/0.44 => ( member_a @ ( F2 @ X5 ) @ B3 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betwE
% 0.18/0.44 thf(fact_295_bij__betwE,axiom,
% 0.18/0.44 ! [F2: a > complex,A2: set_a,B3: set_complex] :
% 0.18/0.44 ( ( bij_betw_a_complex @ F2 @ A2 @ B3 )
% 0.18/0.44 => ! [X5: a] :
% 0.18/0.44 ( ( member_a @ X5 @ A2 )
% 0.18/0.44 => ( member_complex @ ( F2 @ X5 ) @ B3 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betwE
% 0.18/0.44 thf(fact_296_eq__id__iff,axiom,
% 0.18/0.44 ! [F2: complex > complex] :
% 0.18/0.44 ( ( ! [X: complex] :
% 0.18/0.44 ( ( F2 @ X )
% 0.18/0.44 = X ) )
% 0.18/0.44 = ( F2 = id_complex ) ) ).
% 0.18/0.44
% 0.18/0.44 % eq_id_iff
% 0.18/0.44 thf(fact_297_eq__id__iff,axiom,
% 0.18/0.44 ! [F2: a > a] :
% 0.18/0.44 ( ( ! [X: a] :
% 0.18/0.44 ( ( F2 @ X )
% 0.18/0.44 = X ) )
% 0.18/0.44 = ( F2 = id_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % eq_id_iff
% 0.18/0.44 thf(fact_298_bij__betw__inv,axiom,
% 0.18/0.44 ! [F2: complex > a,A2: set_complex,B3: set_a] :
% 0.18/0.44 ( ( bij_betw_complex_a @ F2 @ A2 @ B3 )
% 0.18/0.44 => ? [G4: a > complex] : ( bij_betw_a_complex @ G4 @ B3 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_inv
% 0.18/0.44 thf(fact_299_bij__betw__inv,axiom,
% 0.18/0.44 ! [F2: a > complex,A2: set_a,B3: set_complex] :
% 0.18/0.44 ( ( bij_betw_a_complex @ F2 @ A2 @ B3 )
% 0.18/0.44 => ? [G4: complex > a] : ( bij_betw_complex_a @ G4 @ B3 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_inv
% 0.18/0.44 thf(fact_300_bij__betw__cong,axiom,
% 0.18/0.44 ! [A2: set_complex,F2: complex > a,G2: complex > a,A7: set_a] :
% 0.18/0.44 ( ! [A5: complex] :
% 0.18/0.44 ( ( member_complex @ A5 @ A2 )
% 0.18/0.44 => ( ( F2 @ A5 )
% 0.18/0.44 = ( G2 @ A5 ) ) )
% 0.18/0.44 => ( ( bij_betw_complex_a @ F2 @ A2 @ A7 )
% 0.18/0.44 = ( bij_betw_complex_a @ G2 @ A2 @ A7 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_cong
% 0.18/0.44 thf(fact_301_bij__betw__cong,axiom,
% 0.18/0.44 ! [A2: set_a,F2: a > complex,G2: a > complex,A7: set_complex] :
% 0.18/0.44 ( ! [A5: a] :
% 0.18/0.44 ( ( member_a @ A5 @ A2 )
% 0.18/0.44 => ( ( F2 @ A5 )
% 0.18/0.44 = ( G2 @ A5 ) ) )
% 0.18/0.44 => ( ( bij_betw_a_complex @ F2 @ A2 @ A7 )
% 0.18/0.44 = ( bij_betw_a_complex @ G2 @ A2 @ A7 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_cong
% 0.18/0.44 thf(fact_302_bij__betw__apply,axiom,
% 0.18/0.44 ! [F2: complex > a,A2: set_complex,B3: set_a,A: complex] :
% 0.18/0.44 ( ( bij_betw_complex_a @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( ( member_complex @ A @ A2 )
% 0.18/0.44 => ( member_a @ ( F2 @ A ) @ B3 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_apply
% 0.18/0.44 thf(fact_303_bij__betw__apply,axiom,
% 0.18/0.44 ! [F2: a > complex,A2: set_a,B3: set_complex,A: a] :
% 0.18/0.44 ( ( bij_betw_a_complex @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( ( member_a @ A @ A2 )
% 0.18/0.44 => ( member_complex @ ( F2 @ A ) @ B3 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_apply
% 0.18/0.44 thf(fact_304_bij__betw__id__iff,axiom,
% 0.18/0.44 ! [A2: set_complex,B3: set_complex] :
% 0.18/0.44 ( ( bij_be209634132omplex @ id_complex @ A2 @ B3 )
% 0.18/0.44 = ( A2 = B3 ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_id_iff
% 0.18/0.44 thf(fact_305_bij__betw__id__iff,axiom,
% 0.18/0.44 ! [A2: set_a,B3: set_a] :
% 0.18/0.44 ( ( bij_betw_a_a @ id_a @ A2 @ B3 )
% 0.18/0.44 = ( A2 = B3 ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_id_iff
% 0.18/0.44 thf(fact_306_bij__betw__iff__bijections,axiom,
% 0.18/0.44 ( bij_betw_complex_a
% 0.18/0.44 = ( ^ [F: complex > a,A4: set_complex,B4: set_a] :
% 0.18/0.44 ? [G: a > complex] :
% 0.18/0.44 ( ! [X: complex] :
% 0.18/0.44 ( ( member_complex @ X @ A4 )
% 0.18/0.44 => ( ( member_a @ ( F @ X ) @ B4 )
% 0.18/0.44 & ( ( G @ ( F @ X ) )
% 0.18/0.44 = X ) ) )
% 0.18/0.44 & ! [X: a] :
% 0.18/0.44 ( ( member_a @ X @ B4 )
% 0.18/0.44 => ( ( member_complex @ ( G @ X ) @ A4 )
% 0.18/0.44 & ( ( F @ ( G @ X ) )
% 0.18/0.44 = X ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_iff_bijections
% 0.18/0.44 thf(fact_307_bij__betw__iff__bijections,axiom,
% 0.18/0.44 ( bij_betw_a_complex
% 0.18/0.44 = ( ^ [F: a > complex,A4: set_a,B4: set_complex] :
% 0.18/0.44 ? [G: complex > a] :
% 0.18/0.44 ( ! [X: a] :
% 0.18/0.44 ( ( member_a @ X @ A4 )
% 0.18/0.44 => ( ( member_complex @ ( F @ X ) @ B4 )
% 0.18/0.44 & ( ( G @ ( F @ X ) )
% 0.18/0.44 = X ) ) )
% 0.18/0.44 & ! [X: complex] :
% 0.18/0.44 ( ( member_complex @ X @ B4 )
% 0.18/0.44 => ( ( member_a @ ( G @ X ) @ A4 )
% 0.18/0.44 & ( ( F @ ( G @ X ) )
% 0.18/0.44 = X ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_iff_bijections
% 0.18/0.44 thf(fact_308_o__bij,axiom,
% 0.18/0.44 ! [G2: a > a,F2: a > a] :
% 0.18/0.44 ( ( ( comp_a_a_a @ G2 @ F2 )
% 0.18/0.44 = id_a )
% 0.18/0.44 => ( ( ( comp_a_a_a @ F2 @ G2 )
% 0.18/0.44 = id_a )
% 0.18/0.44 => ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % o_bij
% 0.18/0.44 thf(fact_309_o__bij,axiom,
% 0.18/0.44 ! [G2: complex > a,F2: a > complex] :
% 0.18/0.44 ( ( ( comp_complex_a_a @ G2 @ F2 )
% 0.18/0.44 = id_a )
% 0.18/0.44 => ( ( ( comp_a1063143865omplex @ F2 @ G2 )
% 0.18/0.44 = id_complex )
% 0.18/0.44 => ( bij_betw_a_complex @ F2 @ top_top_set_a @ top_top_set_complex ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % o_bij
% 0.18/0.44 thf(fact_310_o__bij,axiom,
% 0.18/0.44 ! [G2: a > complex,F2: complex > a] :
% 0.18/0.44 ( ( ( comp_a1063143865omplex @ G2 @ F2 )
% 0.18/0.44 = id_complex )
% 0.18/0.44 => ( ( ( comp_complex_a_a @ F2 @ G2 )
% 0.18/0.44 = id_a )
% 0.18/0.44 => ( bij_betw_complex_a @ F2 @ top_top_set_complex @ top_top_set_a ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % o_bij
% 0.18/0.44 thf(fact_311_o__bij,axiom,
% 0.18/0.44 ! [G2: complex > complex,F2: complex > complex] :
% 0.18/0.44 ( ( ( comp_c130555887omplex @ G2 @ F2 )
% 0.18/0.44 = id_complex )
% 0.18/0.44 => ( ( ( comp_c130555887omplex @ F2 @ G2 )
% 0.18/0.44 = id_complex )
% 0.18/0.44 => ( bij_be209634132omplex @ F2 @ top_top_set_complex @ top_top_set_complex ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % o_bij
% 0.18/0.44 thf(fact_312_bij__pointE,axiom,
% 0.18/0.44 ! [F2: a > a,Y: a] :
% 0.18/0.44 ( ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a )
% 0.18/0.44 => ~ ! [X4: a] :
% 0.18/0.44 ( ( Y
% 0.18/0.44 = ( F2 @ X4 ) )
% 0.18/0.44 => ~ ! [X6: a] :
% 0.18/0.44 ( ( Y
% 0.18/0.44 = ( F2 @ X6 ) )
% 0.18/0.44 => ( X6 = X4 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_pointE
% 0.18/0.44 thf(fact_313_bij__pointE,axiom,
% 0.18/0.44 ! [F2: a > complex,Y: complex] :
% 0.18/0.44 ( ( bij_betw_a_complex @ F2 @ top_top_set_a @ top_top_set_complex )
% 0.18/0.44 => ~ ! [X4: a] :
% 0.18/0.44 ( ( Y
% 0.18/0.44 = ( F2 @ X4 ) )
% 0.18/0.44 => ~ ! [X6: a] :
% 0.18/0.44 ( ( Y
% 0.18/0.44 = ( F2 @ X6 ) )
% 0.18/0.44 => ( X6 = X4 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_pointE
% 0.18/0.44 thf(fact_314_bij__pointE,axiom,
% 0.18/0.44 ! [F2: complex > a,Y: a] :
% 0.18/0.44 ( ( bij_betw_complex_a @ F2 @ top_top_set_complex @ top_top_set_a )
% 0.18/0.44 => ~ ! [X4: complex] :
% 0.18/0.44 ( ( Y
% 0.18/0.44 = ( F2 @ X4 ) )
% 0.18/0.44 => ~ ! [X6: complex] :
% 0.18/0.44 ( ( Y
% 0.18/0.44 = ( F2 @ X6 ) )
% 0.18/0.44 => ( X6 = X4 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_pointE
% 0.18/0.44 thf(fact_315_bij__pointE,axiom,
% 0.18/0.44 ! [F2: complex > complex,Y: complex] :
% 0.18/0.44 ( ( bij_be209634132omplex @ F2 @ top_top_set_complex @ top_top_set_complex )
% 0.18/0.44 => ~ ! [X4: complex] :
% 0.18/0.44 ( ( Y
% 0.18/0.44 = ( F2 @ X4 ) )
% 0.18/0.44 => ~ ! [X6: complex] :
% 0.18/0.44 ( ( Y
% 0.18/0.44 = ( F2 @ X6 ) )
% 0.18/0.44 => ( X6 = X4 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_pointE
% 0.18/0.44 thf(fact_316_bij__betw__trans,axiom,
% 0.18/0.44 ! [F2: real > real,A2: set_real,B3: set_real,G2: real > a,C2: set_a] :
% 0.18/0.44 ( ( bij_betw_real_real @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( ( bij_betw_real_a @ G2 @ B3 @ C2 )
% 0.18/0.44 => ( bij_betw_real_a @ ( comp_real_a_real @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_trans
% 0.18/0.44 thf(fact_317_bij__betw__trans,axiom,
% 0.18/0.44 ! [F2: real > a,A2: set_real,B3: set_a,G2: a > a,C2: set_a] :
% 0.18/0.44 ( ( bij_betw_real_a @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( ( bij_betw_a_a @ G2 @ B3 @ C2 )
% 0.18/0.44 => ( bij_betw_real_a @ ( comp_a_a_real @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_trans
% 0.18/0.44 thf(fact_318_bij__betw__trans,axiom,
% 0.18/0.44 ! [F2: a > a,A2: set_a,B3: set_a,G2: a > a,C2: set_a] :
% 0.18/0.44 ( ( bij_betw_a_a @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( ( bij_betw_a_a @ G2 @ B3 @ C2 )
% 0.18/0.44 => ( bij_betw_a_a @ ( comp_a_a_a @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_trans
% 0.18/0.44 thf(fact_319_bij__betw__trans,axiom,
% 0.18/0.44 ! [F2: complex > complex,A2: set_complex,B3: set_complex,G2: complex > a,C2: set_a] :
% 0.18/0.44 ( ( bij_be209634132omplex @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( ( bij_betw_complex_a @ G2 @ B3 @ C2 )
% 0.18/0.44 => ( bij_betw_complex_a @ ( comp_c274302683omplex @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_trans
% 0.18/0.44 thf(fact_320_bij__betw__trans,axiom,
% 0.18/0.44 ! [F2: real > a,A2: set_real,B3: set_a,G2: a > complex,C2: set_complex] :
% 0.18/0.44 ( ( bij_betw_real_a @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( ( bij_betw_a_complex @ G2 @ B3 @ C2 )
% 0.18/0.44 => ( bij_be122140626omplex @ ( comp_a_complex_real @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_trans
% 0.18/0.44 thf(fact_321_bij__betw__trans,axiom,
% 0.18/0.44 ! [F2: a > a,A2: set_a,B3: set_a,G2: a > complex,C2: set_complex] :
% 0.18/0.44 ( ( bij_betw_a_a @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( ( bij_betw_a_complex @ G2 @ B3 @ C2 )
% 0.18/0.44 => ( bij_betw_a_complex @ ( comp_a_complex_a @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_trans
% 0.18/0.44 thf(fact_322_bij__betw__trans,axiom,
% 0.18/0.44 ! [F2: complex > a,A2: set_complex,B3: set_a,G2: a > a,C2: set_a] :
% 0.18/0.44 ( ( bij_betw_complex_a @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( ( bij_betw_a_a @ G2 @ B3 @ C2 )
% 0.18/0.44 => ( bij_betw_complex_a @ ( comp_a_a_complex @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_trans
% 0.18/0.44 thf(fact_323_bij__betw__trans,axiom,
% 0.18/0.44 ! [F2: complex > a,A2: set_complex,B3: set_a,G2: a > complex,C2: set_complex] :
% 0.18/0.44 ( ( bij_betw_complex_a @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( ( bij_betw_a_complex @ G2 @ B3 @ C2 )
% 0.18/0.44 => ( bij_be209634132omplex @ ( comp_a1063143865omplex @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_trans
% 0.18/0.44 thf(fact_324_bij__betw__trans,axiom,
% 0.18/0.44 ! [F2: a > complex,A2: set_a,B3: set_complex,G2: complex > complex,C2: set_complex] :
% 0.18/0.44 ( ( bij_betw_a_complex @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( ( bij_be209634132omplex @ G2 @ B3 @ C2 )
% 0.18/0.44 => ( bij_betw_a_complex @ ( comp_c124850173plex_a @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_trans
% 0.18/0.44 thf(fact_325_bij__betw__trans,axiom,
% 0.18/0.44 ! [F2: a > complex,A2: set_a,B3: set_complex,G2: complex > a,C2: set_a] :
% 0.18/0.44 ( ( bij_betw_a_complex @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( ( bij_betw_complex_a @ G2 @ B3 @ C2 )
% 0.18/0.44 => ( bij_betw_a_a @ ( comp_complex_a_a @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_trans
% 0.18/0.44 thf(fact_326_bij__betw__comp__iff,axiom,
% 0.18/0.44 ! [F2: real > real,A2: set_real,A7: set_real,F3: real > a,A8: set_a] :
% 0.18/0.44 ( ( bij_betw_real_real @ F2 @ A2 @ A7 )
% 0.18/0.44 => ( ( bij_betw_real_a @ F3 @ A7 @ A8 )
% 0.18/0.44 = ( bij_betw_real_a @ ( comp_real_a_real @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_comp_iff
% 0.18/0.44 thf(fact_327_bij__betw__comp__iff,axiom,
% 0.18/0.44 ! [F2: real > a,A2: set_real,A7: set_a,F3: a > a,A8: set_a] :
% 0.18/0.44 ( ( bij_betw_real_a @ F2 @ A2 @ A7 )
% 0.18/0.44 => ( ( bij_betw_a_a @ F3 @ A7 @ A8 )
% 0.18/0.44 = ( bij_betw_real_a @ ( comp_a_a_real @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_comp_iff
% 0.18/0.44 thf(fact_328_bij__betw__comp__iff,axiom,
% 0.18/0.44 ! [F2: a > a,A2: set_a,A7: set_a,F3: a > a,A8: set_a] :
% 0.18/0.44 ( ( bij_betw_a_a @ F2 @ A2 @ A7 )
% 0.18/0.44 => ( ( bij_betw_a_a @ F3 @ A7 @ A8 )
% 0.18/0.44 = ( bij_betw_a_a @ ( comp_a_a_a @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_comp_iff
% 0.18/0.44 thf(fact_329_bij__betw__comp__iff,axiom,
% 0.18/0.44 ! [F2: complex > complex,A2: set_complex,A7: set_complex,F3: complex > a,A8: set_a] :
% 0.18/0.44 ( ( bij_be209634132omplex @ F2 @ A2 @ A7 )
% 0.18/0.44 => ( ( bij_betw_complex_a @ F3 @ A7 @ A8 )
% 0.18/0.44 = ( bij_betw_complex_a @ ( comp_c274302683omplex @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_comp_iff
% 0.18/0.44 thf(fact_330_bij__betw__comp__iff,axiom,
% 0.18/0.44 ! [F2: real > a,A2: set_real,A7: set_a,F3: a > complex,A8: set_complex] :
% 0.18/0.44 ( ( bij_betw_real_a @ F2 @ A2 @ A7 )
% 0.18/0.44 => ( ( bij_betw_a_complex @ F3 @ A7 @ A8 )
% 0.18/0.44 = ( bij_be122140626omplex @ ( comp_a_complex_real @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_comp_iff
% 0.18/0.44 thf(fact_331_bij__betw__comp__iff,axiom,
% 0.18/0.44 ! [F2: a > a,A2: set_a,A7: set_a,F3: a > complex,A8: set_complex] :
% 0.18/0.44 ( ( bij_betw_a_a @ F2 @ A2 @ A7 )
% 0.18/0.44 => ( ( bij_betw_a_complex @ F3 @ A7 @ A8 )
% 0.18/0.44 = ( bij_betw_a_complex @ ( comp_a_complex_a @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_comp_iff
% 0.18/0.44 thf(fact_332_bij__betw__comp__iff,axiom,
% 0.18/0.44 ! [F2: complex > a,A2: set_complex,A7: set_a,F3: a > a,A8: set_a] :
% 0.18/0.44 ( ( bij_betw_complex_a @ F2 @ A2 @ A7 )
% 0.18/0.44 => ( ( bij_betw_a_a @ F3 @ A7 @ A8 )
% 0.18/0.44 = ( bij_betw_complex_a @ ( comp_a_a_complex @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_comp_iff
% 0.18/0.44 thf(fact_333_bij__betw__comp__iff,axiom,
% 0.18/0.44 ! [F2: complex > a,A2: set_complex,A7: set_a,F3: a > complex,A8: set_complex] :
% 0.18/0.44 ( ( bij_betw_complex_a @ F2 @ A2 @ A7 )
% 0.18/0.44 => ( ( bij_betw_a_complex @ F3 @ A7 @ A8 )
% 0.18/0.44 = ( bij_be209634132omplex @ ( comp_a1063143865omplex @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_comp_iff
% 0.18/0.44 thf(fact_334_bij__betw__comp__iff,axiom,
% 0.18/0.44 ! [F2: a > complex,A2: set_a,A7: set_complex,F3: complex > complex,A8: set_complex] :
% 0.18/0.44 ( ( bij_betw_a_complex @ F2 @ A2 @ A7 )
% 0.18/0.44 => ( ( bij_be209634132omplex @ F3 @ A7 @ A8 )
% 0.18/0.44 = ( bij_betw_a_complex @ ( comp_c124850173plex_a @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_comp_iff
% 0.18/0.44 thf(fact_335_bij__betw__comp__iff,axiom,
% 0.18/0.44 ! [F2: a > complex,A2: set_a,A7: set_complex,F3: complex > a,A8: set_a] :
% 0.18/0.44 ( ( bij_betw_a_complex @ F2 @ A2 @ A7 )
% 0.18/0.44 => ( ( bij_betw_complex_a @ F3 @ A7 @ A8 )
% 0.18/0.44 = ( bij_betw_a_a @ ( comp_complex_a_a @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_comp_iff
% 0.18/0.44 thf(fact_336_bij__betw__imp__inj__on,axiom,
% 0.18/0.44 ! [F2: complex > a,A2: set_complex,B3: set_a] :
% 0.18/0.44 ( ( bij_betw_complex_a @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( inj_on_complex_a @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_imp_inj_on
% 0.18/0.44 thf(fact_337_bij__betw__imp__inj__on,axiom,
% 0.18/0.44 ! [F2: a > complex,A2: set_a,B3: set_complex] :
% 0.18/0.44 ( ( bij_betw_a_complex @ F2 @ A2 @ B3 )
% 0.18/0.44 => ( inj_on_a_complex @ F2 @ A2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % bij_betw_imp_inj_on
% 0.18/0.44 thf(fact_338_pointfree__idE,axiom,
% 0.18/0.44 ! [F2: a > complex,G2: complex > a,X2: complex] :
% 0.18/0.44 ( ( ( comp_a1063143865omplex @ F2 @ G2 )
% 0.18/0.44 = id_complex )
% 0.18/0.44 => ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.44 = X2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % pointfree_idE
% 0.18/0.44 thf(fact_339_pointfree__idE,axiom,
% 0.18/0.44 ! [F2: complex > a,G2: a > complex,X2: a] :
% 0.18/0.44 ( ( ( comp_complex_a_a @ F2 @ G2 )
% 0.18/0.44 = id_a )
% 0.18/0.44 => ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.44 = X2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % pointfree_idE
% 0.18/0.44 thf(fact_340_pointfree__idE,axiom,
% 0.18/0.44 ! [F2: a > a,G2: a > a,X2: a] :
% 0.18/0.44 ( ( ( comp_a_a_a @ F2 @ G2 )
% 0.18/0.44 = id_a )
% 0.18/0.44 => ( ( F2 @ ( G2 @ X2 ) )
% 0.18/0.44 = X2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % pointfree_idE
% 0.18/0.44 thf(fact_341_comp__eq__id__dest,axiom,
% 0.18/0.44 ! [A: a > complex,B: real > a,C: real > complex,V: real] :
% 0.18/0.44 ( ( ( comp_a_complex_real @ A @ B )
% 0.18/0.44 = ( comp_c595887981x_real @ id_complex @ C ) )
% 0.18/0.44 => ( ( A @ ( B @ V ) )
% 0.18/0.44 = ( C @ V ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % comp_eq_id_dest
% 0.18/0.44 thf(fact_342_comp__eq__id__dest,axiom,
% 0.18/0.44 ! [A: a > complex,B: complex > a,C: complex > complex,V: complex] :
% 0.18/0.44 ( ( ( comp_a1063143865omplex @ A @ B )
% 0.18/0.44 = ( comp_c130555887omplex @ id_complex @ C ) )
% 0.18/0.44 => ( ( A @ ( B @ V ) )
% 0.18/0.44 = ( C @ V ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % comp_eq_id_dest
% 0.18/0.44 thf(fact_343_comp__eq__id__dest,axiom,
% 0.18/0.44 ! [A: complex > a,B: a > complex,C: a > a,V: a] :
% 0.18/0.44 ( ( ( comp_complex_a_a @ A @ B )
% 0.18/0.44 = ( comp_a_a_a @ id_a @ C ) )
% 0.18/0.44 => ( ( A @ ( B @ V ) )
% 0.18/0.44 = ( C @ V ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % comp_eq_id_dest
% 0.18/0.44 thf(fact_344_comp__eq__id__dest,axiom,
% 0.18/0.44 ! [A: real > a,B: real > real,C: real > a,V: real] :
% 0.18/0.44 ( ( ( comp_real_a_real @ A @ B )
% 0.18/0.44 = ( comp_a_a_real @ id_a @ C ) )
% 0.18/0.44 => ( ( A @ ( B @ V ) )
% 0.18/0.44 = ( C @ V ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % comp_eq_id_dest
% 0.18/0.44 thf(fact_345_comp__eq__id__dest,axiom,
% 0.18/0.44 ! [A: a > complex,B: a > a,C: a > complex,V: a] :
% 0.18/0.44 ( ( ( comp_a_complex_a @ A @ B )
% 0.18/0.44 = ( comp_c124850173plex_a @ id_complex @ C ) )
% 0.18/0.44 => ( ( A @ ( B @ V ) )
% 0.18/0.44 = ( C @ V ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % comp_eq_id_dest
% 0.18/0.44 thf(fact_346_comp__eq__id__dest,axiom,
% 0.18/0.44 ! [A: a > a,B: complex > a,C: complex > a,V: complex] :
% 0.18/0.44 ( ( ( comp_a_a_complex @ A @ B )
% 0.18/0.44 = ( comp_a_a_complex @ id_a @ C ) )
% 0.18/0.44 => ( ( A @ ( B @ V ) )
% 0.18/0.44 = ( C @ V ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % comp_eq_id_dest
% 0.18/0.44 thf(fact_347_comp__eq__id__dest,axiom,
% 0.18/0.44 ! [A: a > a,B: real > a,C: real > a,V: real] :
% 0.18/0.44 ( ( ( comp_a_a_real @ A @ B )
% 0.18/0.44 = ( comp_a_a_real @ id_a @ C ) )
% 0.18/0.44 => ( ( A @ ( B @ V ) )
% 0.18/0.44 = ( C @ V ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % comp_eq_id_dest
% 0.18/0.44 thf(fact_348_comp__eq__id__dest,axiom,
% 0.18/0.44 ! [A: a > a,B: a > a,C: a > a,V: a] :
% 0.18/0.44 ( ( ( comp_a_a_a @ A @ B )
% 0.18/0.44 = ( comp_a_a_a @ id_a @ C ) )
% 0.18/0.44 => ( ( A @ ( B @ V ) )
% 0.18/0.44 = ( C @ V ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % comp_eq_id_dest
% 0.18/0.44 thf(fact_349_arc__imp__path,axiom,
% 0.18/0.44 ! [G2: real > complex] :
% 0.18/0.44 ( ( path_arc_complex @ G2 )
% 0.18/0.44 => ( path_path_complex @ G2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % arc_imp_path
% 0.18/0.44 thf(fact_350_inj__on__id,axiom,
% 0.18/0.44 ! [A2: set_complex] : ( inj_on94911183omplex @ id_complex @ A2 ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_id
% 0.18/0.44 thf(fact_351_inj__on__id,axiom,
% 0.18/0.44 ! [A2: set_a] : ( inj_on_a_a @ id_a @ A2 ) ).
% 0.18/0.44
% 0.18/0.44 % inj_on_id
% 0.18/0.44 thf(fact_352_simple__path__imp__path,axiom,
% 0.18/0.44 ! [G2: real > a] :
% 0.18/0.44 ( ( path_simple_path_a @ G2 )
% 0.18/0.44 => ( path_path_a @ G2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_imp_path
% 0.18/0.44 thf(fact_353_simple__path__imp__path,axiom,
% 0.18/0.44 ! [G2: real > complex] :
% 0.18/0.44 ( ( path_s36253918omplex @ G2 )
% 0.18/0.44 => ( path_path_complex @ G2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % simple_path_imp_path
% 0.18/0.44
% 0.18/0.44 % Conjectures (1)
% 0.18/0.44 thf(conj_0,conjecture,
% 0.18/0.44 ( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
% 0.18/0.44 = ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 3.83/1.99 ---- Embedded in THF ---
% 3.83/2.00 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.83/2.00 %%% Generated on Tue Feb 24 08:28:36 EST 2026
% 3.83/2.00 %%% using '$$dhol' embedding, version 1.3.0.
% 3.83/2.00 %%% Logic specification used:
% 3.83/2.00 %%% thf(spec, logic, $$dhol).
% 3.83/2.00
% 3.83/2.00 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.I8HVgnaxTf/DTF2DTF21628.p
% See solution above
% 3.83/2.00 ------------------------
% 4.12/2.06 ---- Cleaned THF ---
% 4.12/2.06 thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 4.12/2.06 set_real_real: $tType ).
% 4.12/2.06
% 4.12/2.06 thf(ty_n_t__Set__Oset_I_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
% 4.12/2.06 set_a_complex: $tType ).
% 4.12/2.06
% 4.12/2.06 thf(ty_n_t__Set__Oset_I_062_It__Complex__Ocomplex_Mtf__a_J_J,type,
% 4.12/2.06 set_complex_a: $tType ).
% 4.12/2.06
% 4.12/2.06 thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mtf__a_J_J,type,
% 4.12/2.06 set_real_a: $tType ).
% 4.12/2.06
% 4.12/2.06 thf(ty_n_t__Set__Oset_It__Complex__Ocomplex_J,type,
% 4.12/2.06 set_complex: $tType ).
% 4.12/2.06
% 4.12/2.06 thf(ty_n_t__Set__Oset_I_062_Itf__a_Mtf__a_J_J,type,
% 4.12/2.06 set_a_a: $tType ).
% 4.12/2.06
% 4.12/2.06 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 4.12/2.06 set_real: $tType ).
% 4.12/2.06
% 4.12/2.06 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 4.12/2.06 set_a: $tType ).
% 4.12/2.06
% 4.12/2.06 thf(ty_n_t__Complex__Ocomplex,type,
% 4.12/2.06 complex: $tType ).
% 4.12/2.06
% 4.12/2.06 thf(ty_n_t__Real__Oreal,type,
% 4.12/2.06 real: $tType ).
% 4.12/2.06
% 4.12/2.06 thf(ty_n_tf__a,type,
% 4.12/2.06 a: $tType ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 4.12/2.06 bij_be209634132omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001tf__a,type,
% 4.12/2.06 bij_betw_complex_a: ( complex > a ) > set_complex > set_a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Obij__betw_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 4.12/2.06 bij_be122140626omplex: ( real > complex ) > set_real > set_complex > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Obij__betw_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.12/2.06 bij_betw_real_real: ( real > real ) > set_real > set_real > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Obij__betw_001t__Real__Oreal_001tf__a,type,
% 4.12/2.06 bij_betw_real_a: ( real > a ) > set_real > set_a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Obij__betw_001tf__a_001t__Complex__Ocomplex,type,
% 4.12/2.06 bij_betw_a_complex: ( a > complex ) > set_a > set_complex > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Obij__betw_001tf__a_001tf__a,type,
% 4.12/2.06 bij_betw_a_a: ( a > a ) > set_a > set_a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 4.12/2.06 comp_c130555887omplex: ( complex > complex ) > ( complex > complex ) > complex > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 4.12/2.06 comp_c595887981x_real: ( complex > complex ) > ( real > complex ) > real > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001tf__a,type,
% 4.12/2.06 comp_c124850173plex_a: ( complex > complex ) > ( a > complex ) > a > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.12/2.06 comp_c819638635l_real: ( complex > real ) > ( real > complex ) > real > real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Real__Oreal_001tf__a,type,
% 4.12/2.06 comp_complex_real_a: ( complex > real ) > ( a > complex ) > a > real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001tf__a_001t__Complex__Ocomplex,type,
% 4.12/2.06 comp_c274302683omplex: ( complex > a ) > ( complex > complex ) > complex > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001tf__a_001t__Real__Oreal,type,
% 4.12/2.06 comp_complex_a_real: ( complex > a ) > ( real > complex ) > real > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001tf__a_001tf__a,type,
% 4.12/2.06 comp_complex_a_a: ( complex > a ) > ( a > complex ) > a > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 4.12/2.06 comp_r667767405omplex: ( real > complex ) > ( complex > real ) > complex > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 4.12/2.06 comp_r701421291x_real: ( real > complex ) > ( real > real ) > real > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Complex__Ocomplex_001tf__a,type,
% 4.12/2.06 comp_real_complex_a: ( real > complex ) > ( a > real ) > a > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 4.12/2.06 comp_r422820971omplex: ( real > real ) > ( complex > real ) > complex > real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.12/2.06 comp_real_real_real: ( real > real ) > ( real > real ) > real > real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Real__Oreal_001tf__a,type,
% 4.12/2.06 comp_real_real_a: ( real > real ) > ( a > real ) > a > real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001tf__a_001t__Complex__Ocomplex,type,
% 4.12/2.06 comp_real_a_complex: ( real > a ) > ( complex > real ) > complex > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001tf__a_001t__Real__Oreal,type,
% 4.12/2.06 comp_real_a_real: ( real > a ) > ( real > real ) > real > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001tf__a_001tf__a,type,
% 4.12/2.06 comp_real_a_a: ( real > a ) > ( a > real ) > a > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001tf__a_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 4.12/2.06 comp_a1063143865omplex: ( a > complex ) > ( complex > a ) > complex > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001tf__a_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 4.12/2.06 comp_a_complex_real: ( a > complex ) > ( real > a ) > real > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001tf__a_001t__Complex__Ocomplex_001tf__a,type,
% 4.12/2.06 comp_a_complex_a: ( a > complex ) > ( a > a ) > a > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001tf__a_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 4.12/2.06 comp_a_real_complex: ( a > real ) > ( complex > a ) > complex > real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001tf__a_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.12/2.06 comp_a_real_real: ( a > real ) > ( real > a ) > real > real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001tf__a_001t__Real__Oreal_001tf__a,type,
% 4.12/2.06 comp_a_real_a: ( a > real ) > ( a > a ) > a > real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001t__Complex__Ocomplex,type,
% 4.12/2.06 comp_a_a_complex: ( a > a ) > ( complex > a ) > complex > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001t__Real__Oreal,type,
% 4.12/2.06 comp_a_a_real: ( a > a ) > ( real > a ) > real > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001tf__a,type,
% 4.12/2.06 comp_a_a_a: ( a > a ) > ( a > a ) > a > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oid_001_062_It__Complex__Ocomplex_Mtf__a_J,type,
% 4.12/2.06 id_complex_a: ( complex > a ) > complex > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oid_001_062_It__Real__Oreal_Mtf__a_J,type,
% 4.12/2.06 id_real_a: ( real > a ) > real > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oid_001_062_Itf__a_Mtf__a_J,type,
% 4.12/2.06 id_a_a: ( a > a ) > a > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oid_001t__Complex__Ocomplex,type,
% 4.12/2.06 id_complex: complex > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oid_001t__Real__Oreal,type,
% 4.12/2.06 id_real: real > real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oid_001tf__a,type,
% 4.12/2.06 id_a: a > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001_062_It__Complex__Ocomplex_Mtf__a_J_001_062_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 4.12/2.06 inj_on893405649omplex: ( ( complex > a ) > complex > complex ) > set_complex_a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001_062_It__Complex__Ocomplex_Mtf__a_J_001_062_It__Complex__Ocomplex_Mtf__a_J,type,
% 4.12/2.06 inj_on1576005937plex_a: ( ( complex > a ) > complex > a ) > set_complex_a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001_062_It__Real__Oreal_Mt__Real__Oreal_J_001_062_It__Real__Oreal_Mtf__a_J,type,
% 4.12/2.06 inj_on958237983real_a: ( ( real > real ) > real > a ) > set_real_real > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001_062_It__Real__Oreal_Mtf__a_J_001_062_It__Real__Oreal_Mt__Complex__Ocomplex_J,type,
% 4.12/2.06 inj_on319905617omplex: ( ( real > a ) > real > complex ) > set_real_a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001_062_It__Real__Oreal_Mtf__a_J_001_062_It__Real__Oreal_Mtf__a_J,type,
% 4.12/2.06 inj_on_real_a_real_a: ( ( real > a ) > real > a ) > set_real_a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001_062_Itf__a_Mt__Complex__Ocomplex_J_001_062_Itf__a_Mtf__a_J,type,
% 4.12/2.06 inj_on_a_complex_a_a: ( ( a > complex ) > a > a ) > set_a_complex > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mt__Complex__Ocomplex_J,type,
% 4.12/2.06 inj_on_a_a_a_complex: ( ( a > a ) > a > complex ) > set_a_a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J,type,
% 4.12/2.06 inj_on_a_a_a_a: ( ( a > a ) > a > a ) > set_a_a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 4.12/2.06 inj_on94911183omplex: ( complex > complex ) > set_complex > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001t__Complex__Ocomplex_001tf__a,type,
% 4.12/2.06 inj_on_complex_a: ( complex > a ) > set_complex > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 4.12/2.06 inj_on_real_complex: ( real > complex ) > set_real > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.12/2.06 inj_on_real_real: ( real > real ) > set_real > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001tf__a,type,
% 4.12/2.06 inj_on_real_a: ( real > a ) > set_real > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001tf__a_001t__Complex__Ocomplex,type,
% 4.12/2.06 inj_on_a_complex: ( a > complex ) > set_a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Fun_Oinj__on_001tf__a_001tf__a,type,
% 4.12/2.06 inj_on_a_a: ( a > a ) > set_a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex,type,
% 4.12/2.06 zero_zero_complex: complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Groups_Ozero__class_Ozero_001tf__a,type,
% 4.12/2.06 zero_zero_a: a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 4.12/2.06 top_top_complex_o: complex > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Orderings_Otop__class_Otop_001_062_Itf__a_M_Eo_J,type,
% 4.12/2.06 top_top_a_o: a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Complex__Ocomplex_Mtf__a_J_J,type,
% 4.12/2.06 top_to525076535plex_a: set_complex_a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 4.12/2.06 top_to1446257885l_real: set_real_real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Real__Oreal_Mtf__a_J_J,type,
% 4.12/2.06 top_top_set_real_a: set_real_a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
% 4.12/2.06 top_to2109114701omplex: set_a_complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_Itf__a_Mtf__a_J_J,type,
% 4.12/2.06 top_top_set_a_a: set_a_a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 4.12/2.06 top_top_set_complex: set_complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.12/2.06 top_top_set_real: set_real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
% 4.12/2.06 top_top_set_a: set_a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Oarc_001t__Complex__Ocomplex,type,
% 4.12/2.06 path_arc_complex: ( real > complex ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Oarc_001t__Real__Oreal,type,
% 4.12/2.06 path_arc_real: ( real > real ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Oarc_001tf__a,type,
% 4.12/2.06 path_arc_a: ( real > a ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Opath_001t__Complex__Ocomplex,type,
% 4.12/2.06 path_path_complex: ( real > complex ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Opath_001t__Real__Oreal,type,
% 4.12/2.06 path_path_real: ( real > real ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Opath_001tf__a,type,
% 4.12/2.06 path_path_a: ( real > a ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Opathfinish_001t__Complex__Ocomplex,type,
% 4.12/2.06 path_p769714271omplex: ( real > complex ) > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Opathfinish_001t__Real__Oreal,type,
% 4.12/2.06 path_pathfinish_real: ( real > real ) > real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Opathfinish_001tf__a,type,
% 4.12/2.06 path_pathfinish_a: ( real > a ) > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Opathstart_001t__Complex__Ocomplex,type,
% 4.12/2.06 path_p797330068omplex: ( real > complex ) > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Opathstart_001t__Real__Oreal,type,
% 4.12/2.06 path_pathstart_real: ( real > real ) > real ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Opathstart_001tf__a,type,
% 4.12/2.06 path_pathstart_a: ( real > a ) > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Orectpath,type,
% 4.12/2.06 path_rectpath: complex > complex > real > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Osimple__path_001t__Complex__Ocomplex,type,
% 4.12/2.06 path_s36253918omplex: ( real > complex ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Osimple__path_001t__Real__Oreal,type,
% 4.12/2.06 path_s1005760220h_real: ( real > real ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Path__Connected_Osimple__path_001tf__a,type,
% 4.12/2.06 path_simple_path_a: ( real > a ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Poincare__Bendixson__Mirabelle__pwkwpzhsyu_Oc1__on__open__R2_Ocomplex__of_001tf__a,type,
% 4.12/2.06 poinca1910941596x_of_a: a > complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Poincare__Bendixson__Mirabelle__pwkwpzhsyu_Oc1__on__open__R2_Oreal__of_001tf__a,type,
% 4.12/2.06 poinca837721858l_of_a: complex > a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Complex__Ocomplex_001tf__a,type,
% 4.12/2.06 real_V762982918plex_a: ( complex > a ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001tf__a_001t__Complex__Ocomplex,type,
% 4.12/2.06 real_V912435428omplex: ( a > complex ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Real__Vector__Spaces_Obounded__linear__axioms_001t__Complex__Ocomplex_001tf__a,type,
% 4.12/2.06 real_V301987619plex_a: ( complex > a ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Real__Vector__Spaces_Obounded__linear__axioms_001tf__a_001t__Complex__Ocomplex,type,
% 4.12/2.06 real_V451440129omplex: ( a > complex ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Real__Vector__Spaces_Olinear_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 4.12/2.06 real_V670066493omplex: ( complex > complex ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Real__Vector__Spaces_Olinear_001t__Complex__Ocomplex_001tf__a,type,
% 4.12/2.06 real_V1327653935plex_a: ( complex > a ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Real__Vector__Spaces_Olinear_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 4.12/2.06 real_V1948715323omplex: ( real > complex ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Real__Vector__Spaces_Olinear_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.12/2.06 real_V1354572473l_real: ( real > real ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Real__Vector__Spaces_Olinear_001t__Real__Oreal_001tf__a,type,
% 4.12/2.06 real_V779700657real_a: ( real > a ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Real__Vector__Spaces_Olinear_001tf__a_001t__Complex__Ocomplex,type,
% 4.12/2.06 real_V1477106445omplex: ( a > complex ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Real__Vector__Spaces_Olinear_001tf__a_001tf__a,type,
% 4.12/2.06 real_V202220639ar_a_a: ( a > a ) > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 4.12/2.06 collect_complex: ( complex > $o ) > set_complex ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_Set_OCollect_001tf__a,type,
% 4.12/2.06 collect_a: ( a > $o ) > set_a ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 4.12/2.06 member_complex: complex > set_complex > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_c_member_001tf__a,type,
% 4.12/2.06 member_a: a > set_a > $o ).
% 4.12/2.06
% 4.12/2.06 thf(sy_v_c,type,
% 4.12/2.06 c: real > a ).
% 4.12/2.06
% 4.12/2.06 thf(fact_0_assms_I2_J,axiom,
% 4.12/2.06 ( ( path_pathfinish_a @ c )
% 4.12/2.06 = ( path_pathstart_a @ c ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_1_assms_I1_J,axiom,
% 4.12/2.06 path_simple_path_a @ c ).
% 4.12/2.06
% 4.12/2.06 thf(fact_2_a1,axiom,
% 4.12/2.06 path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_3_comp__apply,axiom,
% 4.12/2.06 ( comp_real_a_real
% 4.12/2.06 = ( ^ [F: real > a,G: real > real,X: real] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_4_comp__apply,axiom,
% 4.12/2.06 ( comp_a_complex_a
% 4.12/2.06 = ( ^ [F: a > complex,G: a > a,X: a] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_5_comp__apply,axiom,
% 4.12/2.06 ( comp_a_a_complex
% 4.12/2.06 = ( ^ [F: a > a,G: complex > a,X: complex] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_6_comp__apply,axiom,
% 4.12/2.06 ( comp_a_a_real
% 4.12/2.06 = ( ^ [F: a > a,G: real > a,X: real] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_7_comp__apply,axiom,
% 4.12/2.06 ( comp_a_a_a
% 4.12/2.06 = ( ^ [F: a > a,G: a > a,X: a] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_8_comp__apply,axiom,
% 4.12/2.06 ( comp_a_complex_real
% 4.12/2.06 = ( ^ [F: a > complex,G: real > a,X: real] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_9_comp__apply,axiom,
% 4.12/2.06 ( comp_a1063143865omplex
% 4.12/2.06 = ( ^ [F: a > complex,G: complex > a,X: complex] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_10_comp__apply,axiom,
% 4.12/2.06 ( comp_complex_a_a
% 4.12/2.06 = ( ^ [F: complex > a,G: a > complex,X: a] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_11_pathfinish__compose,axiom,
% 4.12/2.06 ! [F2: real > a,P: real > real] :
% 4.12/2.06 ( ( path_pathfinish_a @ ( comp_real_a_real @ F2 @ P ) )
% 4.12/2.06 = ( F2 @ ( path_pathfinish_real @ P ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_12_pathfinish__compose,axiom,
% 4.12/2.06 ! [F2: complex > complex,P: real > complex] :
% 4.12/2.06 ( ( path_p769714271omplex @ ( comp_c595887981x_real @ F2 @ P ) )
% 4.12/2.06 = ( F2 @ ( path_p769714271omplex @ P ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_13_pathfinish__compose,axiom,
% 4.12/2.06 ! [F2: a > complex,P: real > a] :
% 4.12/2.06 ( ( path_p769714271omplex @ ( comp_a_complex_real @ F2 @ P ) )
% 4.12/2.06 = ( F2 @ ( path_pathfinish_a @ P ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_14_pathfinish__compose,axiom,
% 4.12/2.06 ! [F2: complex > a,P: real > complex] :
% 4.12/2.06 ( ( path_pathfinish_a @ ( comp_complex_a_real @ F2 @ P ) )
% 4.12/2.06 = ( F2 @ ( path_p769714271omplex @ P ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_15_pathfinish__compose,axiom,
% 4.12/2.06 ! [F2: a > a,P: real > a] :
% 4.12/2.06 ( ( path_pathfinish_a @ ( comp_a_a_real @ F2 @ P ) )
% 4.12/2.06 = ( F2 @ ( path_pathfinish_a @ P ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_16_pathstart__compose,axiom,
% 4.12/2.06 ! [F2: real > a,P: real > real] :
% 4.12/2.06 ( ( path_pathstart_a @ ( comp_real_a_real @ F2 @ P ) )
% 4.12/2.06 = ( F2 @ ( path_pathstart_real @ P ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_17_pathstart__compose,axiom,
% 4.12/2.06 ! [F2: complex > complex,P: real > complex] :
% 4.12/2.06 ( ( path_p797330068omplex @ ( comp_c595887981x_real @ F2 @ P ) )
% 4.12/2.06 = ( F2 @ ( path_p797330068omplex @ P ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_18_pathstart__compose,axiom,
% 4.12/2.06 ! [F2: a > complex,P: real > a] :
% 4.12/2.06 ( ( path_p797330068omplex @ ( comp_a_complex_real @ F2 @ P ) )
% 4.12/2.06 = ( F2 @ ( path_pathstart_a @ P ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_19_pathstart__compose,axiom,
% 4.12/2.06 ! [F2: complex > a,P: real > complex] :
% 4.12/2.06 ( ( path_pathstart_a @ ( comp_complex_a_real @ F2 @ P ) )
% 4.12/2.06 = ( F2 @ ( path_p797330068omplex @ P ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_20_pathstart__compose,axiom,
% 4.12/2.06 ! [F2: a > a,P: real > a] :
% 4.12/2.06 ( ( path_pathstart_a @ ( comp_a_a_real @ F2 @ P ) )
% 4.12/2.06 = ( F2 @ ( path_pathstart_a @ P ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_21_complex__of__bounded__linear,axiom,
% 4.12/2.06 real_V912435428omplex @ poinca1910941596x_of_a ).
% 4.12/2.06
% 4.12/2.06 thf(fact_22_complex__of__linear,axiom,
% 4.12/2.06 real_V1477106445omplex @ poinca1910941596x_of_a ).
% 4.12/2.06
% 4.12/2.06 thf(fact_23_comp__def,axiom,
% 4.12/2.06 ( comp_real_a_real
% 4.12/2.06 = ( ^ [F: real > a,G: real > real,X: real] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_24_comp__def,axiom,
% 4.12/2.06 ( comp_a_complex_a
% 4.12/2.06 = ( ^ [F: a > complex,G: a > a,X: a] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_25_comp__def,axiom,
% 4.12/2.06 ( comp_a_a_complex
% 4.12/2.06 = ( ^ [F: a > a,G: complex > a,X: complex] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_26_comp__def,axiom,
% 4.12/2.06 ( comp_a_a_real
% 4.12/2.06 = ( ^ [F: a > a,G: real > a,X: real] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_27_comp__def,axiom,
% 4.12/2.06 ( comp_a_a_a
% 4.12/2.06 = ( ^ [F: a > a,G: a > a,X: a] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_28_comp__def,axiom,
% 4.12/2.06 ( comp_a_complex_real
% 4.12/2.06 = ( ^ [F: a > complex,G: real > a,X: real] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_29_comp__def,axiom,
% 4.12/2.06 ( comp_a1063143865omplex
% 4.12/2.06 = ( ^ [F: a > complex,G: complex > a,X: complex] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_30_comp__def,axiom,
% 4.12/2.06 ( comp_complex_a_a
% 4.12/2.06 = ( ^ [F: complex > a,G: a > complex,X: a] : ( F @ ( G @ X ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_31_comp__assoc,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a,H: real > real] :
% 4.12/2.06 ( ( comp_r701421291x_real @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_complex_real @ F2 @ ( comp_real_a_real @ G2 @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_32_comp__assoc,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a,H: complex > real] :
% 4.12/2.06 ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_33_comp__assoc,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: complex > a,H: a > complex] :
% 4.12/2.06 ( ( comp_c124850173plex_a @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_complex_a @ F2 @ ( comp_complex_a_a @ G2 @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_34_comp__assoc,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: complex > a,H: real > complex] :
% 4.12/2.06 ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_complex_real @ F2 @ ( comp_complex_a_real @ G2 @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_35_comp__assoc,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: complex > a,H: complex > complex] :
% 4.12/2.06 ( ( comp_c130555887omplex @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a1063143865omplex @ F2 @ ( comp_c274302683omplex @ G2 @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_36_comp__assoc,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: a > complex,H: real > a] :
% 4.12/2.06 ( ( comp_a_a_real @ ( comp_complex_a_a @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_complex_a_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_37_comp__assoc,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: a > complex,H: complex > a] :
% 4.12/2.06 ( ( comp_a_a_complex @ ( comp_complex_a_a @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_c274302683omplex @ F2 @ ( comp_a1063143865omplex @ G2 @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_38_comp__assoc,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: a > complex,H: a > a] :
% 4.12/2.06 ( ( comp_a_a_a @ ( comp_complex_a_a @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_complex_a_a @ F2 @ ( comp_a_complex_a @ G2 @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_39_comp__assoc,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: a > complex,H: real > a] :
% 4.12/2.06 ( ( comp_a_complex_real @ ( comp_c124850173plex_a @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_c595887981x_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_40_comp__assoc,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: a > a,H: real > a] :
% 4.12/2.06 ( ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_complex_real @ F2 @ ( comp_a_a_real @ G2 @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_41_comp__eq__dest,axiom,
% 4.12/2.06 ! [A: a > complex,B: real > a,C: a > complex,D: real > a,V: real] :
% 4.12/2.06 ( ( ( comp_a_complex_real @ A @ B )
% 4.12/2.06 = ( comp_a_complex_real @ C @ D ) )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ ( D @ V ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_42_comp__eq__dest,axiom,
% 4.12/2.06 ! [A: a > complex,B: complex > a,C: a > complex,D: complex > a,V: complex] :
% 4.12/2.06 ( ( ( comp_a1063143865omplex @ A @ B )
% 4.12/2.06 = ( comp_a1063143865omplex @ C @ D ) )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ ( D @ V ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_43_comp__eq__dest,axiom,
% 4.12/2.06 ! [A: complex > a,B: a > complex,C: complex > a,D: a > complex,V: a] :
% 4.12/2.06 ( ( ( comp_complex_a_a @ A @ B )
% 4.12/2.06 = ( comp_complex_a_a @ C @ D ) )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ ( D @ V ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_44_comp__eq__dest,axiom,
% 4.12/2.06 ! [A: complex > a,B: a > complex,C: a > a,D: a > a,V: a] :
% 4.12/2.06 ( ( ( comp_complex_a_a @ A @ B )
% 4.12/2.06 = ( comp_a_a_a @ C @ D ) )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ ( D @ V ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_45_comp__eq__dest,axiom,
% 4.12/2.06 ! [A: real > a,B: real > real,C: real > a,D: real > real,V: real] :
% 4.12/2.06 ( ( ( comp_real_a_real @ A @ B )
% 4.12/2.06 = ( comp_real_a_real @ C @ D ) )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ ( D @ V ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_46_comp__eq__dest,axiom,
% 4.12/2.06 ! [A: real > a,B: real > real,C: a > a,D: real > a,V: real] :
% 4.12/2.06 ( ( ( comp_real_a_real @ A @ B )
% 4.12/2.06 = ( comp_a_a_real @ C @ D ) )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ ( D @ V ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_47_comp__eq__dest,axiom,
% 4.12/2.06 ! [A: a > complex,B: a > a,C: a > complex,D: a > a,V: a] :
% 4.12/2.06 ( ( ( comp_a_complex_a @ A @ B )
% 4.12/2.06 = ( comp_a_complex_a @ C @ D ) )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ ( D @ V ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_48_comp__eq__dest,axiom,
% 4.12/2.06 ! [A: a > a,B: complex > a,C: a > a,D: complex > a,V: complex] :
% 4.12/2.06 ( ( ( comp_a_a_complex @ A @ B )
% 4.12/2.06 = ( comp_a_a_complex @ C @ D ) )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ ( D @ V ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_49_comp__eq__dest,axiom,
% 4.12/2.06 ! [A: a > a,B: real > a,C: real > a,D: real > real,V: real] :
% 4.12/2.06 ( ( ( comp_a_a_real @ A @ B )
% 4.12/2.06 = ( comp_real_a_real @ C @ D ) )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ ( D @ V ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_50_comp__eq__dest,axiom,
% 4.12/2.06 ! [A: a > a,B: real > a,C: a > a,D: real > a,V: real] :
% 4.12/2.06 ( ( ( comp_a_a_real @ A @ B )
% 4.12/2.06 = ( comp_a_a_real @ C @ D ) )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ ( D @ V ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_51_comp__eq__elim,axiom,
% 4.12/2.06 ! [A: a > complex,B: real > a,C: a > complex,D: real > a] :
% 4.12/2.06 ( ( ( comp_a_complex_real @ A @ B )
% 4.12/2.06 = ( comp_a_complex_real @ C @ D ) )
% 4.12/2.06 => ! [V2: real] :
% 4.12/2.06 ( ( A @ ( B @ V2 ) )
% 4.12/2.06 = ( C @ ( D @ V2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_52_comp__eq__elim,axiom,
% 4.12/2.06 ! [A: a > complex,B: complex > a,C: a > complex,D: complex > a] :
% 4.12/2.06 ( ( ( comp_a1063143865omplex @ A @ B )
% 4.12/2.06 = ( comp_a1063143865omplex @ C @ D ) )
% 4.12/2.06 => ! [V2: complex] :
% 4.12/2.06 ( ( A @ ( B @ V2 ) )
% 4.12/2.06 = ( C @ ( D @ V2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_53_comp__eq__elim,axiom,
% 4.12/2.06 ! [A: complex > a,B: a > complex,C: complex > a,D: a > complex] :
% 4.12/2.06 ( ( ( comp_complex_a_a @ A @ B )
% 4.12/2.06 = ( comp_complex_a_a @ C @ D ) )
% 4.12/2.06 => ! [V2: a] :
% 4.12/2.06 ( ( A @ ( B @ V2 ) )
% 4.12/2.06 = ( C @ ( D @ V2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_54_comp__eq__elim,axiom,
% 4.12/2.06 ! [A: complex > a,B: a > complex,C: a > a,D: a > a] :
% 4.12/2.06 ( ( ( comp_complex_a_a @ A @ B )
% 4.12/2.06 = ( comp_a_a_a @ C @ D ) )
% 4.12/2.06 => ! [V2: a] :
% 4.12/2.06 ( ( A @ ( B @ V2 ) )
% 4.12/2.06 = ( C @ ( D @ V2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_55_comp__eq__elim,axiom,
% 4.12/2.06 ! [A: real > a,B: real > real,C: real > a,D: real > real] :
% 4.12/2.06 ( ( ( comp_real_a_real @ A @ B )
% 4.12/2.06 = ( comp_real_a_real @ C @ D ) )
% 4.12/2.06 => ! [V2: real] :
% 4.12/2.06 ( ( A @ ( B @ V2 ) )
% 4.12/2.06 = ( C @ ( D @ V2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_56_comp__eq__elim,axiom,
% 4.12/2.06 ! [A: real > a,B: real > real,C: a > a,D: real > a] :
% 4.12/2.06 ( ( ( comp_real_a_real @ A @ B )
% 4.12/2.06 = ( comp_a_a_real @ C @ D ) )
% 4.12/2.06 => ! [V2: real] :
% 4.12/2.06 ( ( A @ ( B @ V2 ) )
% 4.12/2.06 = ( C @ ( D @ V2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_57_comp__eq__elim,axiom,
% 4.12/2.06 ! [A: a > complex,B: a > a,C: a > complex,D: a > a] :
% 4.12/2.06 ( ( ( comp_a_complex_a @ A @ B )
% 4.12/2.06 = ( comp_a_complex_a @ C @ D ) )
% 4.12/2.06 => ! [V2: a] :
% 4.12/2.06 ( ( A @ ( B @ V2 ) )
% 4.12/2.06 = ( C @ ( D @ V2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_58_comp__eq__elim,axiom,
% 4.12/2.06 ! [A: a > a,B: complex > a,C: a > a,D: complex > a] :
% 4.12/2.06 ( ( ( comp_a_a_complex @ A @ B )
% 4.12/2.06 = ( comp_a_a_complex @ C @ D ) )
% 4.12/2.06 => ! [V2: complex] :
% 4.12/2.06 ( ( A @ ( B @ V2 ) )
% 4.12/2.06 = ( C @ ( D @ V2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_59_comp__eq__elim,axiom,
% 4.12/2.06 ! [A: a > a,B: real > a,C: real > a,D: real > real] :
% 4.12/2.06 ( ( ( comp_a_a_real @ A @ B )
% 4.12/2.06 = ( comp_real_a_real @ C @ D ) )
% 4.12/2.06 => ! [V2: real] :
% 4.12/2.06 ( ( A @ ( B @ V2 ) )
% 4.12/2.06 = ( C @ ( D @ V2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_60_comp__eq__elim,axiom,
% 4.12/2.06 ! [A: a > a,B: real > a,C: a > a,D: real > a] :
% 4.12/2.06 ( ( ( comp_a_a_real @ A @ B )
% 4.12/2.06 = ( comp_a_a_real @ C @ D ) )
% 4.12/2.06 => ! [V2: real] :
% 4.12/2.06 ( ( A @ ( B @ V2 ) )
% 4.12/2.06 = ( C @ ( D @ V2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_61_comp__cong,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: real > a,X3: real] :
% 4.12/2.06 ( ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.06 = ( F3 @ ( G3 @ X3 ) ) )
% 4.12/2.06 => ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
% 4.12/2.06 = ( comp_a_complex_real @ F3 @ G3 @ X3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_62_comp__cong,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: complex > a,X3: complex] :
% 4.12/2.06 ( ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.06 = ( F3 @ ( G3 @ X3 ) ) )
% 4.12/2.06 => ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
% 4.12/2.06 = ( comp_a1063143865omplex @ F3 @ G3 @ X3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_63_comp__cong,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: a > a,X3: a] :
% 4.12/2.06 ( ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.06 = ( F3 @ ( G3 @ X3 ) ) )
% 4.12/2.06 => ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
% 4.12/2.06 = ( comp_a_complex_a @ F3 @ G3 @ X3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_64_comp__cong,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: complex > a,X2: complex,F3: a > complex,G3: real > a,X3: real] :
% 4.12/2.06 ( ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.06 = ( F3 @ ( G3 @ X3 ) ) )
% 4.12/2.06 => ( ( comp_a1063143865omplex @ F2 @ G2 @ X2 )
% 4.12/2.06 = ( comp_a_complex_real @ F3 @ G3 @ X3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_65_comp__cong,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: complex > a,X2: complex,F3: a > complex,G3: complex > a,X3: complex] :
% 4.12/2.06 ( ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.06 = ( F3 @ ( G3 @ X3 ) ) )
% 4.12/2.06 => ( ( comp_a1063143865omplex @ F2 @ G2 @ X2 )
% 4.12/2.06 = ( comp_a1063143865omplex @ F3 @ G3 @ X3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_66_comp__cong,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: complex > a,X2: complex,F3: a > complex,G3: a > a,X3: a] :
% 4.12/2.06 ( ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.06 = ( F3 @ ( G3 @ X3 ) ) )
% 4.12/2.06 => ( ( comp_a1063143865omplex @ F2 @ G2 @ X2 )
% 4.12/2.06 = ( comp_a_complex_a @ F3 @ G3 @ X3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_67_comp__cong,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: a > complex,X2: a,F3: complex > a,G3: a > complex,X3: a] :
% 4.12/2.06 ( ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.06 = ( F3 @ ( G3 @ X3 ) ) )
% 4.12/2.06 => ( ( comp_complex_a_a @ F2 @ G2 @ X2 )
% 4.12/2.06 = ( comp_complex_a_a @ F3 @ G3 @ X3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_68_comp__cong,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: a > complex,X2: a,F3: real > a,G3: real > real,X3: real] :
% 4.12/2.06 ( ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.06 = ( F3 @ ( G3 @ X3 ) ) )
% 4.12/2.06 => ( ( comp_complex_a_a @ F2 @ G2 @ X2 )
% 4.12/2.06 = ( comp_real_a_real @ F3 @ G3 @ X3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_69_comp__cong,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: a > complex,X2: a,F3: a > a,G3: complex > a,X3: complex] :
% 4.12/2.06 ( ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.06 = ( F3 @ ( G3 @ X3 ) ) )
% 4.12/2.06 => ( ( comp_complex_a_a @ F2 @ G2 @ X2 )
% 4.12/2.06 = ( comp_a_a_complex @ F3 @ G3 @ X3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_70_comp__cong,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: a > complex,X2: a,F3: a > a,G3: real > a,X3: real] :
% 4.12/2.06 ( ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.06 = ( F3 @ ( G3 @ X3 ) ) )
% 4.12/2.06 => ( ( comp_complex_a_a @ F2 @ G2 @ X2 )
% 4.12/2.06 = ( comp_a_a_real @ F3 @ G3 @ X3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_71_comp__eq__dest__lhs,axiom,
% 4.12/2.06 ! [A: a > complex,B: real > a,C: real > complex,V: real] :
% 4.12/2.06 ( ( ( comp_a_complex_real @ A @ B )
% 4.12/2.06 = C )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ V ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_72_comp__eq__dest__lhs,axiom,
% 4.12/2.06 ! [A: a > complex,B: complex > a,C: complex > complex,V: complex] :
% 4.12/2.06 ( ( ( comp_a1063143865omplex @ A @ B )
% 4.12/2.06 = C )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ V ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_73_comp__eq__dest__lhs,axiom,
% 4.12/2.06 ! [A: complex > a,B: a > complex,C: a > a,V: a] :
% 4.12/2.06 ( ( ( comp_complex_a_a @ A @ B )
% 4.12/2.06 = C )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ V ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_74_comp__eq__dest__lhs,axiom,
% 4.12/2.06 ! [A: real > a,B: real > real,C: real > a,V: real] :
% 4.12/2.06 ( ( ( comp_real_a_real @ A @ B )
% 4.12/2.06 = C )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ V ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_75_comp__eq__dest__lhs,axiom,
% 4.12/2.06 ! [A: a > complex,B: a > a,C: a > complex,V: a] :
% 4.12/2.06 ( ( ( comp_a_complex_a @ A @ B )
% 4.12/2.06 = C )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ V ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_76_comp__eq__dest__lhs,axiom,
% 4.12/2.06 ! [A: a > a,B: complex > a,C: complex > a,V: complex] :
% 4.12/2.06 ( ( ( comp_a_a_complex @ A @ B )
% 4.12/2.06 = C )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ V ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_77_comp__eq__dest__lhs,axiom,
% 4.12/2.06 ! [A: a > a,B: real > a,C: real > a,V: real] :
% 4.12/2.06 ( ( ( comp_a_a_real @ A @ B )
% 4.12/2.06 = C )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ V ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_78_comp__eq__dest__lhs,axiom,
% 4.12/2.06 ! [A: a > a,B: a > a,C: a > a,V: a] :
% 4.12/2.06 ( ( ( comp_a_a_a @ A @ B )
% 4.12/2.06 = C )
% 4.12/2.06 => ( ( A @ ( B @ V ) )
% 4.12/2.06 = ( C @ V ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_79_pathstart__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: real > complex] :
% 4.12/2.06 ( ( real_V670066493omplex @ F2 )
% 4.12/2.06 => ( ( path_p797330068omplex @ ( comp_c595887981x_real @ F2 @ G2 ) )
% 4.12/2.06 = ( F2 @ ( path_p797330068omplex @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_80_pathstart__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: real > a,G2: real > real] :
% 4.12/2.06 ( ( real_V779700657real_a @ F2 )
% 4.12/2.06 => ( ( path_pathstart_a @ ( comp_real_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( F2 @ ( path_pathstart_real @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_81_pathstart__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: a > a,G2: real > a] :
% 4.12/2.06 ( ( real_V202220639ar_a_a @ F2 )
% 4.12/2.06 => ( ( path_pathstart_a @ ( comp_a_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( F2 @ ( path_pathstart_a @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_82_pathstart__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a] :
% 4.12/2.06 ( ( real_V1477106445omplex @ F2 )
% 4.12/2.06 => ( ( path_p797330068omplex @ ( comp_a_complex_real @ F2 @ G2 ) )
% 4.12/2.06 = ( F2 @ ( path_pathstart_a @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_83_pathstart__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: real > complex] :
% 4.12/2.06 ( ( real_V1327653935plex_a @ F2 )
% 4.12/2.06 => ( ( path_pathstart_a @ ( comp_complex_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( F2 @ ( path_p797330068omplex @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_84_pathfinish__linear__image,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: real > complex] :
% 4.12/2.06 ( ( real_V670066493omplex @ F2 )
% 4.12/2.06 => ( ( path_p769714271omplex @ ( comp_c595887981x_real @ F2 @ G2 ) )
% 4.12/2.06 = ( F2 @ ( path_p769714271omplex @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_85_pathfinish__linear__image,axiom,
% 4.12/2.06 ! [F2: real > a,G2: real > real] :
% 4.12/2.06 ( ( real_V779700657real_a @ F2 )
% 4.12/2.06 => ( ( path_pathfinish_a @ ( comp_real_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( F2 @ ( path_pathfinish_real @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_86_pathfinish__linear__image,axiom,
% 4.12/2.06 ! [F2: a > a,G2: real > a] :
% 4.12/2.06 ( ( real_V202220639ar_a_a @ F2 )
% 4.12/2.06 => ( ( path_pathfinish_a @ ( comp_a_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( F2 @ ( path_pathfinish_a @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_87_pathfinish__linear__image,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a] :
% 4.12/2.06 ( ( real_V1477106445omplex @ F2 )
% 4.12/2.06 => ( ( path_p769714271omplex @ ( comp_a_complex_real @ F2 @ G2 ) )
% 4.12/2.06 = ( F2 @ ( path_pathfinish_a @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_88_pathfinish__linear__image,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: real > complex] :
% 4.12/2.06 ( ( real_V1327653935plex_a @ F2 )
% 4.12/2.06 => ( ( path_pathfinish_a @ ( comp_complex_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( F2 @ ( path_p769714271omplex @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_89_bounded__linear_Olinear,axiom,
% 4.12/2.06 ! [F2: a > complex] :
% 4.12/2.06 ( ( real_V912435428omplex @ F2 )
% 4.12/2.06 => ( real_V1477106445omplex @ F2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_90_bounded__linear_Olinear,axiom,
% 4.12/2.06 ! [F2: complex > a] :
% 4.12/2.06 ( ( real_V762982918plex_a @ F2 )
% 4.12/2.06 => ( real_V1327653935plex_a @ F2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_91_linear__conv__bounded__linear,axiom,
% 4.12/2.06 real_V1477106445omplex = real_V912435428omplex ).
% 4.12/2.06
% 4.12/2.06 thf(fact_92_linear__conv__bounded__linear,axiom,
% 4.12/2.06 real_V1327653935plex_a = real_V762982918plex_a ).
% 4.12/2.06
% 4.12/2.06 thf(fact_93_linear__compose,axiom,
% 4.12/2.06 ! [F2: real > real,G2: real > a] :
% 4.12/2.06 ( ( real_V1354572473l_real @ F2 )
% 4.12/2.06 => ( ( real_V779700657real_a @ G2 )
% 4.12/2.06 => ( real_V779700657real_a @ ( comp_real_a_real @ G2 @ F2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_94_linear__compose,axiom,
% 4.12/2.06 ! [F2: real > a,G2: a > a] :
% 4.12/2.06 ( ( real_V779700657real_a @ F2 )
% 4.12/2.06 => ( ( real_V202220639ar_a_a @ G2 )
% 4.12/2.06 => ( real_V779700657real_a @ ( comp_a_a_real @ G2 @ F2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_95_linear__compose,axiom,
% 4.12/2.06 ! [F2: a > a,G2: a > a] :
% 4.12/2.06 ( ( real_V202220639ar_a_a @ F2 )
% 4.12/2.06 => ( ( real_V202220639ar_a_a @ G2 )
% 4.12/2.06 => ( real_V202220639ar_a_a @ ( comp_a_a_a @ G2 @ F2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_96_linear__compose,axiom,
% 4.12/2.06 ! [F2: real > a,G2: a > complex] :
% 4.12/2.06 ( ( real_V779700657real_a @ F2 )
% 4.12/2.06 => ( ( real_V1477106445omplex @ G2 )
% 4.12/2.06 => ( real_V1948715323omplex @ ( comp_a_complex_real @ G2 @ F2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_97_linear__compose,axiom,
% 4.12/2.06 ! [F2: a > a,G2: a > complex] :
% 4.12/2.06 ( ( real_V202220639ar_a_a @ F2 )
% 4.12/2.06 => ( ( real_V1477106445omplex @ G2 )
% 4.12/2.06 => ( real_V1477106445omplex @ ( comp_a_complex_a @ G2 @ F2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_98_linear__compose,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: complex > a] :
% 4.12/2.06 ( ( real_V670066493omplex @ F2 )
% 4.12/2.06 => ( ( real_V1327653935plex_a @ G2 )
% 4.12/2.06 => ( real_V1327653935plex_a @ ( comp_c274302683omplex @ G2 @ F2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_99_linear__compose,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: complex > complex] :
% 4.12/2.06 ( ( real_V1477106445omplex @ F2 )
% 4.12/2.06 => ( ( real_V670066493omplex @ G2 )
% 4.12/2.06 => ( real_V1477106445omplex @ ( comp_c124850173plex_a @ G2 @ F2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_100_linear__compose,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: complex > a] :
% 4.12/2.06 ( ( real_V1477106445omplex @ F2 )
% 4.12/2.06 => ( ( real_V1327653935plex_a @ G2 )
% 4.12/2.06 => ( real_V202220639ar_a_a @ ( comp_complex_a_a @ G2 @ F2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_101_linear__compose,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: a > a] :
% 4.12/2.06 ( ( real_V1327653935plex_a @ F2 )
% 4.12/2.06 => ( ( real_V202220639ar_a_a @ G2 )
% 4.12/2.06 => ( real_V1327653935plex_a @ ( comp_a_a_complex @ G2 @ F2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_102_linear__compose,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: a > complex] :
% 4.12/2.06 ( ( real_V1327653935plex_a @ F2 )
% 4.12/2.06 => ( ( real_V1477106445omplex @ G2 )
% 4.12/2.06 => ( real_V670066493omplex @ ( comp_a1063143865omplex @ G2 @ F2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_103__092_060open_062_092_060And_062g_O_Ainj_Acomplex__of_A_092_060Longrightarrow_062_Asimple__path_A_Icomplex__of_A_092_060circ_062_Ag_J_A_061_Asimple__path_Ag_092_060close_062,axiom,
% 4.12/2.06 ! [G2: real > a] :
% 4.12/2.06 ( ( inj_on_a_complex @ poinca1910941596x_of_a @ top_top_set_a )
% 4.12/2.06 => ( ( path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ G2 ) )
% 4.12/2.06 = ( path_simple_path_a @ G2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_104_pathfinish__rectpath,axiom,
% 4.12/2.06 ! [A1: complex,A3: complex] :
% 4.12/2.06 ( ( path_p769714271omplex @ ( path_rectpath @ A1 @ A3 ) )
% 4.12/2.06 = A1 ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_105_pathstart__rectpath,axiom,
% 4.12/2.06 ! [A1: complex,A3: complex] :
% 4.12/2.06 ( ( path_p797330068omplex @ ( path_rectpath @ A1 @ A3 ) )
% 4.12/2.06 = A1 ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_106_bounded__linear_Obounded__linear,axiom,
% 4.12/2.06 ! [F2: a > complex] :
% 4.12/2.06 ( ( real_V912435428omplex @ F2 )
% 4.12/2.06 => ( real_V912435428omplex @ F2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_107_bounded__linear_Obounded__linear,axiom,
% 4.12/2.06 ! [F2: complex > a] :
% 4.12/2.06 ( ( real_V762982918plex_a @ F2 )
% 4.12/2.06 => ( real_V762982918plex_a @ F2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_108_rewriteR__comp__comp2,axiom,
% 4.12/2.06 ! [G2: real > real,H: a > real,R1: complex > real,R2: a > complex,F2: real > a,L: complex > a] :
% 4.12/2.06 ( ( ( comp_real_real_a @ G2 @ H )
% 4.12/2.06 = ( comp_complex_real_a @ R1 @ R2 ) )
% 4.12/2.06 => ( ( ( comp_real_a_complex @ F2 @ R1 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_real_a_a @ ( comp_real_a_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_complex_a_a @ L @ R2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_109_rewriteR__comp__comp2,axiom,
% 4.12/2.06 ! [G2: real > real,H: complex > real,R1: a > real,R2: complex > a,F2: real > a,L: a > a] :
% 4.12/2.06 ( ( ( comp_r422820971omplex @ G2 @ H )
% 4.12/2.06 = ( comp_a_real_complex @ R1 @ R2 ) )
% 4.12/2.06 => ( ( ( comp_real_a_a @ F2 @ R1 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_real_a_complex @ ( comp_real_a_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_a_complex @ L @ R2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_110_rewriteR__comp__comp2,axiom,
% 4.12/2.06 ! [G2: real > real,H: a > real,R1: a > real,R2: a > a,F2: real > a,L: a > a] :
% 4.12/2.06 ( ( ( comp_real_real_a @ G2 @ H )
% 4.12/2.06 = ( comp_a_real_a @ R1 @ R2 ) )
% 4.12/2.06 => ( ( ( comp_real_a_a @ F2 @ R1 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_real_a_a @ ( comp_real_a_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_a_a @ L @ R2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_111_rewriteR__comp__comp2,axiom,
% 4.12/2.06 ! [G2: real > real,H: real > real,R1: a > real,R2: real > a,F2: real > a,L: a > a] :
% 4.12/2.06 ( ( ( comp_real_real_real @ G2 @ H )
% 4.12/2.06 = ( comp_a_real_real @ R1 @ R2 ) )
% 4.12/2.06 => ( ( ( comp_real_a_a @ F2 @ R1 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_real_a_real @ ( comp_real_a_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_a_real @ L @ R2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_112_rewriteR__comp__comp2,axiom,
% 4.12/2.06 ! [G2: complex > real,H: a > complex,R1: real > real,R2: a > real,F2: real > a,L: real > a] :
% 4.12/2.06 ( ( ( comp_complex_real_a @ G2 @ H )
% 4.12/2.06 = ( comp_real_real_a @ R1 @ R2 ) )
% 4.12/2.06 => ( ( ( comp_real_a_real @ F2 @ R1 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_complex_a_a @ ( comp_real_a_complex @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_real_a_a @ L @ R2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_113_rewriteR__comp__comp2,axiom,
% 4.12/2.06 ! [G2: real > real,H: real > real,R1: real > real,R2: real > real,F2: real > a,L: real > a] :
% 4.12/2.06 ( ( ( comp_real_real_real @ G2 @ H )
% 4.12/2.06 = ( comp_real_real_real @ R1 @ R2 ) )
% 4.12/2.06 => ( ( ( comp_real_a_real @ F2 @ R1 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_real_a_real @ ( comp_real_a_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_real_a_real @ L @ R2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_114_rewriteR__comp__comp2,axiom,
% 4.12/2.06 ! [G2: a > real,H: complex > a,R1: real > real,R2: complex > real,F2: real > a,L: real > a] :
% 4.12/2.06 ( ( ( comp_a_real_complex @ G2 @ H )
% 4.12/2.06 = ( comp_r422820971omplex @ R1 @ R2 ) )
% 4.12/2.06 => ( ( ( comp_real_a_real @ F2 @ R1 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_a_a_complex @ ( comp_real_a_a @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_real_a_complex @ L @ R2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_115_rewriteR__comp__comp2,axiom,
% 4.12/2.06 ! [G2: a > real,H: real > a,R1: real > real,R2: real > real,F2: real > a,L: real > a] :
% 4.12/2.06 ( ( ( comp_a_real_real @ G2 @ H )
% 4.12/2.06 = ( comp_real_real_real @ R1 @ R2 ) )
% 4.12/2.06 => ( ( ( comp_real_a_real @ F2 @ R1 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_a_a_real @ ( comp_real_a_a @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_real_a_real @ L @ R2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_116_rewriteR__comp__comp2,axiom,
% 4.12/2.06 ! [G2: a > real,H: a > a,R1: real > real,R2: a > real,F2: real > a,L: real > a] :
% 4.12/2.06 ( ( ( comp_a_real_a @ G2 @ H )
% 4.12/2.06 = ( comp_real_real_a @ R1 @ R2 ) )
% 4.12/2.06 => ( ( ( comp_real_a_real @ F2 @ R1 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_a_a_a @ ( comp_real_a_a @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_real_a_a @ L @ R2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_117_rewriteR__comp__comp2,axiom,
% 4.12/2.06 ! [G2: real > complex,H: real > real,R1: a > complex,R2: real > a,F2: complex > a,L: a > a] :
% 4.12/2.06 ( ( ( comp_r701421291x_real @ G2 @ H )
% 4.12/2.06 = ( comp_a_complex_real @ R1 @ R2 ) )
% 4.12/2.06 => ( ( ( comp_complex_a_a @ F2 @ R1 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_real_a_real @ ( comp_complex_a_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_a_real @ L @ R2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_118_rewriteL__comp__comp2,axiom,
% 4.12/2.06 ! [F2: real > a,G2: a > real,L1: complex > a,L2: a > complex,H: real > a,R: real > complex] :
% 4.12/2.06 ( ( ( comp_real_a_a @ F2 @ G2 )
% 4.12/2.06 = ( comp_complex_a_a @ L1 @ L2 ) )
% 4.12/2.06 => ( ( ( comp_a_complex_real @ L2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_real_a_real @ F2 @ ( comp_a_real_real @ G2 @ H ) )
% 4.12/2.06 = ( comp_complex_a_real @ L1 @ R ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_119_rewriteL__comp__comp2,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: real > complex,L1: real > a,L2: real > real,H: a > real,R: a > real] :
% 4.12/2.06 ( ( ( comp_complex_a_real @ F2 @ G2 )
% 4.12/2.06 = ( comp_real_a_real @ L1 @ L2 ) )
% 4.12/2.06 => ( ( ( comp_real_real_a @ L2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_complex_a_a @ F2 @ ( comp_real_complex_a @ G2 @ H ) )
% 4.12/2.06 = ( comp_real_a_a @ L1 @ R ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_120_rewriteL__comp__comp2,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: a > complex,L1: a > complex,L2: a > a,H: complex > a,R: complex > a] :
% 4.12/2.06 ( ( ( comp_c124850173plex_a @ F2 @ G2 )
% 4.12/2.06 = ( comp_a_complex_a @ L1 @ L2 ) )
% 4.12/2.06 => ( ( ( comp_a_a_complex @ L2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_c130555887omplex @ F2 @ ( comp_a1063143865omplex @ G2 @ H ) )
% 4.12/2.06 = ( comp_a1063143865omplex @ L1 @ R ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_121_rewriteL__comp__comp2,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: a > complex,L1: a > complex,L2: a > a,H: real > a,R: real > a] :
% 4.12/2.06 ( ( ( comp_c124850173plex_a @ F2 @ G2 )
% 4.12/2.06 = ( comp_a_complex_a @ L1 @ L2 ) )
% 4.12/2.06 => ( ( ( comp_a_a_real @ L2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_c595887981x_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) )
% 4.12/2.06 = ( comp_a_complex_real @ L1 @ R ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_122_rewriteL__comp__comp2,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: a > complex,L1: a > complex,L2: a > a,H: a > a,R: a > a] :
% 4.12/2.06 ( ( ( comp_c124850173plex_a @ F2 @ G2 )
% 4.12/2.06 = ( comp_a_complex_a @ L1 @ L2 ) )
% 4.12/2.06 => ( ( ( comp_a_a_a @ L2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_c124850173plex_a @ F2 @ ( comp_a_complex_a @ G2 @ H ) )
% 4.12/2.06 = ( comp_a_complex_a @ L1 @ R ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_123_rewriteL__comp__comp2,axiom,
% 4.12/2.06 ! [F2: real > a,G2: complex > real,L1: a > a,L2: complex > a,H: real > complex,R: real > a] :
% 4.12/2.06 ( ( ( comp_real_a_complex @ F2 @ G2 )
% 4.12/2.06 = ( comp_a_a_complex @ L1 @ L2 ) )
% 4.12/2.06 => ( ( ( comp_complex_a_real @ L2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_real_a_real @ F2 @ ( comp_c819638635l_real @ G2 @ H ) )
% 4.12/2.06 = ( comp_a_a_real @ L1 @ R ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_124_rewriteL__comp__comp2,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: complex > complex,L1: a > a,L2: complex > a,H: a > complex,R: a > a] :
% 4.12/2.06 ( ( ( comp_c274302683omplex @ F2 @ G2 )
% 4.12/2.06 = ( comp_a_a_complex @ L1 @ L2 ) )
% 4.12/2.06 => ( ( ( comp_complex_a_a @ L2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_complex_a_a @ F2 @ ( comp_c124850173plex_a @ G2 @ H ) )
% 4.12/2.06 = ( comp_a_a_a @ L1 @ R ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_125_rewriteL__comp__comp2,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: real > complex,L1: a > a,L2: real > a,H: a > real,R: a > a] :
% 4.12/2.06 ( ( ( comp_complex_a_real @ F2 @ G2 )
% 4.12/2.06 = ( comp_a_a_real @ L1 @ L2 ) )
% 4.12/2.06 => ( ( ( comp_real_a_a @ L2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_complex_a_a @ F2 @ ( comp_real_complex_a @ G2 @ H ) )
% 4.12/2.06 = ( comp_a_a_a @ L1 @ R ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_126_rewriteL__comp__comp2,axiom,
% 4.12/2.06 ! [F2: real > a,G2: a > real,L1: a > a,L2: a > a,H: real > a,R: real > a] :
% 4.12/2.06 ( ( ( comp_real_a_a @ F2 @ G2 )
% 4.12/2.06 = ( comp_a_a_a @ L1 @ L2 ) )
% 4.12/2.06 => ( ( ( comp_a_a_real @ L2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_real_a_real @ F2 @ ( comp_a_real_real @ G2 @ H ) )
% 4.12/2.06 = ( comp_a_a_real @ L1 @ R ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_127_rewriteL__comp__comp2,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a,L1: a > complex,L2: real > a,H: complex > real,R: complex > a] :
% 4.12/2.06 ( ( ( comp_a_complex_real @ F2 @ G2 )
% 4.12/2.06 = ( comp_a_complex_real @ L1 @ L2 ) )
% 4.12/2.06 => ( ( ( comp_real_a_complex @ L2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) )
% 4.12/2.06 = ( comp_a1063143865omplex @ L1 @ R ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_128_rewriteR__comp__comp,axiom,
% 4.12/2.06 ! [G2: real > a,H: complex > real,R: complex > a,F2: a > complex] :
% 4.12/2.06 ( ( ( comp_real_a_complex @ G2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a1063143865omplex @ F2 @ R ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_129_rewriteR__comp__comp,axiom,
% 4.12/2.06 ! [G2: real > a,H: a > real,R: a > a,F2: a > complex] :
% 4.12/2.06 ( ( ( comp_real_a_a @ G2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_real_complex_a @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_complex_a @ F2 @ R ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_130_rewriteR__comp__comp,axiom,
% 4.12/2.06 ! [G2: complex > a,H: real > complex,R: real > a,F2: a > complex] :
% 4.12/2.06 ( ( ( comp_complex_a_real @ G2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_complex_real @ F2 @ R ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_131_rewriteR__comp__comp,axiom,
% 4.12/2.06 ! [G2: complex > a,H: complex > complex,R: complex > a,F2: a > complex] :
% 4.12/2.06 ( ( ( comp_c274302683omplex @ G2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_c130555887omplex @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a1063143865omplex @ F2 @ R ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_132_rewriteR__comp__comp,axiom,
% 4.12/2.06 ! [G2: complex > a,H: complex > complex,R: complex > a,F2: a > a] :
% 4.12/2.06 ( ( ( comp_c274302683omplex @ G2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_c274302683omplex @ ( comp_a_a_complex @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_a_complex @ F2 @ R ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_133_rewriteR__comp__comp,axiom,
% 4.12/2.06 ! [G2: complex > a,H: real > complex,R: real > a,F2: a > a] :
% 4.12/2.06 ( ( ( comp_complex_a_real @ G2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_complex_a_real @ ( comp_a_a_complex @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_a_real @ F2 @ R ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_134_rewriteR__comp__comp,axiom,
% 4.12/2.06 ! [G2: real > a,H: complex > real,R: complex > a,F2: a > a] :
% 4.12/2.06 ( ( ( comp_real_a_complex @ G2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_real_a_complex @ ( comp_a_a_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_a_complex @ F2 @ R ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_135_rewriteR__comp__comp,axiom,
% 4.12/2.06 ! [G2: real > a,H: a > real,R: a > a,F2: a > a] :
% 4.12/2.06 ( ( ( comp_real_a_a @ G2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_real_a_a @ ( comp_a_a_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_a_a_a @ F2 @ R ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_136_rewriteR__comp__comp,axiom,
% 4.12/2.06 ! [G2: complex > complex,H: a > complex,R: a > complex,F2: complex > a] :
% 4.12/2.06 ( ( ( comp_c124850173plex_a @ G2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_complex_a_a @ ( comp_c274302683omplex @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_complex_a_a @ F2 @ R ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_137_rewriteR__comp__comp,axiom,
% 4.12/2.06 ! [G2: real > real,H: real > real,R: real > real,F2: real > a] :
% 4.12/2.06 ( ( ( comp_real_real_real @ G2 @ H )
% 4.12/2.06 = R )
% 4.12/2.06 => ( ( comp_real_a_real @ ( comp_real_a_real @ F2 @ G2 ) @ H )
% 4.12/2.06 = ( comp_real_a_real @ F2 @ R ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_138_rewriteL__comp__comp,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: a > complex,L: a > complex,H: real > a] :
% 4.12/2.06 ( ( ( comp_c124850173plex_a @ F2 @ G2 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_c595887981x_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) )
% 4.12/2.06 = ( comp_a_complex_real @ L @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_139_rewriteL__comp__comp,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: a > complex,L: a > complex,H: complex > a] :
% 4.12/2.06 ( ( ( comp_c124850173plex_a @ F2 @ G2 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_c130555887omplex @ F2 @ ( comp_a1063143865omplex @ G2 @ H ) )
% 4.12/2.06 = ( comp_a1063143865omplex @ L @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_140_rewriteL__comp__comp,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: a > complex,L: a > complex,H: a > a] :
% 4.12/2.06 ( ( ( comp_c124850173plex_a @ F2 @ G2 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_c124850173plex_a @ F2 @ ( comp_a_complex_a @ G2 @ H ) )
% 4.12/2.06 = ( comp_a_complex_a @ L @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_141_rewriteL__comp__comp,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: complex > complex,L: complex > a,H: a > complex] :
% 4.12/2.06 ( ( ( comp_c274302683omplex @ F2 @ G2 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_complex_a_a @ F2 @ ( comp_c124850173plex_a @ G2 @ H ) )
% 4.12/2.06 = ( comp_complex_a_a @ L @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_142_rewriteL__comp__comp,axiom,
% 4.12/2.06 ! [F2: real > a,G2: a > real,L: a > a,H: real > a] :
% 4.12/2.06 ( ( ( comp_real_a_a @ F2 @ G2 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_real_a_real @ F2 @ ( comp_a_real_real @ G2 @ H ) )
% 4.12/2.06 = ( comp_a_a_real @ L @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_143_rewriteL__comp__comp,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a,L: real > complex,H: real > real] :
% 4.12/2.06 ( ( ( comp_a_complex_real @ F2 @ G2 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_a_complex_real @ F2 @ ( comp_real_a_real @ G2 @ H ) )
% 4.12/2.06 = ( comp_r701421291x_real @ L @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_144_rewriteL__comp__comp,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a,L: real > complex,H: complex > real] :
% 4.12/2.06 ( ( ( comp_a_complex_real @ F2 @ G2 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) )
% 4.12/2.06 = ( comp_r667767405omplex @ L @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_145_rewriteL__comp__comp,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a,L: real > complex,H: a > real] :
% 4.12/2.06 ( ( ( comp_a_complex_real @ F2 @ G2 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_a_complex_a @ F2 @ ( comp_real_a_a @ G2 @ H ) )
% 4.12/2.06 = ( comp_real_complex_a @ L @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_146_rewriteL__comp__comp,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: complex > a,L: complex > complex,H: real > complex] :
% 4.12/2.06 ( ( ( comp_a1063143865omplex @ F2 @ G2 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_a_complex_real @ F2 @ ( comp_complex_a_real @ G2 @ H ) )
% 4.12/2.06 = ( comp_c595887981x_real @ L @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_147_rewriteL__comp__comp,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: complex > a,L: complex > complex,H: complex > complex] :
% 4.12/2.06 ( ( ( comp_a1063143865omplex @ F2 @ G2 )
% 4.12/2.06 = L )
% 4.12/2.06 => ( ( comp_a1063143865omplex @ F2 @ ( comp_c274302683omplex @ G2 @ H ) )
% 4.12/2.06 = ( comp_c130555887omplex @ L @ H ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_148_injD,axiom,
% 4.12/2.06 ! [F2: a > complex,X2: a,Y: a] :
% 4.12/2.06 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( ( F2 @ X2 )
% 4.12/2.06 = ( F2 @ Y ) )
% 4.12/2.06 => ( X2 = Y ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_149_injD,axiom,
% 4.12/2.06 ! [F2: complex > a,X2: complex,Y: complex] :
% 4.12/2.06 ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 4.12/2.06 => ( ( ( F2 @ X2 )
% 4.12/2.06 = ( F2 @ Y ) )
% 4.12/2.06 => ( X2 = Y ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_150_injI,axiom,
% 4.12/2.06 ! [F2: a > complex] :
% 4.12/2.06 ( ! [X4: a,Y2: a] :
% 4.12/2.06 ( ( ( F2 @ X4 )
% 4.12/2.06 = ( F2 @ Y2 ) )
% 4.12/2.06 => ( X4 = Y2 ) )
% 4.12/2.06 => ( inj_on_a_complex @ F2 @ top_top_set_a ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_151_injI,axiom,
% 4.12/2.06 ! [F2: complex > a] :
% 4.12/2.06 ( ! [X4: complex,Y2: complex] :
% 4.12/2.06 ( ( ( F2 @ X4 )
% 4.12/2.06 = ( F2 @ Y2 ) )
% 4.12/2.06 => ( X4 = Y2 ) )
% 4.12/2.06 => ( inj_on_complex_a @ F2 @ top_top_set_complex ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_152_inj__eq,axiom,
% 4.12/2.06 ! [F2: a > complex,X2: a,Y: a] :
% 4.12/2.06 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( ( F2 @ X2 )
% 4.12/2.06 = ( F2 @ Y ) )
% 4.12/2.06 = ( X2 = Y ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_153_inj__eq,axiom,
% 4.12/2.06 ! [F2: complex > a,X2: complex,Y: complex] :
% 4.12/2.06 ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 4.12/2.06 => ( ( ( F2 @ X2 )
% 4.12/2.06 = ( F2 @ Y ) )
% 4.12/2.06 = ( X2 = Y ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_154_inj__def,axiom,
% 4.12/2.06 ! [F2: a > complex] :
% 4.12/2.06 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 = ( ! [X: a,Y3: a] :
% 4.12/2.06 ( ( ( F2 @ X )
% 4.12/2.06 = ( F2 @ Y3 ) )
% 4.12/2.06 => ( X = Y3 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_155_inj__def,axiom,
% 4.12/2.06 ! [F2: complex > a] :
% 4.12/2.06 ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 4.12/2.06 = ( ! [X: complex,Y3: complex] :
% 4.12/2.06 ( ( ( F2 @ X )
% 4.12/2.06 = ( F2 @ Y3 ) )
% 4.12/2.06 => ( X = Y3 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_156_inj__onD,axiom,
% 4.12/2.06 ! [F2: a > complex,A2: set_a,X2: a,Y: a] :
% 4.12/2.06 ( ( inj_on_a_complex @ F2 @ A2 )
% 4.12/2.06 => ( ( ( F2 @ X2 )
% 4.12/2.06 = ( F2 @ Y ) )
% 4.12/2.06 => ( ( member_a @ X2 @ A2 )
% 4.12/2.06 => ( ( member_a @ Y @ A2 )
% 4.12/2.06 => ( X2 = Y ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_157_inj__onD,axiom,
% 4.12/2.06 ! [F2: complex > a,A2: set_complex,X2: complex,Y: complex] :
% 4.12/2.06 ( ( inj_on_complex_a @ F2 @ A2 )
% 4.12/2.06 => ( ( ( F2 @ X2 )
% 4.12/2.06 = ( F2 @ Y ) )
% 4.12/2.06 => ( ( member_complex @ X2 @ A2 )
% 4.12/2.06 => ( ( member_complex @ Y @ A2 )
% 4.12/2.06 => ( X2 = Y ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_158_inj__onI,axiom,
% 4.12/2.06 ! [A2: set_a,F2: a > complex] :
% 4.12/2.06 ( ! [X4: a,Y2: a] :
% 4.12/2.06 ( ( member_a @ X4 @ A2 )
% 4.12/2.06 => ( ( member_a @ Y2 @ A2 )
% 4.12/2.06 => ( ( ( F2 @ X4 )
% 4.12/2.06 = ( F2 @ Y2 ) )
% 4.12/2.06 => ( X4 = Y2 ) ) ) )
% 4.12/2.06 => ( inj_on_a_complex @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_159_inj__onI,axiom,
% 4.12/2.06 ! [A2: set_complex,F2: complex > a] :
% 4.12/2.06 ( ! [X4: complex,Y2: complex] :
% 4.12/2.06 ( ( member_complex @ X4 @ A2 )
% 4.12/2.06 => ( ( member_complex @ Y2 @ A2 )
% 4.12/2.06 => ( ( ( F2 @ X4 )
% 4.12/2.06 = ( F2 @ Y2 ) )
% 4.12/2.06 => ( X4 = Y2 ) ) ) )
% 4.12/2.06 => ( inj_on_complex_a @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_160_inj__on__def,axiom,
% 4.12/2.06 ( inj_on_a_complex
% 4.12/2.06 = ( ^ [F: a > complex,A4: set_a] :
% 4.12/2.06 ! [X: a] :
% 4.12/2.06 ( ( member_a @ X @ A4 )
% 4.12/2.06 => ! [Y3: a] :
% 4.12/2.06 ( ( member_a @ Y3 @ A4 )
% 4.12/2.06 => ( ( ( F @ X )
% 4.12/2.06 = ( F @ Y3 ) )
% 4.12/2.06 => ( X = Y3 ) ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_161_inj__on__def,axiom,
% 4.12/2.06 ( inj_on_complex_a
% 4.12/2.06 = ( ^ [F: complex > a,A4: set_complex] :
% 4.12/2.06 ! [X: complex] :
% 4.12/2.06 ( ( member_complex @ X @ A4 )
% 4.12/2.06 => ! [Y3: complex] :
% 4.12/2.06 ( ( member_complex @ Y3 @ A4 )
% 4.12/2.06 => ( ( ( F @ X )
% 4.12/2.06 = ( F @ Y3 ) )
% 4.12/2.06 => ( X = Y3 ) ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_162_inj__on__cong,axiom,
% 4.12/2.06 ! [A2: set_a,F2: a > complex,G2: a > complex] :
% 4.12/2.06 ( ! [A5: a] :
% 4.12/2.06 ( ( member_a @ A5 @ A2 )
% 4.12/2.06 => ( ( F2 @ A5 )
% 4.12/2.06 = ( G2 @ A5 ) ) )
% 4.12/2.06 => ( ( inj_on_a_complex @ F2 @ A2 )
% 4.12/2.06 = ( inj_on_a_complex @ G2 @ A2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_163_inj__on__cong,axiom,
% 4.12/2.06 ! [A2: set_complex,F2: complex > a,G2: complex > a] :
% 4.12/2.06 ( ! [A5: complex] :
% 4.12/2.06 ( ( member_complex @ A5 @ A2 )
% 4.12/2.06 => ( ( F2 @ A5 )
% 4.12/2.06 = ( G2 @ A5 ) ) )
% 4.12/2.06 => ( ( inj_on_complex_a @ F2 @ A2 )
% 4.12/2.06 = ( inj_on_complex_a @ G2 @ A2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_164_inj__on__eq__iff,axiom,
% 4.12/2.06 ! [F2: a > complex,A2: set_a,X2: a,Y: a] :
% 4.12/2.06 ( ( inj_on_a_complex @ F2 @ A2 )
% 4.12/2.06 => ( ( member_a @ X2 @ A2 )
% 4.12/2.06 => ( ( member_a @ Y @ A2 )
% 4.12/2.06 => ( ( ( F2 @ X2 )
% 4.12/2.06 = ( F2 @ Y ) )
% 4.12/2.06 = ( X2 = Y ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_165_inj__on__eq__iff,axiom,
% 4.12/2.06 ! [F2: complex > a,A2: set_complex,X2: complex,Y: complex] :
% 4.12/2.06 ( ( inj_on_complex_a @ F2 @ A2 )
% 4.12/2.06 => ( ( member_complex @ X2 @ A2 )
% 4.12/2.06 => ( ( member_complex @ Y @ A2 )
% 4.12/2.06 => ( ( ( F2 @ X2 )
% 4.12/2.06 = ( F2 @ Y ) )
% 4.12/2.06 = ( X2 = Y ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_166_inj__on__contraD,axiom,
% 4.12/2.06 ! [F2: a > complex,A2: set_a,X2: a,Y: a] :
% 4.12/2.06 ( ( inj_on_a_complex @ F2 @ A2 )
% 4.12/2.06 => ( ( X2 != Y )
% 4.12/2.06 => ( ( member_a @ X2 @ A2 )
% 4.12/2.06 => ( ( member_a @ Y @ A2 )
% 4.12/2.06 => ( ( F2 @ X2 )
% 4.12/2.06 != ( F2 @ Y ) ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_167_inj__on__contraD,axiom,
% 4.12/2.06 ! [F2: complex > a,A2: set_complex,X2: complex,Y: complex] :
% 4.12/2.06 ( ( inj_on_complex_a @ F2 @ A2 )
% 4.12/2.06 => ( ( X2 != Y )
% 4.12/2.06 => ( ( member_complex @ X2 @ A2 )
% 4.12/2.06 => ( ( member_complex @ Y @ A2 )
% 4.12/2.06 => ( ( F2 @ X2 )
% 4.12/2.06 != ( F2 @ Y ) ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_168_inj__on__inverseI,axiom,
% 4.12/2.06 ! [A2: set_a,G2: complex > a,F2: a > complex] :
% 4.12/2.06 ( ! [X4: a] :
% 4.12/2.06 ( ( member_a @ X4 @ A2 )
% 4.12/2.06 => ( ( G2 @ ( F2 @ X4 ) )
% 4.12/2.06 = X4 ) )
% 4.12/2.06 => ( inj_on_a_complex @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_169_inj__on__inverseI,axiom,
% 4.12/2.06 ! [A2: set_complex,G2: a > complex,F2: complex > a] :
% 4.12/2.06 ( ! [X4: complex] :
% 4.12/2.06 ( ( member_complex @ X4 @ A2 )
% 4.12/2.06 => ( ( G2 @ ( F2 @ X4 ) )
% 4.12/2.06 = X4 ) )
% 4.12/2.06 => ( inj_on_complex_a @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_170_inj__compose,axiom,
% 4.12/2.06 ! [F2: real > a,G2: real > real] :
% 4.12/2.06 ( ( inj_on_real_a @ F2 @ top_top_set_real )
% 4.12/2.06 => ( ( inj_on_real_real @ G2 @ top_top_set_real )
% 4.12/2.06 => ( inj_on_real_a @ ( comp_real_a_real @ F2 @ G2 ) @ top_top_set_real ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_171_inj__compose,axiom,
% 4.12/2.06 ! [F2: a > a,G2: real > a] :
% 4.12/2.06 ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( inj_on_real_a @ G2 @ top_top_set_real )
% 4.12/2.06 => ( inj_on_real_a @ ( comp_a_a_real @ F2 @ G2 ) @ top_top_set_real ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_172_inj__compose,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a] :
% 4.12/2.06 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( inj_on_real_a @ G2 @ top_top_set_real )
% 4.12/2.06 => ( inj_on_real_complex @ ( comp_a_complex_real @ F2 @ G2 ) @ top_top_set_real ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_173_inj__compose,axiom,
% 4.12/2.06 ! [F2: a > a,G2: a > a] :
% 4.12/2.06 ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( inj_on_a_a @ G2 @ top_top_set_a )
% 4.12/2.06 => ( inj_on_a_a @ ( comp_a_a_a @ F2 @ G2 ) @ top_top_set_a ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_174_inj__compose,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: a > a] :
% 4.12/2.06 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( inj_on_a_a @ G2 @ top_top_set_a )
% 4.12/2.06 => ( inj_on_a_complex @ ( comp_a_complex_a @ F2 @ G2 ) @ top_top_set_a ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_175_inj__compose,axiom,
% 4.12/2.06 ! [F2: a > a,G2: complex > a] :
% 4.12/2.06 ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( inj_on_complex_a @ G2 @ top_top_set_complex )
% 4.12/2.06 => ( inj_on_complex_a @ ( comp_a_a_complex @ F2 @ G2 ) @ top_top_set_complex ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_176_inj__compose,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: complex > a] :
% 4.12/2.06 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( inj_on_complex_a @ G2 @ top_top_set_complex )
% 4.12/2.06 => ( inj_on94911183omplex @ ( comp_a1063143865omplex @ F2 @ G2 ) @ top_top_set_complex ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_177_inj__compose,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: a > complex] :
% 4.12/2.06 ( ( inj_on94911183omplex @ F2 @ top_top_set_complex )
% 4.12/2.06 => ( ( inj_on_a_complex @ G2 @ top_top_set_a )
% 4.12/2.06 => ( inj_on_a_complex @ ( comp_c124850173plex_a @ F2 @ G2 ) @ top_top_set_a ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_178_inj__compose,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: a > complex] :
% 4.12/2.06 ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 4.12/2.06 => ( ( inj_on_a_complex @ G2 @ top_top_set_a )
% 4.12/2.06 => ( inj_on_a_a @ ( comp_complex_a_a @ F2 @ G2 ) @ top_top_set_a ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_179_inj__compose,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: complex > complex] :
% 4.12/2.06 ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 4.12/2.06 => ( ( inj_on94911183omplex @ G2 @ top_top_set_complex )
% 4.12/2.06 => ( inj_on_complex_a @ ( comp_c274302683omplex @ F2 @ G2 ) @ top_top_set_complex ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_180_inj__on__imageI2,axiom,
% 4.12/2.06 ! [F3: a > complex,F2: real > a,A2: set_real] :
% 4.12/2.06 ( ( inj_on_real_complex @ ( comp_a_complex_real @ F3 @ F2 ) @ A2 )
% 4.12/2.06 => ( inj_on_real_a @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_181_inj__on__imageI2,axiom,
% 4.12/2.06 ! [F3: real > a,F2: real > real,A2: set_real] :
% 4.12/2.06 ( ( inj_on_real_a @ ( comp_real_a_real @ F3 @ F2 ) @ A2 )
% 4.12/2.06 => ( inj_on_real_real @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_182_inj__on__imageI2,axiom,
% 4.12/2.06 ! [F3: a > a,F2: real > a,A2: set_real] :
% 4.12/2.06 ( ( inj_on_real_a @ ( comp_a_a_real @ F3 @ F2 ) @ A2 )
% 4.12/2.06 => ( inj_on_real_a @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_183_inj__on__imageI2,axiom,
% 4.12/2.06 ! [F3: a > a,F2: a > a,A2: set_a] :
% 4.12/2.06 ( ( inj_on_a_a @ ( comp_a_a_a @ F3 @ F2 ) @ A2 )
% 4.12/2.06 => ( inj_on_a_a @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_184_inj__on__imageI2,axiom,
% 4.12/2.06 ! [F3: complex > a,F2: a > complex,A2: set_a] :
% 4.12/2.06 ( ( inj_on_a_a @ ( comp_complex_a_a @ F3 @ F2 ) @ A2 )
% 4.12/2.06 => ( inj_on_a_complex @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_185_inj__on__imageI2,axiom,
% 4.12/2.06 ! [F3: a > complex,F2: complex > a,A2: set_complex] :
% 4.12/2.06 ( ( inj_on94911183omplex @ ( comp_a1063143865omplex @ F3 @ F2 ) @ A2 )
% 4.12/2.06 => ( inj_on_complex_a @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_186_inj__on__imageI2,axiom,
% 4.12/2.06 ! [F3: a > complex,F2: a > a,A2: set_a] :
% 4.12/2.06 ( ( inj_on_a_complex @ ( comp_a_complex_a @ F3 @ F2 ) @ A2 )
% 4.12/2.06 => ( inj_on_a_a @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_187_inj__on__imageI2,axiom,
% 4.12/2.06 ! [F3: complex > complex,F2: a > complex,A2: set_a] :
% 4.12/2.06 ( ( inj_on_a_complex @ ( comp_c124850173plex_a @ F3 @ F2 ) @ A2 )
% 4.12/2.06 => ( inj_on_a_complex @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_188_inj__on__imageI2,axiom,
% 4.12/2.06 ! [F3: a > a,F2: complex > a,A2: set_complex] :
% 4.12/2.06 ( ( inj_on_complex_a @ ( comp_a_a_complex @ F3 @ F2 ) @ A2 )
% 4.12/2.06 => ( inj_on_complex_a @ F2 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_189_simple__path__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: real > a,G2: real > real] :
% 4.12/2.06 ( ( real_V779700657real_a @ F2 )
% 4.12/2.06 => ( ( inj_on_real_a @ F2 @ top_top_set_real )
% 4.12/2.06 => ( ( path_simple_path_a @ ( comp_real_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_s1005760220h_real @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_190_simple__path__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: a > a,G2: real > a] :
% 4.12/2.06 ( ( real_V202220639ar_a_a @ F2 )
% 4.12/2.06 => ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( path_simple_path_a @ ( comp_a_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_simple_path_a @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_191_simple__path__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: real > complex] :
% 4.12/2.06 ( ( real_V1327653935plex_a @ F2 )
% 4.12/2.06 => ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 4.12/2.06 => ( ( path_simple_path_a @ ( comp_complex_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_s36253918omplex @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_192_simple__path__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a] :
% 4.12/2.06 ( ( real_V1477106445omplex @ F2 )
% 4.12/2.06 => ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( path_s36253918omplex @ ( comp_a_complex_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_simple_path_a @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_193_simple__path__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: real > complex] :
% 4.12/2.06 ( ( real_V670066493omplex @ F2 )
% 4.12/2.06 => ( ( inj_on94911183omplex @ F2 @ top_top_set_complex )
% 4.12/2.06 => ( ( path_s36253918omplex @ ( comp_c595887981x_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_s36253918omplex @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_194_fun_Oinj__map,axiom,
% 4.12/2.06 ! [F2: real > a] :
% 4.12/2.06 ( ( inj_on_real_a @ F2 @ top_top_set_real )
% 4.12/2.06 => ( inj_on958237983real_a @ ( comp_real_a_real @ F2 ) @ top_to1446257885l_real ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_195_fun_Oinj__map,axiom,
% 4.12/2.06 ! [F2: a > a] :
% 4.12/2.06 ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 4.12/2.06 => ( inj_on1576005937plex_a @ ( comp_a_a_complex @ F2 ) @ top_to525076535plex_a ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_196_fun_Oinj__map,axiom,
% 4.12/2.06 ! [F2: a > a] :
% 4.12/2.06 ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 4.12/2.06 => ( inj_on_real_a_real_a @ ( comp_a_a_real @ F2 ) @ top_top_set_real_a ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_197_fun_Oinj__map,axiom,
% 4.12/2.06 ! [F2: a > a] :
% 4.12/2.06 ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 4.12/2.06 => ( inj_on_a_a_a_a @ ( comp_a_a_a @ F2 ) @ top_top_set_a_a ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_198_fun_Oinj__map,axiom,
% 4.12/2.06 ! [F2: a > complex] :
% 4.12/2.06 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 => ( inj_on319905617omplex @ ( comp_a_complex_real @ F2 ) @ top_top_set_real_a ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_199_fun_Oinj__map,axiom,
% 4.12/2.06 ! [F2: a > complex] :
% 4.12/2.06 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 => ( inj_on893405649omplex @ ( comp_a1063143865omplex @ F2 ) @ top_to525076535plex_a ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_200_fun_Oinj__map,axiom,
% 4.12/2.06 ! [F2: a > complex] :
% 4.12/2.06 ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 => ( inj_on_a_a_a_complex @ ( comp_a_complex_a @ F2 ) @ top_top_set_a_a ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_201_fun_Oinj__map,axiom,
% 4.12/2.06 ! [F2: complex > a] :
% 4.12/2.06 ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 4.12/2.06 => ( inj_on_a_complex_a_a @ ( comp_complex_a_a @ F2 ) @ top_to2109114701omplex ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_202_real__of__bounded__linear,axiom,
% 4.12/2.06 real_V762982918plex_a @ poinca837721858l_of_a ).
% 4.12/2.06
% 4.12/2.06 thf(fact_203_real__of__linear,axiom,
% 4.12/2.06 real_V1327653935plex_a @ poinca837721858l_of_a ).
% 4.12/2.06
% 4.12/2.06 thf(fact_204_iso__tuple__UNIV__I,axiom,
% 4.12/2.06 ! [X2: a] : ( member_a @ X2 @ top_top_set_a ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_205_iso__tuple__UNIV__I,axiom,
% 4.12/2.06 ! [X2: complex] : ( member_complex @ X2 @ top_top_set_complex ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_206_UNIV__I,axiom,
% 4.12/2.06 ! [X2: a] : ( member_a @ X2 @ top_top_set_a ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_207_UNIV__I,axiom,
% 4.12/2.06 ! [X2: complex] : ( member_complex @ X2 @ top_top_set_complex ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_208_bounded__linear_Ointro,axiom,
% 4.12/2.06 ! [F2: a > complex] :
% 4.12/2.06 ( ( real_V1477106445omplex @ F2 )
% 4.12/2.06 => ( ( real_V451440129omplex @ F2 )
% 4.12/2.06 => ( real_V912435428omplex @ F2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_209_bounded__linear_Ointro,axiom,
% 4.12/2.06 ! [F2: complex > a] :
% 4.12/2.06 ( ( real_V1327653935plex_a @ F2 )
% 4.12/2.06 => ( ( real_V301987619plex_a @ F2 )
% 4.12/2.06 => ( real_V762982918plex_a @ F2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_210_bounded__linear__def,axiom,
% 4.12/2.06 ( real_V912435428omplex
% 4.12/2.06 = ( ^ [F: a > complex] :
% 4.12/2.06 ( ( real_V1477106445omplex @ F )
% 4.12/2.06 & ( real_V451440129omplex @ F ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_211_bounded__linear__def,axiom,
% 4.12/2.06 ( real_V762982918plex_a
% 4.12/2.06 = ( ^ [F: complex > a] :
% 4.12/2.06 ( ( real_V1327653935plex_a @ F )
% 4.12/2.06 & ( real_V301987619plex_a @ F ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_212_arc__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: real > a,G2: real > real] :
% 4.12/2.06 ( ( real_V779700657real_a @ F2 )
% 4.12/2.06 => ( ( inj_on_real_a @ F2 @ top_top_set_real )
% 4.12/2.06 => ( ( path_arc_a @ ( comp_real_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_arc_real @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_213_arc__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: a > a,G2: real > a] :
% 4.12/2.06 ( ( real_V202220639ar_a_a @ F2 )
% 4.12/2.06 => ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( path_arc_a @ ( comp_a_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_arc_a @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_214_arc__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a] :
% 4.12/2.06 ( ( real_V1477106445omplex @ F2 )
% 4.12/2.06 => ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( path_arc_complex @ ( comp_a_complex_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_arc_a @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_215_arc__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: real > complex] :
% 4.12/2.06 ( ( real_V1327653935plex_a @ F2 )
% 4.12/2.06 => ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 4.12/2.06 => ( ( path_arc_a @ ( comp_complex_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_arc_complex @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_216_real__of__inj,axiom,
% 4.12/2.06 inj_on_complex_a @ poinca837721858l_of_a @ top_top_set_complex ).
% 4.12/2.06
% 4.12/2.06 thf(fact_217_top__set__def,axiom,
% 4.12/2.06 ( top_top_set_a
% 4.12/2.06 = ( collect_a @ top_top_a_o ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_218_top__set__def,axiom,
% 4.12/2.06 ( top_top_set_complex
% 4.12/2.06 = ( collect_complex @ top_top_complex_o ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_219_arc__imp__simple__path,axiom,
% 4.12/2.06 ! [G2: real > a] :
% 4.12/2.06 ( ( path_arc_a @ G2 )
% 4.12/2.06 => ( path_simple_path_a @ G2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_220_arc__imp__simple__path,axiom,
% 4.12/2.06 ! [G2: real > complex] :
% 4.12/2.06 ( ( path_arc_complex @ G2 )
% 4.12/2.06 => ( path_s36253918omplex @ G2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_221_arc__distinct__ends,axiom,
% 4.12/2.06 ! [G2: real > complex] :
% 4.12/2.06 ( ( path_arc_complex @ G2 )
% 4.12/2.06 => ( ( path_p769714271omplex @ G2 )
% 4.12/2.06 != ( path_p797330068omplex @ G2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_222_arc__distinct__ends,axiom,
% 4.12/2.06 ! [G2: real > a] :
% 4.12/2.06 ( ( path_arc_a @ G2 )
% 4.12/2.06 => ( ( path_pathfinish_a @ G2 )
% 4.12/2.06 != ( path_pathstart_a @ G2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_223_bounded__linear_Oaxioms_I2_J,axiom,
% 4.12/2.06 ! [F2: a > complex] :
% 4.12/2.06 ( ( real_V912435428omplex @ F2 )
% 4.12/2.06 => ( real_V451440129omplex @ F2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_224_bounded__linear_Oaxioms_I2_J,axiom,
% 4.12/2.06 ! [F2: complex > a] :
% 4.12/2.06 ( ( real_V762982918plex_a @ F2 )
% 4.12/2.06 => ( real_V301987619plex_a @ F2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_225_UNIV__eq__I,axiom,
% 4.12/2.06 ! [A2: set_a] :
% 4.12/2.06 ( ! [X4: a] : ( member_a @ X4 @ A2 )
% 4.12/2.06 => ( top_top_set_a = A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_226_UNIV__eq__I,axiom,
% 4.12/2.06 ! [A2: set_complex] :
% 4.12/2.06 ( ! [X4: complex] : ( member_complex @ X4 @ A2 )
% 4.12/2.06 => ( top_top_set_complex = A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_227_UNIV__witness,axiom,
% 4.12/2.06 ? [X4: a] : ( member_a @ X4 @ top_top_set_a ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_228_UNIV__witness,axiom,
% 4.12/2.06 ? [X4: complex] : ( member_complex @ X4 @ top_top_set_complex ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_229_simple__path__imp__arc,axiom,
% 4.12/2.06 ! [G2: real > a] :
% 4.12/2.06 ( ( path_simple_path_a @ G2 )
% 4.12/2.06 => ( ( ( path_pathfinish_a @ G2 )
% 4.12/2.06 != ( path_pathstart_a @ G2 ) )
% 4.12/2.06 => ( path_arc_a @ G2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_230_simple__path__imp__arc,axiom,
% 4.12/2.06 ! [G2: real > complex] :
% 4.12/2.06 ( ( path_s36253918omplex @ G2 )
% 4.12/2.06 => ( ( ( path_p769714271omplex @ G2 )
% 4.12/2.06 != ( path_p797330068omplex @ G2 ) )
% 4.12/2.06 => ( path_arc_complex @ G2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_231_simple__path__eq__arc,axiom,
% 4.12/2.06 ! [G2: real > a] :
% 4.12/2.06 ( ( ( path_pathfinish_a @ G2 )
% 4.12/2.06 != ( path_pathstart_a @ G2 ) )
% 4.12/2.06 => ( ( path_simple_path_a @ G2 )
% 4.12/2.06 = ( path_arc_a @ G2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_232_simple__path__eq__arc,axiom,
% 4.12/2.06 ! [G2: real > complex] :
% 4.12/2.06 ( ( ( path_p769714271omplex @ G2 )
% 4.12/2.06 != ( path_p797330068omplex @ G2 ) )
% 4.12/2.06 => ( ( path_s36253918omplex @ G2 )
% 4.12/2.06 = ( path_arc_complex @ G2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_233_simple__path__cases,axiom,
% 4.12/2.06 ! [G2: real > a] :
% 4.12/2.06 ( ( path_simple_path_a @ G2 )
% 4.12/2.06 => ( ( path_arc_a @ G2 )
% 4.12/2.06 | ( ( path_pathfinish_a @ G2 )
% 4.12/2.06 = ( path_pathstart_a @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_234_simple__path__cases,axiom,
% 4.12/2.06 ! [G2: real > complex] :
% 4.12/2.06 ( ( path_s36253918omplex @ G2 )
% 4.12/2.06 => ( ( path_arc_complex @ G2 )
% 4.12/2.06 | ( ( path_p769714271omplex @ G2 )
% 4.12/2.06 = ( path_p797330068omplex @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_235_arc__simple__path,axiom,
% 4.12/2.06 ( path_arc_a
% 4.12/2.06 = ( ^ [G: real > a] :
% 4.12/2.06 ( ( path_simple_path_a @ G )
% 4.12/2.06 & ( ( path_pathfinish_a @ G )
% 4.12/2.06 != ( path_pathstart_a @ G ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_236_arc__simple__path,axiom,
% 4.12/2.06 ( path_arc_complex
% 4.12/2.06 = ( ^ [G: real > complex] :
% 4.12/2.06 ( ( path_s36253918omplex @ G )
% 4.12/2.06 & ( ( path_p769714271omplex @ G )
% 4.12/2.06 != ( path_p797330068omplex @ G ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_237_fun_Omap__comp,axiom,
% 4.12/2.06 ! [G2: complex > complex,F2: a > complex,V: real > a] :
% 4.12/2.06 ( ( comp_c595887981x_real @ G2 @ ( comp_a_complex_real @ F2 @ V ) )
% 4.12/2.06 = ( comp_a_complex_real @ ( comp_c124850173plex_a @ G2 @ F2 ) @ V ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_238_fun_Omap__comp,axiom,
% 4.12/2.06 ! [G2: complex > a,F2: a > complex,V: real > a] :
% 4.12/2.06 ( ( comp_complex_a_real @ G2 @ ( comp_a_complex_real @ F2 @ V ) )
% 4.12/2.06 = ( comp_a_a_real @ ( comp_complex_a_a @ G2 @ F2 ) @ V ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_239_fun_Omap__comp,axiom,
% 4.12/2.06 ! [G2: complex > complex,F2: a > complex,V: complex > a] :
% 4.12/2.06 ( ( comp_c130555887omplex @ G2 @ ( comp_a1063143865omplex @ F2 @ V ) )
% 4.12/2.06 = ( comp_a1063143865omplex @ ( comp_c124850173plex_a @ G2 @ F2 ) @ V ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_240_fun_Omap__comp,axiom,
% 4.12/2.06 ! [G2: complex > a,F2: a > complex,V: complex > a] :
% 4.12/2.06 ( ( comp_c274302683omplex @ G2 @ ( comp_a1063143865omplex @ F2 @ V ) )
% 4.12/2.06 = ( comp_a_a_complex @ ( comp_complex_a_a @ G2 @ F2 ) @ V ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_241_fun_Omap__comp,axiom,
% 4.12/2.06 ! [G2: complex > complex,F2: a > complex,V: a > a] :
% 4.12/2.06 ( ( comp_c124850173plex_a @ G2 @ ( comp_a_complex_a @ F2 @ V ) )
% 4.12/2.06 = ( comp_a_complex_a @ ( comp_c124850173plex_a @ G2 @ F2 ) @ V ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_242_fun_Omap__comp,axiom,
% 4.12/2.06 ! [G2: a > complex,F2: complex > a,V: real > complex] :
% 4.12/2.06 ( ( comp_a_complex_real @ G2 @ ( comp_complex_a_real @ F2 @ V ) )
% 4.12/2.06 = ( comp_c595887981x_real @ ( comp_a1063143865omplex @ G2 @ F2 ) @ V ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_243_fun_Omap__comp,axiom,
% 4.12/2.06 ! [G2: a > complex,F2: real > a,V: real > real] :
% 4.12/2.06 ( ( comp_a_complex_real @ G2 @ ( comp_real_a_real @ F2 @ V ) )
% 4.12/2.06 = ( comp_r701421291x_real @ ( comp_a_complex_real @ G2 @ F2 ) @ V ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_244_fun_Omap__comp,axiom,
% 4.12/2.06 ! [G2: a > complex,F2: a > a,V: real > a] :
% 4.12/2.06 ( ( comp_a_complex_real @ G2 @ ( comp_a_a_real @ F2 @ V ) )
% 4.12/2.06 = ( comp_a_complex_real @ ( comp_a_complex_a @ G2 @ F2 ) @ V ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_245_fun_Omap__comp,axiom,
% 4.12/2.06 ! [G2: a > complex,F2: real > a,V: complex > real] :
% 4.12/2.06 ( ( comp_a1063143865omplex @ G2 @ ( comp_real_a_complex @ F2 @ V ) )
% 4.12/2.06 = ( comp_r667767405omplex @ ( comp_a_complex_real @ G2 @ F2 ) @ V ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_246_fun_Omap__comp,axiom,
% 4.12/2.06 ! [G2: a > complex,F2: complex > a,V: complex > complex] :
% 4.12/2.06 ( ( comp_a1063143865omplex @ G2 @ ( comp_c274302683omplex @ F2 @ V ) )
% 4.12/2.06 = ( comp_c130555887omplex @ ( comp_a1063143865omplex @ G2 @ F2 ) @ V ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_247_complex__of__real__of,axiom,
% 4.12/2.06 ( ( comp_a1063143865omplex @ poinca1910941596x_of_a @ poinca837721858l_of_a )
% 4.12/2.06 = id_complex ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_248_real__of__complex__of,axiom,
% 4.12/2.06 ( ( comp_complex_a_a @ poinca837721858l_of_a @ poinca1910941596x_of_a )
% 4.12/2.06 = id_a ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_249_real__of__bij,axiom,
% 4.12/2.06 bij_betw_complex_a @ poinca837721858l_of_a @ top_top_set_complex @ top_top_set_a ).
% 4.12/2.06
% 4.12/2.06 thf(fact_250_complex__of__bij,axiom,
% 4.12/2.06 bij_betw_a_complex @ poinca1910941596x_of_a @ top_top_set_a @ top_top_set_complex ).
% 4.12/2.06
% 4.12/2.06 thf(fact_251_linear__injective__left__inverse,axiom,
% 4.12/2.06 ! [F2: a > a] :
% 4.12/2.06 ( ( real_V202220639ar_a_a @ F2 )
% 4.12/2.06 => ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 4.12/2.06 => ? [G4: a > a] :
% 4.12/2.06 ( ( real_V202220639ar_a_a @ G4 )
% 4.12/2.06 & ( ( comp_a_a_a @ G4 @ F2 )
% 4.12/2.06 = id_a ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_252_linear__injective__left__inverse,axiom,
% 4.12/2.06 ! [F2: a > complex] :
% 4.12/2.06 ( ( real_V1477106445omplex @ F2 )
% 4.12/2.06 => ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 => ? [G4: complex > a] :
% 4.12/2.06 ( ( real_V1327653935plex_a @ G4 )
% 4.12/2.06 & ( ( comp_complex_a_a @ G4 @ F2 )
% 4.12/2.06 = id_a ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_253_linear__injective__left__inverse,axiom,
% 4.12/2.06 ! [F2: complex > a] :
% 4.12/2.06 ( ( real_V1327653935plex_a @ F2 )
% 4.12/2.06 => ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 4.12/2.06 => ? [G4: a > complex] :
% 4.12/2.06 ( ( real_V1477106445omplex @ G4 )
% 4.12/2.06 & ( ( comp_a1063143865omplex @ G4 @ F2 )
% 4.12/2.06 = id_complex ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_254_path__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: real > a,G2: real > real] :
% 4.12/2.06 ( ( real_V779700657real_a @ F2 )
% 4.12/2.06 => ( ( inj_on_real_a @ F2 @ top_top_set_real )
% 4.12/2.06 => ( ( path_path_a @ ( comp_real_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_path_real @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_255_path__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: a > a,G2: real > a] :
% 4.12/2.06 ( ( real_V202220639ar_a_a @ F2 )
% 4.12/2.06 => ( ( inj_on_a_a @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( path_path_a @ ( comp_a_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_path_a @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_256_path__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: complex > complex,G2: real > complex] :
% 4.12/2.06 ( ( real_V670066493omplex @ F2 )
% 4.12/2.06 => ( ( inj_on94911183omplex @ F2 @ top_top_set_complex )
% 4.12/2.06 => ( ( path_path_complex @ ( comp_c595887981x_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_path_complex @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_257_path__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: a > complex,G2: real > a] :
% 4.12/2.06 ( ( real_V1477106445omplex @ F2 )
% 4.12/2.06 => ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 => ( ( path_path_complex @ ( comp_a_complex_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_path_a @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_258_path__linear__image__eq,axiom,
% 4.12/2.06 ! [F2: complex > a,G2: real > complex] :
% 4.12/2.06 ( ( real_V1327653935plex_a @ F2 )
% 4.12/2.06 => ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 4.12/2.06 => ( ( path_path_a @ ( comp_complex_a_real @ F2 @ G2 ) )
% 4.12/2.06 = ( path_path_complex @ G2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_259_linear__inj__iff__eq__0,axiom,
% 4.12/2.06 ! [F2: a > complex] :
% 4.12/2.06 ( ( real_V1477106445omplex @ F2 )
% 4.12/2.06 => ( ( inj_on_a_complex @ F2 @ top_top_set_a )
% 4.12/2.06 = ( ! [X: a] :
% 4.12/2.06 ( ( ( F2 @ X )
% 4.12/2.06 = zero_zero_complex )
% 4.12/2.06 => ( X = zero_zero_a ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_260_linear__inj__iff__eq__0,axiom,
% 4.12/2.06 ! [F2: complex > a] :
% 4.12/2.06 ( ( real_V1327653935plex_a @ F2 )
% 4.12/2.06 => ( ( inj_on_complex_a @ F2 @ top_top_set_complex )
% 4.12/2.06 = ( ! [X: complex] :
% 4.12/2.06 ( ( ( F2 @ X )
% 4.12/2.06 = zero_zero_a )
% 4.12/2.06 => ( X = zero_zero_complex ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_261_type__copy__map__cong0,axiom,
% 4.12/2.06 ! [M: real > a,G2: real > real,X2: real,N: a > a,H: real > a,F2: a > complex] :
% 4.12/2.06 ( ( ( M @ ( G2 @ X2 ) )
% 4.12/2.06 = ( N @ ( H @ X2 ) ) )
% 4.12/2.06 => ( ( comp_r701421291x_real @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
% 4.12/2.06 = ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_262_type__copy__map__cong0,axiom,
% 4.12/2.06 ! [M: real > a,G2: complex > real,X2: complex,N: a > a,H: complex > a,F2: a > complex] :
% 4.12/2.06 ( ( ( M @ ( G2 @ X2 ) )
% 4.12/2.06 = ( N @ ( H @ X2 ) ) )
% 4.12/2.06 => ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
% 4.12/2.06 = ( comp_a1063143865omplex @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_263_type__copy__map__cong0,axiom,
% 4.12/2.06 ! [M: real > a,G2: a > real,X2: a,N: a > a,H: a > a,F2: a > complex] :
% 4.12/2.06 ( ( ( M @ ( G2 @ X2 ) )
% 4.12/2.06 = ( N @ ( H @ X2 ) ) )
% 4.12/2.06 => ( ( comp_real_complex_a @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
% 4.12/2.06 = ( comp_a_complex_a @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_264_type__copy__map__cong0,axiom,
% 4.12/2.06 ! [M: complex > a,G2: real > complex,X2: real,N: a > a,H: real > a,F2: a > complex] :
% 4.12/2.06 ( ( ( M @ ( G2 @ X2 ) )
% 4.12/2.06 = ( N @ ( H @ X2 ) ) )
% 4.12/2.06 => ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ M ) @ G2 @ X2 )
% 4.12/2.06 = ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_265_type__copy__map__cong0,axiom,
% 4.12/2.06 ! [M: complex > a,G2: complex > complex,X2: complex,N: a > a,H: complex > a,F2: a > complex] :
% 4.12/2.06 ( ( ( M @ ( G2 @ X2 ) )
% 4.12/2.06 = ( N @ ( H @ X2 ) ) )
% 4.12/2.06 => ( ( comp_c130555887omplex @ ( comp_a1063143865omplex @ F2 @ M ) @ G2 @ X2 )
% 4.12/2.06 = ( comp_a1063143865omplex @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_266_type__copy__map__cong0,axiom,
% 4.12/2.06 ! [M: complex > a,G2: a > complex,X2: a,N: a > a,H: a > a,F2: a > complex] :
% 4.12/2.06 ( ( ( M @ ( G2 @ X2 ) )
% 4.12/2.06 = ( N @ ( H @ X2 ) ) )
% 4.12/2.06 => ( ( comp_c124850173plex_a @ ( comp_a1063143865omplex @ F2 @ M ) @ G2 @ X2 )
% 4.12/2.06 = ( comp_a_complex_a @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_267_type__copy__map__cong0,axiom,
% 4.12/2.06 ! [M: real > real,G2: a > real,X2: a,N: complex > real,H: a > complex,F2: real > a] :
% 4.12/2.06 ( ( ( M @ ( G2 @ X2 ) )
% 4.12/2.06 = ( N @ ( H @ X2 ) ) )
% 4.12/2.06 => ( ( comp_real_a_a @ ( comp_real_a_real @ F2 @ M ) @ G2 @ X2 )
% 4.12/2.06 = ( comp_complex_a_a @ ( comp_real_a_complex @ F2 @ N ) @ H @ X2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_268_type__copy__map__cong0,axiom,
% 4.12/2.06 ! [M: real > real,G2: complex > real,X2: complex,N: a > real,H: complex > a,F2: real > a] :
% 4.12/2.06 ( ( ( M @ ( G2 @ X2 ) )
% 4.12/2.06 = ( N @ ( H @ X2 ) ) )
% 4.12/2.06 => ( ( comp_real_a_complex @ ( comp_real_a_real @ F2 @ M ) @ G2 @ X2 )
% 4.12/2.06 = ( comp_a_a_complex @ ( comp_real_a_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_269_type__copy__map__cong0,axiom,
% 4.12/2.06 ! [M: real > real,G2: a > real,X2: a,N: a > real,H: a > a,F2: real > a] :
% 4.12/2.06 ( ( ( M @ ( G2 @ X2 ) )
% 4.12/2.06 = ( N @ ( H @ X2 ) ) )
% 4.12/2.06 => ( ( comp_real_a_a @ ( comp_real_a_real @ F2 @ M ) @ G2 @ X2 )
% 4.12/2.06 = ( comp_a_a_a @ ( comp_real_a_a @ F2 @ N ) @ H @ X2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_270_type__copy__map__cong0,axiom,
% 4.12/2.06 ! [M: complex > a,G2: real > complex,X2: real,N: real > a,H: real > real,F2: a > a] :
% 4.12/2.06 ( ( ( M @ ( G2 @ X2 ) )
% 4.12/2.06 = ( N @ ( H @ X2 ) ) )
% 4.12/2.06 => ( ( comp_complex_a_real @ ( comp_a_a_complex @ F2 @ M ) @ G2 @ X2 )
% 4.12/2.06 = ( comp_real_a_real @ ( comp_a_a_real @ F2 @ N ) @ H @ X2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_271_id__apply,axiom,
% 4.12/2.06 ( id_complex
% 4.12/2.06 = ( ^ [X: complex] : X ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_272_id__apply,axiom,
% 4.12/2.06 ( id_a
% 4.12/2.06 = ( ^ [X: a] : X ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_273_path__rectpath,axiom,
% 4.12/2.06 ! [A: complex,B: complex] : ( path_path_complex @ ( path_rectpath @ A @ B ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_274_comp__id,axiom,
% 4.12/2.06 ! [F2: real > a] :
% 4.12/2.06 ( ( comp_real_a_real @ F2 @ id_real )
% 4.12/2.06 = F2 ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_275_comp__id,axiom,
% 4.12/2.06 ! [F2: a > complex] :
% 4.12/2.06 ( ( comp_a_complex_a @ F2 @ id_a )
% 4.12/2.06 = F2 ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_276_comp__id,axiom,
% 4.12/2.06 ! [F2: a > a] :
% 4.12/2.06 ( ( comp_a_a_a @ F2 @ id_a )
% 4.12/2.06 = F2 ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_277_id__comp,axiom,
% 4.12/2.06 ! [G2: complex > a] :
% 4.12/2.06 ( ( comp_a_a_complex @ id_a @ G2 )
% 4.12/2.06 = G2 ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_278_id__comp,axiom,
% 4.12/2.06 ! [G2: real > a] :
% 4.12/2.06 ( ( comp_a_a_real @ id_a @ G2 )
% 4.12/2.06 = G2 ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_279_id__comp,axiom,
% 4.12/2.06 ! [G2: a > a] :
% 4.12/2.06 ( ( comp_a_a_a @ id_a @ G2 )
% 4.12/2.06 = G2 ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_280_fun_Omap__id,axiom,
% 4.12/2.06 ! [T: complex > a] :
% 4.12/2.06 ( ( comp_a_a_complex @ id_a @ T )
% 4.12/2.06 = T ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_281_fun_Omap__id,axiom,
% 4.12/2.06 ! [T: real > a] :
% 4.12/2.06 ( ( comp_a_a_real @ id_a @ T )
% 4.12/2.06 = T ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_282_fun_Omap__id,axiom,
% 4.12/2.06 ! [T: a > a] :
% 4.12/2.06 ( ( comp_a_a_a @ id_a @ T )
% 4.12/2.06 = T ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_283_bij__betw__id,axiom,
% 4.12/2.06 ! [A2: set_complex] : ( bij_be209634132omplex @ id_complex @ A2 @ A2 ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_284_bij__betw__id,axiom,
% 4.12/2.06 ! [A2: set_a] : ( bij_betw_a_a @ id_a @ A2 @ A2 ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_285_bij__id,axiom,
% 4.12/2.06 bij_betw_a_a @ id_a @ top_top_set_a @ top_top_set_a ).
% 4.12/2.06
% 4.12/2.06 thf(fact_286_bij__id,axiom,
% 4.12/2.06 bij_be209634132omplex @ id_complex @ top_top_set_complex @ top_top_set_complex ).
% 4.12/2.06
% 4.12/2.06 thf(fact_287_DEADID_Oin__rel,axiom,
% 4.12/2.06 ( ( ^ [Y4: a,Z: a] : ( Y4 = Z ) )
% 4.12/2.06 = ( ^ [A6: a,B2: a] :
% 4.12/2.06 ? [Z2: a] :
% 4.12/2.06 ( ( member_a @ Z2 @ top_top_set_a )
% 4.12/2.06 & ( ( id_a @ Z2 )
% 4.12/2.06 = A6 )
% 4.12/2.06 & ( ( id_a @ Z2 )
% 4.12/2.06 = B2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_288_DEADID_Oin__rel,axiom,
% 4.12/2.06 ( ( ^ [Y4: complex,Z: complex] : ( Y4 = Z ) )
% 4.12/2.06 = ( ^ [A6: complex,B2: complex] :
% 4.12/2.06 ? [Z2: complex] :
% 4.12/2.06 ( ( member_complex @ Z2 @ top_top_set_complex )
% 4.12/2.06 & ( ( id_complex @ Z2 )
% 4.12/2.06 = A6 )
% 4.12/2.06 & ( ( id_complex @ Z2 )
% 4.12/2.06 = B2 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_289_fun_Omap__id0,axiom,
% 4.12/2.06 ( ( comp_a_a_complex @ id_a )
% 4.12/2.06 = id_complex_a ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_290_fun_Omap__id0,axiom,
% 4.12/2.06 ( ( comp_a_a_real @ id_a )
% 4.12/2.06 = id_real_a ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_291_fun_Omap__id0,axiom,
% 4.12/2.06 ( ( comp_a_a_a @ id_a )
% 4.12/2.06 = id_a_a ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_292_id__def,axiom,
% 4.12/2.06 ( id_complex
% 4.12/2.06 = ( ^ [X: complex] : X ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_293_id__def,axiom,
% 4.12/2.06 ( id_a
% 4.12/2.06 = ( ^ [X: a] : X ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_294_bij__betwE,axiom,
% 4.12/2.06 ! [F2: complex > a,A2: set_complex,B3: set_a] :
% 4.12/2.06 ( ( bij_betw_complex_a @ F2 @ A2 @ B3 )
% 4.12/2.06 => ! [X5: complex] :
% 4.12/2.06 ( ( member_complex @ X5 @ A2 )
% 4.12/2.06 => ( member_a @ ( F2 @ X5 ) @ B3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_295_bij__betwE,axiom,
% 4.12/2.06 ! [F2: a > complex,A2: set_a,B3: set_complex] :
% 4.12/2.06 ( ( bij_betw_a_complex @ F2 @ A2 @ B3 )
% 4.12/2.06 => ! [X5: a] :
% 4.12/2.06 ( ( member_a @ X5 @ A2 )
% 4.12/2.06 => ( member_complex @ ( F2 @ X5 ) @ B3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_296_eq__id__iff,axiom,
% 4.12/2.06 ! [F2: complex > complex] :
% 4.12/2.06 ( ( ! [X: complex] :
% 4.12/2.06 ( ( F2 @ X )
% 4.12/2.06 = X ) )
% 4.12/2.06 = ( F2 = id_complex ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_297_eq__id__iff,axiom,
% 4.12/2.06 ! [F2: a > a] :
% 4.12/2.06 ( ( ! [X: a] :
% 4.12/2.06 ( ( F2 @ X )
% 4.12/2.06 = X ) )
% 4.12/2.06 = ( F2 = id_a ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_298_bij__betw__inv,axiom,
% 4.12/2.06 ! [F2: complex > a,A2: set_complex,B3: set_a] :
% 4.12/2.06 ( ( bij_betw_complex_a @ F2 @ A2 @ B3 )
% 4.12/2.06 => ? [G4: a > complex] : ( bij_betw_a_complex @ G4 @ B3 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_299_bij__betw__inv,axiom,
% 4.12/2.06 ! [F2: a > complex,A2: set_a,B3: set_complex] :
% 4.12/2.06 ( ( bij_betw_a_complex @ F2 @ A2 @ B3 )
% 4.12/2.06 => ? [G4: complex > a] : ( bij_betw_complex_a @ G4 @ B3 @ A2 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_300_bij__betw__cong,axiom,
% 4.12/2.06 ! [A2: set_complex,F2: complex > a,G2: complex > a,A7: set_a] :
% 4.12/2.06 ( ! [A5: complex] :
% 4.12/2.06 ( ( member_complex @ A5 @ A2 )
% 4.12/2.06 => ( ( F2 @ A5 )
% 4.12/2.06 = ( G2 @ A5 ) ) )
% 4.12/2.06 => ( ( bij_betw_complex_a @ F2 @ A2 @ A7 )
% 4.12/2.06 = ( bij_betw_complex_a @ G2 @ A2 @ A7 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_301_bij__betw__cong,axiom,
% 4.12/2.06 ! [A2: set_a,F2: a > complex,G2: a > complex,A7: set_complex] :
% 4.12/2.06 ( ! [A5: a] :
% 4.12/2.06 ( ( member_a @ A5 @ A2 )
% 4.12/2.06 => ( ( F2 @ A5 )
% 4.12/2.06 = ( G2 @ A5 ) ) )
% 4.12/2.06 => ( ( bij_betw_a_complex @ F2 @ A2 @ A7 )
% 4.12/2.06 = ( bij_betw_a_complex @ G2 @ A2 @ A7 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_302_bij__betw__apply,axiom,
% 4.12/2.06 ! [F2: complex > a,A2: set_complex,B3: set_a,A: complex] :
% 4.12/2.06 ( ( bij_betw_complex_a @ F2 @ A2 @ B3 )
% 4.12/2.06 => ( ( member_complex @ A @ A2 )
% 4.12/2.06 => ( member_a @ ( F2 @ A ) @ B3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_303_bij__betw__apply,axiom,
% 4.12/2.06 ! [F2: a > complex,A2: set_a,B3: set_complex,A: a] :
% 4.12/2.06 ( ( bij_betw_a_complex @ F2 @ A2 @ B3 )
% 4.12/2.06 => ( ( member_a @ A @ A2 )
% 4.12/2.06 => ( member_complex @ ( F2 @ A ) @ B3 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_304_bij__betw__id__iff,axiom,
% 4.12/2.06 ! [A2: set_complex,B3: set_complex] :
% 4.12/2.06 ( ( bij_be209634132omplex @ id_complex @ A2 @ B3 )
% 4.12/2.06 = ( A2 = B3 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_305_bij__betw__id__iff,axiom,
% 4.12/2.06 ! [A2: set_a,B3: set_a] :
% 4.12/2.06 ( ( bij_betw_a_a @ id_a @ A2 @ B3 )
% 4.12/2.06 = ( A2 = B3 ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_306_bij__betw__iff__bijections,axiom,
% 4.12/2.06 ( bij_betw_complex_a
% 4.12/2.06 = ( ^ [F: complex > a,A4: set_complex,B4: set_a] :
% 4.12/2.06 ? [G: a > complex] :
% 4.12/2.06 ( ! [X: complex] :
% 4.12/2.06 ( ( member_complex @ X @ A4 )
% 4.12/2.06 => ( ( member_a @ ( F @ X ) @ B4 )
% 4.12/2.06 & ( ( G @ ( F @ X ) )
% 4.12/2.06 = X ) ) )
% 4.12/2.06 & ! [X: a] :
% 4.12/2.06 ( ( member_a @ X @ B4 )
% 4.12/2.06 => ( ( member_complex @ ( G @ X ) @ A4 )
% 4.12/2.06 & ( ( F @ ( G @ X ) )
% 4.12/2.06 = X ) ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_307_bij__betw__iff__bijections,axiom,
% 4.12/2.06 ( bij_betw_a_complex
% 4.12/2.06 = ( ^ [F: a > complex,A4: set_a,B4: set_complex] :
% 4.12/2.06 ? [G: complex > a] :
% 4.12/2.06 ( ! [X: a] :
% 4.12/2.06 ( ( member_a @ X @ A4 )
% 4.12/2.06 => ( ( member_complex @ ( F @ X ) @ B4 )
% 4.12/2.06 & ( ( G @ ( F @ X ) )
% 4.12/2.06 = X ) ) )
% 4.12/2.06 & ! [X: complex] :
% 4.12/2.06 ( ( member_complex @ X @ B4 )
% 4.12/2.06 => ( ( member_a @ ( G @ X ) @ A4 )
% 4.12/2.06 & ( ( F @ ( G @ X ) )
% 4.12/2.06 = X ) ) ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_308_o__bij,axiom,
% 4.12/2.06 ! [G2: a > a,F2: a > a] :
% 4.12/2.06 ( ( ( comp_a_a_a @ G2 @ F2 )
% 4.12/2.06 = id_a )
% 4.12/2.06 => ( ( ( comp_a_a_a @ F2 @ G2 )
% 4.12/2.06 = id_a )
% 4.12/2.06 => ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_309_o__bij,axiom,
% 4.12/2.06 ! [G2: complex > a,F2: a > complex] :
% 4.12/2.06 ( ( ( comp_complex_a_a @ G2 @ F2 )
% 4.12/2.06 = id_a )
% 4.12/2.06 => ( ( ( comp_a1063143865omplex @ F2 @ G2 )
% 4.12/2.06 = id_complex )
% 4.12/2.06 => ( bij_betw_a_complex @ F2 @ top_top_set_a @ top_top_set_complex ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_310_o__bij,axiom,
% 4.12/2.06 ! [G2: a > complex,F2: complex > a] :
% 4.12/2.06 ( ( ( comp_a1063143865omplex @ G2 @ F2 )
% 4.12/2.06 = id_complex )
% 4.12/2.06 => ( ( ( comp_complex_a_a @ F2 @ G2 )
% 4.12/2.06 = id_a )
% 4.12/2.06 => ( bij_betw_complex_a @ F2 @ top_top_set_complex @ top_top_set_a ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_311_o__bij,axiom,
% 4.12/2.06 ! [G2: complex > complex,F2: complex > complex] :
% 4.12/2.06 ( ( ( comp_c130555887omplex @ G2 @ F2 )
% 4.12/2.06 = id_complex )
% 4.12/2.06 => ( ( ( comp_c130555887omplex @ F2 @ G2 )
% 4.12/2.06 = id_complex )
% 4.12/2.06 => ( bij_be209634132omplex @ F2 @ top_top_set_complex @ top_top_set_complex ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_312_bij__pointE,axiom,
% 4.12/2.06 ! [F2: a > a,Y: a] :
% 4.12/2.06 ( ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a )
% 4.12/2.06 => ~ ! [X4: a] :
% 4.12/2.06 ( ( Y
% 4.12/2.06 = ( F2 @ X4 ) )
% 4.12/2.06 => ~ ! [X6: a] :
% 4.12/2.06 ( ( Y
% 4.12/2.06 = ( F2 @ X6 ) )
% 4.12/2.06 => ( X6 = X4 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_313_bij__pointE,axiom,
% 4.12/2.06 ! [F2: a > complex,Y: complex] :
% 4.12/2.06 ( ( bij_betw_a_complex @ F2 @ top_top_set_a @ top_top_set_complex )
% 4.12/2.06 => ~ ! [X4: a] :
% 4.12/2.06 ( ( Y
% 4.12/2.06 = ( F2 @ X4 ) )
% 4.12/2.06 => ~ ! [X6: a] :
% 4.12/2.06 ( ( Y
% 4.12/2.06 = ( F2 @ X6 ) )
% 4.12/2.06 => ( X6 = X4 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_314_bij__pointE,axiom,
% 4.12/2.06 ! [F2: complex > a,Y: a] :
% 4.12/2.06 ( ( bij_betw_complex_a @ F2 @ top_top_set_complex @ top_top_set_a )
% 4.12/2.06 => ~ ! [X4: complex] :
% 4.12/2.06 ( ( Y
% 4.12/2.06 = ( F2 @ X4 ) )
% 4.12/2.06 => ~ ! [X6: complex] :
% 4.12/2.06 ( ( Y
% 4.12/2.06 = ( F2 @ X6 ) )
% 4.12/2.06 => ( X6 = X4 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_315_bij__pointE,axiom,
% 4.12/2.06 ! [F2: complex > complex,Y: complex] :
% 4.12/2.06 ( ( bij_be209634132omplex @ F2 @ top_top_set_complex @ top_top_set_complex )
% 4.12/2.06 => ~ ! [X4: complex] :
% 4.12/2.06 ( ( Y
% 4.12/2.06 = ( F2 @ X4 ) )
% 4.12/2.06 => ~ ! [X6: complex] :
% 4.12/2.06 ( ( Y
% 4.12/2.06 = ( F2 @ X6 ) )
% 4.12/2.06 => ( X6 = X4 ) ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_316_bij__betw__trans,axiom,
% 4.12/2.06 ! [F2: real > real,A2: set_real,B3: set_real,G2: real > a,C2: set_a] :
% 4.12/2.06 ( ( bij_betw_real_real @ F2 @ A2 @ B3 )
% 4.12/2.06 => ( ( bij_betw_real_a @ G2 @ B3 @ C2 )
% 4.12/2.06 => ( bij_betw_real_a @ ( comp_real_a_real @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_317_bij__betw__trans,axiom,
% 4.12/2.06 ! [F2: real > a,A2: set_real,B3: set_a,G2: a > a,C2: set_a] :
% 4.12/2.06 ( ( bij_betw_real_a @ F2 @ A2 @ B3 )
% 4.12/2.06 => ( ( bij_betw_a_a @ G2 @ B3 @ C2 )
% 4.12/2.06 => ( bij_betw_real_a @ ( comp_a_a_real @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_318_bij__betw__trans,axiom,
% 4.12/2.06 ! [F2: a > a,A2: set_a,B3: set_a,G2: a > a,C2: set_a] :
% 4.12/2.06 ( ( bij_betw_a_a @ F2 @ A2 @ B3 )
% 4.12/2.06 => ( ( bij_betw_a_a @ G2 @ B3 @ C2 )
% 4.12/2.06 => ( bij_betw_a_a @ ( comp_a_a_a @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_319_bij__betw__trans,axiom,
% 4.12/2.06 ! [F2: complex > complex,A2: set_complex,B3: set_complex,G2: complex > a,C2: set_a] :
% 4.12/2.06 ( ( bij_be209634132omplex @ F2 @ A2 @ B3 )
% 4.12/2.06 => ( ( bij_betw_complex_a @ G2 @ B3 @ C2 )
% 4.12/2.06 => ( bij_betw_complex_a @ ( comp_c274302683omplex @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_320_bij__betw__trans,axiom,
% 4.12/2.06 ! [F2: real > a,A2: set_real,B3: set_a,G2: a > complex,C2: set_complex] :
% 4.12/2.06 ( ( bij_betw_real_a @ F2 @ A2 @ B3 )
% 4.12/2.06 => ( ( bij_betw_a_complex @ G2 @ B3 @ C2 )
% 4.12/2.06 => ( bij_be122140626omplex @ ( comp_a_complex_real @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_321_bij__betw__trans,axiom,
% 4.12/2.06 ! [F2: a > a,A2: set_a,B3: set_a,G2: a > complex,C2: set_complex] :
% 4.12/2.06 ( ( bij_betw_a_a @ F2 @ A2 @ B3 )
% 4.12/2.06 => ( ( bij_betw_a_complex @ G2 @ B3 @ C2 )
% 4.12/2.06 => ( bij_betw_a_complex @ ( comp_a_complex_a @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_322_bij__betw__trans,axiom,
% 4.12/2.06 ! [F2: complex > a,A2: set_complex,B3: set_a,G2: a > a,C2: set_a] :
% 4.12/2.06 ( ( bij_betw_complex_a @ F2 @ A2 @ B3 )
% 4.12/2.06 => ( ( bij_betw_a_a @ G2 @ B3 @ C2 )
% 4.12/2.06 => ( bij_betw_complex_a @ ( comp_a_a_complex @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_323_bij__betw__trans,axiom,
% 4.12/2.06 ! [F2: complex > a,A2: set_complex,B3: set_a,G2: a > complex,C2: set_complex] :
% 4.12/2.06 ( ( bij_betw_complex_a @ F2 @ A2 @ B3 )
% 4.12/2.06 => ( ( bij_betw_a_complex @ G2 @ B3 @ C2 )
% 4.12/2.06 => ( bij_be209634132omplex @ ( comp_a1063143865omplex @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_324_bij__betw__trans,axiom,
% 4.12/2.06 ! [F2: a > complex,A2: set_a,B3: set_complex,G2: complex > complex,C2: set_complex] :
% 4.12/2.06 ( ( bij_betw_a_complex @ F2 @ A2 @ B3 )
% 4.12/2.06 => ( ( bij_be209634132omplex @ G2 @ B3 @ C2 )
% 4.12/2.06 => ( bij_betw_a_complex @ ( comp_c124850173plex_a @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_325_bij__betw__trans,axiom,
% 4.12/2.06 ! [F2: a > complex,A2: set_a,B3: set_complex,G2: complex > a,C2: set_a] :
% 4.12/2.06 ( ( bij_betw_a_complex @ F2 @ A2 @ B3 )
% 4.12/2.06 => ( ( bij_betw_complex_a @ G2 @ B3 @ C2 )
% 4.12/2.06 => ( bij_betw_a_a @ ( comp_complex_a_a @ G2 @ F2 ) @ A2 @ C2 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_326_bij__betw__comp__iff,axiom,
% 4.12/2.06 ! [F2: real > real,A2: set_real,A7: set_real,F3: real > a,A8: set_a] :
% 4.12/2.06 ( ( bij_betw_real_real @ F2 @ A2 @ A7 )
% 4.12/2.06 => ( ( bij_betw_real_a @ F3 @ A7 @ A8 )
% 4.12/2.06 = ( bij_betw_real_a @ ( comp_real_a_real @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_327_bij__betw__comp__iff,axiom,
% 4.12/2.06 ! [F2: real > a,A2: set_real,A7: set_a,F3: a > a,A8: set_a] :
% 4.12/2.06 ( ( bij_betw_real_a @ F2 @ A2 @ A7 )
% 4.12/2.06 => ( ( bij_betw_a_a @ F3 @ A7 @ A8 )
% 4.12/2.06 = ( bij_betw_real_a @ ( comp_a_a_real @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_328_bij__betw__comp__iff,axiom,
% 4.12/2.06 ! [F2: a > a,A2: set_a,A7: set_a,F3: a > a,A8: set_a] :
% 4.12/2.06 ( ( bij_betw_a_a @ F2 @ A2 @ A7 )
% 4.12/2.06 => ( ( bij_betw_a_a @ F3 @ A7 @ A8 )
% 4.12/2.06 = ( bij_betw_a_a @ ( comp_a_a_a @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_329_bij__betw__comp__iff,axiom,
% 4.12/2.06 ! [F2: complex > complex,A2: set_complex,A7: set_complex,F3: complex > a,A8: set_a] :
% 4.12/2.06 ( ( bij_be209634132omplex @ F2 @ A2 @ A7 )
% 4.12/2.06 => ( ( bij_betw_complex_a @ F3 @ A7 @ A8 )
% 4.12/2.06 = ( bij_betw_complex_a @ ( comp_c274302683omplex @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_330_bij__betw__comp__iff,axiom,
% 4.12/2.06 ! [F2: real > a,A2: set_real,A7: set_a,F3: a > complex,A8: set_complex] :
% 4.12/2.06 ( ( bij_betw_real_a @ F2 @ A2 @ A7 )
% 4.12/2.06 => ( ( bij_betw_a_complex @ F3 @ A7 @ A8 )
% 4.12/2.06 = ( bij_be122140626omplex @ ( comp_a_complex_real @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_331_bij__betw__comp__iff,axiom,
% 4.12/2.06 ! [F2: a > a,A2: set_a,A7: set_a,F3: a > complex,A8: set_complex] :
% 4.12/2.06 ( ( bij_betw_a_a @ F2 @ A2 @ A7 )
% 4.12/2.06 => ( ( bij_betw_a_complex @ F3 @ A7 @ A8 )
% 4.12/2.06 = ( bij_betw_a_complex @ ( comp_a_complex_a @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_332_bij__betw__comp__iff,axiom,
% 4.12/2.06 ! [F2: complex > a,A2: set_complex,A7: set_a,F3: a > a,A8: set_a] :
% 4.12/2.06 ( ( bij_betw_complex_a @ F2 @ A2 @ A7 )
% 4.12/2.06 => ( ( bij_betw_a_a @ F3 @ A7 @ A8 )
% 4.12/2.06 = ( bij_betw_complex_a @ ( comp_a_a_complex @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_333_bij__betw__comp__iff,axiom,
% 4.12/2.06 ! [F2: complex > a,A2: set_complex,A7: set_a,F3: a > complex,A8: set_complex] :
% 4.12/2.06 ( ( bij_betw_complex_a @ F2 @ A2 @ A7 )
% 4.12/2.06 => ( ( bij_betw_a_complex @ F3 @ A7 @ A8 )
% 4.12/2.06 = ( bij_be209634132omplex @ ( comp_a1063143865omplex @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_334_bij__betw__comp__iff,axiom,
% 4.12/2.06 ! [F2: a > complex,A2: set_a,A7: set_complex,F3: complex > complex,A8: set_complex] :
% 4.12/2.06 ( ( bij_betw_a_complex @ F2 @ A2 @ A7 )
% 4.12/2.06 => ( ( bij_be209634132omplex @ F3 @ A7 @ A8 )
% 4.12/2.06 = ( bij_betw_a_complex @ ( comp_c124850173plex_a @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_335_bij__betw__comp__iff,axiom,
% 4.12/2.06 ! [F2: a > complex,A2: set_a,A7: set_complex,F3: complex > a,A8: set_a] :
% 4.12/2.06 ( ( bij_betw_a_complex @ F2 @ A2 @ A7 )
% 4.12/2.06 => ( ( bij_betw_complex_a @ F3 @ A7 @ A8 )
% 4.12/2.06 = ( bij_betw_a_a @ ( comp_complex_a_a @ F3 @ F2 ) @ A2 @ A8 ) ) ) ).
% 4.12/2.06
% 4.12/2.06 thf(fact_336_bij__betw__imp__inj__on,axiom,
% 4.12/2.06 ! [F2: complex > a,A2: set_complex,B3: set_a] :
% 4.12/2.06 ( ( bij_betw_complex_a @ F2 @ A2 @ B3 )
% 4.12/2.07 => ( inj_on_complex_a @ F2 @ A2 ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_337_bij__betw__imp__inj__on,axiom,
% 4.12/2.07 ! [F2: a > complex,A2: set_a,B3: set_complex] :
% 4.12/2.07 ( ( bij_betw_a_complex @ F2 @ A2 @ B3 )
% 4.12/2.07 => ( inj_on_a_complex @ F2 @ A2 ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_338_pointfree__idE,axiom,
% 4.12/2.07 ! [F2: a > complex,G2: complex > a,X2: complex] :
% 4.12/2.07 ( ( ( comp_a1063143865omplex @ F2 @ G2 )
% 4.12/2.07 = id_complex )
% 4.12/2.07 => ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.07 = X2 ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_339_pointfree__idE,axiom,
% 4.12/2.07 ! [F2: complex > a,G2: a > complex,X2: a] :
% 4.12/2.07 ( ( ( comp_complex_a_a @ F2 @ G2 )
% 4.12/2.07 = id_a )
% 4.12/2.07 => ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.07 = X2 ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_340_pointfree__idE,axiom,
% 4.12/2.07 ! [F2: a > a,G2: a > a,X2: a] :
% 4.12/2.07 ( ( ( comp_a_a_a @ F2 @ G2 )
% 4.12/2.07 = id_a )
% 4.12/2.07 => ( ( F2 @ ( G2 @ X2 ) )
% 4.12/2.07 = X2 ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_341_comp__eq__id__dest,axiom,
% 4.12/2.07 ! [A: a > complex,B: real > a,C: real > complex,V: real] :
% 4.12/2.07 ( ( ( comp_a_complex_real @ A @ B )
% 4.12/2.07 = ( comp_c595887981x_real @ id_complex @ C ) )
% 4.12/2.07 => ( ( A @ ( B @ V ) )
% 4.12/2.07 = ( C @ V ) ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_342_comp__eq__id__dest,axiom,
% 4.12/2.07 ! [A: a > complex,B: complex > a,C: complex > complex,V: complex] :
% 4.12/2.07 ( ( ( comp_a1063143865omplex @ A @ B )
% 4.12/2.07 = ( comp_c130555887omplex @ id_complex @ C ) )
% 4.12/2.07 => ( ( A @ ( B @ V ) )
% 4.12/2.07 = ( C @ V ) ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_343_comp__eq__id__dest,axiom,
% 4.12/2.07 ! [A: complex > a,B: a > complex,C: a > a,V: a] :
% 4.12/2.07 ( ( ( comp_complex_a_a @ A @ B )
% 4.12/2.07 = ( comp_a_a_a @ id_a @ C ) )
% 4.12/2.07 => ( ( A @ ( B @ V ) )
% 4.12/2.07 = ( C @ V ) ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_344_comp__eq__id__dest,axiom,
% 4.12/2.07 ! [A: real > a,B: real > real,C: real > a,V: real] :
% 4.12/2.07 ( ( ( comp_real_a_real @ A @ B )
% 4.12/2.07 = ( comp_a_a_real @ id_a @ C ) )
% 4.12/2.07 => ( ( A @ ( B @ V ) )
% 4.12/2.07 = ( C @ V ) ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_345_comp__eq__id__dest,axiom,
% 4.12/2.07 ! [A: a > complex,B: a > a,C: a > complex,V: a] :
% 4.12/2.07 ( ( ( comp_a_complex_a @ A @ B )
% 4.12/2.07 = ( comp_c124850173plex_a @ id_complex @ C ) )
% 4.12/2.07 => ( ( A @ ( B @ V ) )
% 4.12/2.07 = ( C @ V ) ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_346_comp__eq__id__dest,axiom,
% 4.12/2.07 ! [A: a > a,B: complex > a,C: complex > a,V: complex] :
% 4.12/2.07 ( ( ( comp_a_a_complex @ A @ B )
% 4.12/2.07 = ( comp_a_a_complex @ id_a @ C ) )
% 4.12/2.07 => ( ( A @ ( B @ V ) )
% 4.12/2.07 = ( C @ V ) ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_347_comp__eq__id__dest,axiom,
% 4.12/2.07 ! [A: a > a,B: real > a,C: real > a,V: real] :
% 4.12/2.07 ( ( ( comp_a_a_real @ A @ B )
% 4.12/2.07 = ( comp_a_a_real @ id_a @ C ) )
% 4.12/2.07 => ( ( A @ ( B @ V ) )
% 4.12/2.07 = ( C @ V ) ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_348_comp__eq__id__dest,axiom,
% 4.12/2.07 ! [A: a > a,B: a > a,C: a > a,V: a] :
% 4.12/2.07 ( ( ( comp_a_a_a @ A @ B )
% 4.12/2.07 = ( comp_a_a_a @ id_a @ C ) )
% 4.12/2.07 => ( ( A @ ( B @ V ) )
% 4.12/2.07 = ( C @ V ) ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_349_arc__imp__path,axiom,
% 4.12/2.07 ! [G2: real > complex] :
% 4.12/2.07 ( ( path_arc_complex @ G2 )
% 4.12/2.07 => ( path_path_complex @ G2 ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_350_inj__on__id,axiom,
% 4.12/2.07 ! [A2: set_complex] : ( inj_on94911183omplex @ id_complex @ A2 ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_351_inj__on__id,axiom,
% 4.12/2.07 ! [A2: set_a] : ( inj_on_a_a @ id_a @ A2 ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_352_simple__path__imp__path,axiom,
% 4.12/2.07 ! [G2: real > a] :
% 4.12/2.07 ( ( path_simple_path_a @ G2 )
% 4.12/2.07 => ( path_path_a @ G2 ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(fact_353_simple__path__imp__path,axiom,
% 4.12/2.07 ! [G2: real > complex] :
% 4.12/2.07 ( ( path_s36253918omplex @ G2 )
% 4.12/2.07 => ( path_path_complex @ G2 ) ) ).
% 4.12/2.07
% 4.12/2.07 thf(conj_0,conjecture,
% 4.12/2.07 ( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
% 4.12/2.07 = ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ) ).
% 4.12/2.07 ------------------------
% 4.12/2.11 % (21729)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_21628 for (2999ds/27Mi)
% 4.12/2.11 % (21730)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21628 for (2999ds/2Mi)
% 4.12/2.11 % (21731)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_21628 for (2999ds/2Mi)
% 4.12/2.11 % (21732)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_21628 for (2999ds/275Mi)
% 4.12/2.11 % (21728)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_21628 for (2999ds/4Mi)
% 4.12/2.11 % (21727)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21628 for (2999ds/183Mi)
% 4.12/2.11 % (21733)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21628 for (2999ds/18Mi)
% 4.12/2.11 % (21730)Instruction limit reached!
% 4.12/2.11 % (21730)------------------------------
% 4.12/2.11 % (21730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.12/2.11 % (21730)Termination reason: Unknown
% 4.12/2.11 % (21730)Termination phase: shuffling
% 4.12/2.11
% 4.12/2.11 % (21730)Memory used [KB]: 1407
% 4.12/2.11 % (21730)Time elapsed: 0.003 s
% 4.12/2.11 % (21730)Instructions burned: 2 (million)
% 4.12/2.11 % (21730)------------------------------
% 4.12/2.11 % (21730)------------------------------
% 4.12/2.11 % (21731)Instruction limit reached!
% 4.12/2.11 % (21731)------------------------------
% 4.12/2.11 % (21731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.12/2.11 % (21731)Termination reason: Unknown
% 4.12/2.11 % (21731)Termination phase: shuffling
% 4.12/2.11
% 4.12/2.11 % (21731)Memory used [KB]: 1407
% 4.12/2.11 % (21731)Time elapsed: 0.004 s
% 4.12/2.11 % (21731)Instructions burned: 3 (million)
% 4.12/2.11 % (21731)------------------------------
% 4.12/2.11 % (21731)------------------------------
% 4.12/2.11 % (21728)Instruction limit reached!
% 4.12/2.11 % (21728)------------------------------
% 4.12/2.11 % (21728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.12/2.11 % (21728)Termination reason: Unknown
% 4.12/2.11 % (21728)Termination phase: shuffling
% 4.12/2.11
% 4.12/2.11 % (21728)Memory used [KB]: 1407
% 4.12/2.11 % (21728)Time elapsed: 0.004 s
% 4.12/2.11 % (21728)Instructions burned: 4 (million)
% 4.12/2.11 % (21728)------------------------------
% 4.12/2.11 % (21728)------------------------------
% 4.12/2.12 % (21733)Instruction limit reached!
% 4.12/2.12 % (21733)------------------------------
% 4.12/2.12 % (21733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.12/2.12 % (21733)Termination reason: Unknown
% 4.12/2.12 % (21733)Termination phase: Property scanning
% 4.12/2.12
% 4.12/2.12 % (21733)Memory used [KB]: 1791
% 4.12/2.12 % (21733)Time elapsed: 0.013 s
% 4.12/2.12 % (21733)Instructions burned: 19 (million)
% 4.12/2.12 % (21733)------------------------------
% 4.12/2.12 % (21733)------------------------------
% 4.12/2.13 % (21729)Instruction limit reached!
% 4.12/2.13 % (21729)------------------------------
% 4.12/2.13 % (21729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.12/2.13 % (21729)Termination reason: Unknown
% 4.12/2.13 % (21729)Termination phase: Property scanning
% 4.12/2.13
% 4.12/2.13 % (21729)Memory used [KB]: 1663
% 4.12/2.13 % (21729)Time elapsed: 0.017 s
% 4.12/2.13 % (21729)Instructions burned: 28 (million)
% 4.12/2.13 % (21729)------------------------------
% 4.12/2.13 % (21729)------------------------------
% 4.18/2.13 % (21735)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_21628 for (2999ds/37Mi)
% 4.18/2.13 % (21734)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21628 for (2999ds/3Mi)
% 4.18/2.13 % (21736)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_21628 for (2999ds/15Mi)
% 4.18/2.13 % (21734)Instruction limit reached!
% 4.18/2.13 % (21734)------------------------------
% 4.18/2.13 % (21734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.13 % (21734)Termination reason: Unknown
% 4.18/2.13 % (21734)Termination phase: shuffling
% 4.18/2.13
% 4.18/2.13 % (21734)Memory used [KB]: 1407
% 4.18/2.13 % (21734)Time elapsed: 0.004 s
% 4.18/2.13 % (21734)Instructions burned: 3 (million)
% 4.18/2.13 % (21734)------------------------------
% 4.18/2.13 % (21734)------------------------------
% 4.18/2.14 % (21732)First to succeed.
% 4.18/2.14 % (21732)Refutation found. Thanks to Tanya!
% 4.18/2.14 % SZS status Theorem for DTF2THF_21628
% 4.18/2.14 % SZS output start Proof for DTF2THF_21628
% 4.18/2.14 thf(type_def_5, type, complex: $tType).
% 4.18/2.14 thf(type_def_7, type, set_complex: $tType).
% 4.18/2.14 thf(type_def_8, type, a: $tType).
% 4.18/2.14 thf(type_def_9, type, set_a: $tType).
% 4.18/2.14 thf(type_def_10, type, real: $tType).
% 4.18/2.14 thf(type_def_11, type, set_real: $tType).
% 4.18/2.14 thf(type_def_12, type, set_complex_a: $tType).
% 4.18/2.14 thf(type_def_13, type, set_real_real: $tType).
% 4.18/2.14 thf(type_def_14, type, set_real_a: $tType).
% 4.18/2.14 thf(type_def_15, type, set_a_complex: $tType).
% 4.18/2.14 thf(type_def_16, type, set_a_a: $tType).
% 4.18/2.14 thf(func_def_0, type, set_real_real: $tType).
% 4.18/2.14 thf(func_def_1, type, set_a_complex: $tType).
% 4.18/2.14 thf(func_def_2, type, set_complex_a: $tType).
% 4.18/2.14 thf(func_def_3, type, set_real_a: $tType).
% 4.18/2.14 thf(func_def_4, type, set_complex: $tType).
% 4.18/2.14 thf(func_def_5, type, set_a_a: $tType).
% 4.18/2.14 thf(func_def_6, type, set_real: $tType).
% 4.18/2.14 thf(func_def_7, type, set_a: $tType).
% 4.18/2.14 thf(func_def_8, type, complex: $tType).
% 4.18/2.14 thf(func_def_9, type, real: $tType).
% 4.18/2.14 thf(func_def_10, type, a: $tType).
% 4.18/2.14 thf(func_def_11, type, bij_be209634132omplex: (complex > complex) > set_complex > set_complex > $o).
% 4.18/2.14 thf(func_def_12, type, bij_betw_complex_a: (complex > a) > set_complex > set_a > $o).
% 4.18/2.14 thf(func_def_13, type, bij_be122140626omplex: (real > complex) > set_real > set_complex > $o).
% 4.18/2.14 thf(func_def_14, type, bij_betw_real_real: (real > real) > set_real > set_real > $o).
% 4.18/2.14 thf(func_def_15, type, bij_betw_real_a: (real > a) > set_real > set_a > $o).
% 4.18/2.14 thf(func_def_16, type, bij_betw_a_complex: (a > complex) > set_a > set_complex > $o).
% 4.18/2.14 thf(func_def_17, type, bij_betw_a_a: (a > a) > set_a > set_a > $o).
% 4.18/2.14 thf(func_def_18, type, comp_c130555887omplex: (complex > complex) > (complex > complex) > complex > complex).
% 4.18/2.14 thf(func_def_19, type, comp_c595887981x_real: (complex > complex) > (real > complex) > real > complex).
% 4.18/2.14 thf(func_def_20, type, comp_c124850173plex_a: (complex > complex) > (a > complex) > a > complex).
% 4.18/2.14 thf(func_def_21, type, comp_c819638635l_real: (complex > real) > (real > complex) > real > real).
% 4.18/2.14 thf(func_def_22, type, comp_complex_real_a: (complex > real) > (a > complex) > a > real).
% 4.18/2.14 thf(func_def_23, type, comp_c274302683omplex: (complex > a) > (complex > complex) > complex > a).
% 4.18/2.14 thf(func_def_24, type, comp_complex_a_real: (complex > a) > (real > complex) > real > a).
% 4.18/2.14 thf(func_def_25, type, comp_complex_a_a: (complex > a) > (a > complex) > a > a).
% 4.18/2.14 thf(func_def_26, type, comp_r667767405omplex: (real > complex) > (complex > real) > complex > complex).
% 4.18/2.14 thf(func_def_27, type, comp_r701421291x_real: (real > complex) > (real > real) > real > complex).
% 4.18/2.14 thf(func_def_28, type, comp_real_complex_a: (real > complex) > (a > real) > a > complex).
% 4.18/2.14 thf(func_def_29, type, comp_r422820971omplex: (real > real) > (complex > real) > complex > real).
% 4.18/2.14 thf(func_def_30, type, comp_real_real_real: (real > real) > (real > real) > real > real).
% 4.18/2.14 thf(func_def_31, type, comp_real_real_a: (real > real) > (a > real) > a > real).
% 4.18/2.14 thf(func_def_32, type, comp_real_a_complex: (real > a) > (complex > real) > complex > a).
% 4.18/2.14 thf(func_def_33, type, comp_real_a_real: (real > a) > (real > real) > real > a).
% 4.18/2.14 thf(func_def_34, type, comp_real_a_a: (real > a) > (a > real) > a > a).
% 4.18/2.14 thf(func_def_35, type, comp_a1063143865omplex: (a > complex) > (complex > a) > complex > complex).
% 4.18/2.14 thf(func_def_36, type, comp_a_complex_real: (a > complex) > (real > a) > real > complex).
% 4.18/2.14 thf(func_def_37, type, comp_a_complex_a: (a > complex) > (a > a) > a > complex).
% 4.18/2.14 thf(func_def_38, type, comp_a_real_complex: (a > real) > (complex > a) > complex > real).
% 4.18/2.14 thf(func_def_39, type, comp_a_real_real: (a > real) > (real > a) > real > real).
% 4.18/2.14 thf(func_def_40, type, comp_a_real_a: (a > real) > (a > a) > a > real).
% 4.18/2.14 thf(func_def_41, type, comp_a_a_complex: (a > a) > (complex > a) > complex > a).
% 4.18/2.14 thf(func_def_42, type, comp_a_a_real: (a > a) > (real > a) > real > a).
% 4.18/2.14 thf(func_def_43, type, comp_a_a_a: (a > a) > (a > a) > a > a).
% 4.18/2.14 thf(func_def_44, type, id_complex_a: (complex > a) > complex > a).
% 4.18/2.14 thf(func_def_45, type, id_real_a: (real > a) > real > a).
% 4.18/2.14 thf(func_def_46, type, id_a_a: (a > a) > a > a).
% 4.18/2.14 thf(func_def_47, type, id_complex: complex > complex).
% 4.18/2.14 thf(func_def_48, type, id_real: real > real).
% 4.18/2.14 thf(func_def_49, type, id_a: a > a).
% 4.18/2.14 thf(func_def_50, type, inj_on893405649omplex: ((complex > a) > complex > complex) > set_complex_a > $o).
% 4.18/2.14 thf(func_def_51, type, inj_on1576005937plex_a: ((complex > a) > complex > a) > set_complex_a > $o).
% 4.18/2.14 thf(func_def_52, type, inj_on958237983real_a: ((real > real) > real > a) > set_real_real > $o).
% 4.18/2.14 thf(func_def_53, type, inj_on319905617omplex: ((real > a) > real > complex) > set_real_a > $o).
% 4.18/2.14 thf(func_def_54, type, inj_on_real_a_real_a: ((real > a) > real > a) > set_real_a > $o).
% 4.18/2.14 thf(func_def_55, type, inj_on_a_complex_a_a: ((a > complex) > a > a) > set_a_complex > $o).
% 4.18/2.14 thf(func_def_56, type, inj_on_a_a_a_complex: ((a > a) > a > complex) > set_a_a > $o).
% 4.18/2.14 thf(func_def_57, type, inj_on_a_a_a_a: ((a > a) > a > a) > set_a_a > $o).
% 4.18/2.14 thf(func_def_58, type, inj_on94911183omplex: (complex > complex) > set_complex > $o).
% 4.18/2.14 thf(func_def_59, type, inj_on_complex_a: (complex > a) > set_complex > $o).
% 4.18/2.14 thf(func_def_60, type, inj_on_real_complex: (real > complex) > set_real > $o).
% 4.18/2.14 thf(func_def_61, type, inj_on_real_real: (real > real) > set_real > $o).
% 4.18/2.14 thf(func_def_62, type, inj_on_real_a: (real > a) > set_real > $o).
% 4.18/2.14 thf(func_def_63, type, inj_on_a_complex: (a > complex) > set_a > $o).
% 4.18/2.14 thf(func_def_64, type, inj_on_a_a: (a > a) > set_a > $o).
% 4.18/2.14 thf(func_def_65, type, zero_zero_complex: complex).
% 4.18/2.14 thf(func_def_66, type, zero_zero_a: a).
% 4.18/2.14 thf(func_def_67, type, top_top_complex_o: complex > $o).
% 4.18/2.14 thf(func_def_68, type, top_top_a_o: a > $o).
% 4.18/2.14 thf(func_def_69, type, top_to525076535plex_a: set_complex_a).
% 4.18/2.14 thf(func_def_70, type, top_to1446257885l_real: set_real_real).
% 4.18/2.14 thf(func_def_71, type, top_top_set_real_a: set_real_a).
% 4.18/2.14 thf(func_def_72, type, top_to2109114701omplex: set_a_complex).
% 4.18/2.14 thf(func_def_73, type, top_top_set_a_a: set_a_a).
% 4.18/2.14 thf(func_def_74, type, top_top_set_complex: set_complex).
% 4.18/2.14 thf(func_def_75, type, top_top_set_real: set_real).
% 4.18/2.14 thf(func_def_76, type, top_top_set_a: set_a).
% 4.18/2.14 thf(func_def_77, type, path_arc_complex: (real > complex) > $o).
% 4.18/2.14 thf(func_def_78, type, path_arc_real: (real > real) > $o).
% 4.18/2.14 thf(func_def_79, type, path_arc_a: (real > a) > $o).
% 4.18/2.14 thf(func_def_80, type, path_path_complex: (real > complex) > $o).
% 4.18/2.14 thf(func_def_81, type, path_path_real: (real > real) > $o).
% 4.18/2.14 thf(func_def_82, type, path_path_a: (real > a) > $o).
% 4.18/2.14 thf(func_def_83, type, path_p769714271omplex: (real > complex) > complex).
% 4.18/2.14 thf(func_def_84, type, path_pathfinish_real: (real > real) > real).
% 4.18/2.14 thf(func_def_85, type, path_pathfinish_a: (real > a) > a).
% 4.18/2.14 thf(func_def_86, type, path_p797330068omplex: (real > complex) > complex).
% 4.18/2.14 thf(func_def_87, type, path_pathstart_real: (real > real) > real).
% 4.18/2.14 thf(func_def_88, type, path_pathstart_a: (real > a) > a).
% 4.18/2.14 thf(func_def_89, type, path_rectpath: complex > complex > real > complex).
% 4.18/2.14 thf(func_def_90, type, path_s36253918omplex: (real > complex) > $o).
% 4.18/2.14 thf(func_def_91, type, path_s1005760220h_real: (real > real) > $o).
% 4.18/2.14 thf(func_def_92, type, path_simple_path_a: (real > a) > $o).
% 4.18/2.14 thf(func_def_93, type, poinca1910941596x_of_a: a > complex).
% 4.18/2.14 thf(func_def_94, type, poinca837721858l_of_a: complex > a).
% 4.18/2.14 thf(func_def_95, type, real_V762982918plex_a: (complex > a) > $o).
% 4.18/2.14 thf(func_def_96, type, real_V912435428omplex: (a > complex) > $o).
% 4.18/2.14 thf(func_def_97, type, real_V301987619plex_a: (complex > a) > $o).
% 4.18/2.14 thf(func_def_98, type, real_V451440129omplex: (a > complex) > $o).
% 4.18/2.14 thf(func_def_99, type, real_V670066493omplex: (complex > complex) > $o).
% 4.18/2.14 thf(func_def_100, type, real_V1327653935plex_a: (complex > a) > $o).
% 4.18/2.14 thf(func_def_101, type, real_V1948715323omplex: (real > complex) > $o).
% 4.18/2.14 thf(func_def_102, type, real_V1354572473l_real: (real > real) > $o).
% 4.18/2.14 thf(func_def_103, type, real_V779700657real_a: (real > a) > $o).
% 4.18/2.14 thf(func_def_104, type, real_V1477106445omplex: (a > complex) > $o).
% 4.18/2.14 thf(func_def_105, type, real_V202220639ar_a_a: (a > a) > $o).
% 4.18/2.14 thf(func_def_106, type, collect_complex: (complex > $o) > set_complex).
% 4.18/2.14 thf(func_def_107, type, collect_a: (a > $o) > set_a).
% 4.18/2.14 thf(func_def_108, type, member_complex: complex > set_complex > $o).
% 4.18/2.14 thf(func_def_109, type, member_a: a > set_a > $o).
% 4.18/2.14 thf(func_def_110, type, c: real > a).
% 4.18/2.14 thf(func_def_126, type, sK0: complex > (a > complex) > a).
% 4.18/2.14 thf(func_def_127, type, sK1: (complex > a) > a > complex).
% 4.18/2.14 thf(func_def_128, type, sK2: (a > complex) > a).
% 4.18/2.14 thf(func_def_129, type, sK3: (a > complex) > a).
% 4.18/2.14 thf(func_def_130, type, sK4: (a > complex) > complex > a).
% 4.18/2.14 thf(func_def_131, type, sK5: (a > complex) > a).
% 4.18/2.14 thf(func_def_132, type, sK6: (a > complex) > a).
% 4.18/2.14 thf(func_def_134, type, ph8: !>[X0: $tType]:(X0)).
% 4.18/2.14 thf(f883,plain,(
% 4.18/2.14 $false),
% 4.18/2.14 inference(subsumption_resolution,[status(thm)],[f882,f844])).
% 4.18/2.14 thf(f844,plain,(
% 4.18/2.14 ( ! [X0 : a > complex,X1 : real > a] : (((path_p769714271omplex @ (comp_a_complex_real @ X0 @ X1)) = (X0 @ (path_pathfinish_a @ X1)))) )),
% 4.18/2.14 inference(cnf_transformation,[status(thm)],[f751])).
% 4.18/2.14 thf(f751,plain,(
% 4.18/2.14 ! [X0 : a > complex,X1 : real > a] : ((path_p769714271omplex @ (comp_a_complex_real @ X0 @ X1)) = (X0 @ (path_pathfinish_a @ X1)))),
% 4.18/2.14 inference(rectify,[status(thm)],[f14])).
% 4.18/2.14 thf(f14,axiom,(
% 4.18/2.14 ! [X3 : a > complex,X4 : real > a] : ((path_p769714271omplex @ (comp_a_complex_real @ X3 @ X4)) = (X3 @ (path_pathfinish_a @ X4)))),
% 4.18/2.14 file('/export/starexec/sandbox/tmp/tmp.I8HVgnaxTf/DTF2THF_21628.p',fact_13_pathfinish__compose)).
% 4.18/2.14 thf(f882,plain,(
% 4.18/2.14 ((path_p769714271omplex @ (comp_a_complex_real @ poinca1910941596x_of_a @ c)) != (poinca1910941596x_of_a @ (path_pathfinish_a @ c)))),
% 4.18/2.14 inference(forward_demodulation,[status(thm)],[f881,f872])).
% 4.18/2.14 thf(f872,plain,(
% 4.18/2.14 ((path_pathfinish_a @ c) = (path_pathstart_a @ c))),
% 4.18/2.14 inference(cnf_transformation,[status(thm)],[f1])).
% 4.18/2.14 thf(f1,axiom,(
% 4.18/2.14 ((path_pathfinish_a @ c) = (path_pathstart_a @ c))),
% 4.18/2.14 file('/export/starexec/sandbox/tmp/tmp.I8HVgnaxTf/DTF2THF_21628.p',fact_0_assms_I2_J)).
% 4.18/2.14 thf(f881,plain,(
% 4.18/2.14 ((path_p769714271omplex @ (comp_a_complex_real @ poinca1910941596x_of_a @ c)) != (poinca1910941596x_of_a @ (path_pathstart_a @ c)))),
% 4.18/2.14 inference(forward_demodulation,[status(thm)],[f821,f845])).
% 4.18/2.14 thf(f845,plain,(
% 4.18/2.14 ( ! [X0 : a > complex,X1 : real > a] : (((path_p797330068omplex @ (comp_a_complex_real @ X0 @ X1)) = (X0 @ (path_pathstart_a @ X1)))) )),
% 4.18/2.14 inference(cnf_transformation,[status(thm)],[f754])).
% 4.18/2.14 thf(f754,plain,(
% 4.18/2.14 ! [X0 : a > complex,X1 : real > a] : ((path_p797330068omplex @ (comp_a_complex_real @ X0 @ X1)) = (X0 @ (path_pathstart_a @ X1)))),
% 4.18/2.14 inference(rectify,[status(thm)],[f19])).
% 4.18/2.14 thf(f19,axiom,(
% 4.18/2.14 ! [X3 : a > complex,X4 : real > a] : ((path_p797330068omplex @ (comp_a_complex_real @ X3 @ X4)) = (X3 @ (path_pathstart_a @ X4)))),
% 4.18/2.14 file('/export/starexec/sandbox/tmp/tmp.I8HVgnaxTf/DTF2THF_21628.p',fact_18_pathstart__compose)).
% 4.18/2.14 thf(f821,plain,(
% 4.18/2.14 ((path_p769714271omplex @ (comp_a_complex_real @ poinca1910941596x_of_a @ c)) != (path_p797330068omplex @ (comp_a_complex_real @ poinca1910941596x_of_a @ c)))),
% 4.18/2.14 inference(cnf_transformation,[status(thm)],[f746])).
% 4.18/2.14 thf(f746,plain,(
% 4.18/2.14 ((path_p769714271omplex @ (comp_a_complex_real @ poinca1910941596x_of_a @ c)) != (path_p797330068omplex @ (comp_a_complex_real @ poinca1910941596x_of_a @ c)))),
% 4.18/2.14 inference(flattening,[status(thm)],[f356])).
% 4.18/2.14 thf(f356,negated_conjecture,(
% 4.18/2.14 ~((path_p769714271omplex @ (comp_a_complex_real @ poinca1910941596x_of_a @ c)) = (path_p797330068omplex @ (comp_a_complex_real @ poinca1910941596x_of_a @ c)))),
% 4.18/2.14 inference(negated_conjecture,[status(cth)],[f355])).
% 4.18/2.14 thf(f355,conjecture,(
% 4.18/2.14 ((path_p769714271omplex @ (comp_a_complex_real @ poinca1910941596x_of_a @ c)) = (path_p797330068omplex @ (comp_a_complex_real @ poinca1910941596x_of_a @ c)))),
% 4.18/2.14 file('/export/starexec/sandbox/tmp/tmp.I8HVgnaxTf/DTF2THF_21628.p',conj_0)).
% 4.18/2.14 % SZS output end Proof for DTF2THF_21628
% 4.18/2.14 % (21732)------------------------------
% 4.18/2.14 % (21732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.14 % (21732)Termination reason: Refutation
% 4.18/2.14
% 4.18/2.14 % (21732)Memory used [KB]: 6396
% 4.18/2.14 % (21732)Time elapsed: 0.031 s
% 4.18/2.14 % (21732)Instructions burned: 48 (million)
% 4.18/2.14 % (21732)------------------------------
% 4.18/2.14 % (21732)------------------------------
% 4.18/2.14 % (21726)Success in time 0.068 s
%------------------------------------------------------------------------------