TPTP Problem File: SLH0274^1.p

%------------------------------------------------------------------------------
% File     : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Archive of Formal Proofs
% Problem  :
% Version  : Especial.
% English  :

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : Quasi_Borel_Spaces/0001_QuasiBorel/prob_00154_005355__15121534_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1858 ( 571 unt; 581 typ;   0 def)
%            Number of atoms       : 3639 (1054 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 12359 ( 174   ~;   3   |; 194   &;10496   @)
%                                         (   0 <=>;1492  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Number of types       :  108 ( 107 usr)
%            Number of type conns  : 2643 (2643   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  477 ( 474 usr;  37 con; 0-3 aty)
%            Number of variables   : 4227 ( 722   ^;3436   !;  69   ?;4227   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 14:08:20.378
%------------------------------------------------------------------------------
% Could-be-implicit typings (107)
thf(ty_n_t__Set__Oset_It__Sigma____Algebra__Omeasure_It__Extended____Nonnegative____Real__Oennreal_J_J,type,
    set_Si97717610131227249nnreal: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mt__Extended____Nonnegative____Real__Oennreal_J_J,type,
    set_re5328672808648366137nnreal: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Extended____Nonnegative____Real__Oennreal_Mt__Real__Oreal_J_J,type,
    set_Ex5658717452565810105l_real: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_Mt__Extended____Nonnegative____Real__Oennreal_J_J,type,
    set_na7716847989478749277nnreal: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Extended____Nonnegative____Real__Oennreal_Mt__Nat__Onat_J_J,type,
    set_Ex1875306066257539165al_nat: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_It__Extended____Nonnegative____Real__Oennreal_J,type,
    sigma_7234349610311085201nnreal: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Extended____Nonnegative____Real__Oennreal_J_J,type,
    set_se4580700918925141924nnreal: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_062_It__Real__Oreal_Mt__Nat__Onat_J_J_J,type,
    set_real_real_nat: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__a_Mt__Extended____Nonnegative____Real__Oennreal_J_J,type,
    set_a_7161065143582548615nnreal: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_062_Itf__a_Mt__Complex__Ocomplex_J_J_J,type,
    set_real_a_complex: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Extended____Nonnegative____Real__Oennreal_Mtf__a_J_J,type,
    set_Ex2249781601450085341real_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Extended____Nonnegative____Real__Oennreal_M_Eo_J_J,type,
    set_Ex70502500924464887real_o: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_062_It__Real__Oreal_Mt__Nat__Onat_J_J,type,
    quasi_borel_real_nat: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_I_062_It__Real__Oreal_Mt__Nat__Onat_J_J,type,
    sigma_6586288717683155060al_nat: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_062_Itf__a_Mt__Real__Oreal_J_J_J,type,
    set_real_a_real: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_062_It__Real__Oreal_Mtf__b_J_J_J,type,
    set_real_real_b: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_062_It__Real__Oreal_Mtf__a_J_J_J,type,
    set_real_real_a: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
    quasi_4365677710772687427omplex: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_I_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
    sigma_2418697800065292186omplex: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_062_It__Real__Oreal_Mt__Nat__Onat_J_J_J,type,
    set_set_real_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_062_Itf__a_Mt__Complex__Ocomplex_J_J_J,type,
    set_set_a_complex: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_062_Itf__a_Mt__Nat__Onat_J_J_J,type,
    set_real_a_nat: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
    set_complex_complex: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mt__Nat__Onat_J_M_Eo_J_J,type,
    set_real_nat_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_Itf__a_Mt__Complex__Ocomplex_J_M_Eo_J_J,type,
    set_a_complex_o: $tType ).

thf(ty_n_t__Set__Oset_It__Sigma____Algebra__Omeasure_It__Real__Oreal_J_J,type,
    set_Si6059263944882162789e_real: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_062_Itf__a_Mt__Real__Oreal_J_J,type,
    quasi_borel_a_real: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_062_It__Real__Oreal_Mtf__b_J_J,type,
    quasi_borel_real_b: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_062_It__Real__Oreal_Mtf__a_J_J,type,
    quasi_borel_real_a: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_I_062_Itf__a_Mt__Real__Oreal_J_J,type,
    sigma_measure_a_real: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_I_062_It__Real__Oreal_Mtf__b_J_J,type,
    sigma_measure_real_b: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_I_062_It__Real__Oreal_Mtf__a_J_J,type,
    sigma_measure_real_a: $tType ).

thf(ty_n_t__Set__Oset_It__Sigma____Algebra__Omeasure_It__Nat__Onat_J_J,type,
    set_Si3048223896905877257re_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_062_Itf__a_Mt__Real__Oreal_J_J_J,type,
    set_set_a_real: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_062_It__Real__Oreal_Mtf__b_J_J_J,type,
    set_set_real_b: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_062_It__Real__Oreal_Mtf__a_J_J_J,type,
    set_set_real_a: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_062_Itf__a_Mt__Nat__Onat_J_J,type,
    quasi_borel_a_nat: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_I_062_Itf__a_Mt__Nat__Onat_J_J,type,
    sigma_measure_a_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Extended____Nonnegative____Real__Oennreal_J,type,
    set_Ex3793607809372303086nnreal: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mt__Complex__Ocomplex_J_J,type,
    set_real_complex: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Complex__Ocomplex_Mt__Real__Oreal_J_J,type,
    set_complex_real: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_062_Itf__a_Mt__Nat__Onat_J_J_J,type,
    set_set_a_nat: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_062_Itf__a_M_Eo_J_J_J,type,
    set_real_a_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_Itf__a_Mt__Real__Oreal_J_M_Eo_J_J,type,
    set_a_real_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mtf__b_J_M_Eo_J_J,type,
    set_real_b_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mtf__a_J_M_Eo_J_J,type,
    set_real_a_o2: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_Itf__a_Mt__Nat__Onat_J_M_Eo_J_J,type,
    set_a_nat_o: $tType ).

thf(ty_n_t__Set__Oset_It__Sigma____Algebra__Omeasure_Itf__b_J_J,type,
    set_Sigma_measure_b: $tType ).

thf(ty_n_t__Set__Oset_It__Sigma____Algebra__Omeasure_Itf__a_J_J,type,
    set_Sigma_measure_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    set_real_real: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_It__Complex__Ocomplex_J,type,
    sigma_3077487657436305159omplex: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_I_062_Itf__a_Mtf__a_J_J,type,
    sigma_measure_a_a: $tType ).

thf(ty_n_t__Set__Oset_It__Sigma____Algebra__Omeasure_I_Eo_J_J,type,
    set_Sigma_measure_o: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Complex__Ocomplex_J_J,type,
    set_set_complex: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_062_Itf__a_Mtf__a_J_J_J,type,
    set_set_a_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mt__Nat__Onat_J_J,type,
    set_real_nat: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_Mt__Real__Oreal_J_J,type,
    set_nat_real: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_062_Itf__a_M_Eo_J_J,type,
    quasi_borel_a_o: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_I_062_Itf__a_M_Eo_J_J,type,
    sigma_measure_a_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
    set_a_complex: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_062_Itf__a_M_Eo_J_J_J,type,
    set_set_a_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_nat_nat: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_J,type,
    set_a_a_o: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_It__Real__Oreal_J,type,
    sigma_measure_real: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_Itf__a_M_Eo_J_M_Eo_J_J,type,
    set_a_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Real__Oreal_J_J,type,
    set_set_real: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_It__Nat__Onat_J,type,
    quasi_borel_nat: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_It__Nat__Onat_J,type,
    sigma_measure_nat: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__a_Mt__Real__Oreal_J_J,type,
    set_a_real: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mtf__b_J_J,type,
    set_real_b: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mtf__a_J_J,type,
    set_real_a: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
    set_set_nat: $tType ).

thf(ty_n_t__Extended____Nonnegative____Real__Oennreal,type,
    extend8495563244428889912nnreal: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__b_Mt__Nat__Onat_J_J,type,
    set_b_nat: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__a_Mt__Nat__Onat_J_J,type,
    set_a_nat: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_Eo_J_J,type,
    set_real_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_Mtf__b_J_J,type,
    set_nat_b: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_Mtf__a_J_J,type,
    set_nat_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_Eo_Mt__Real__Oreal_J_J,type,
    set_o_real: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_M_Eo_J_J,type,
    set_nat_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_Eo_Mt__Nat__Onat_J_J,type,
    set_o_nat: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_Itf__b_J,type,
    quasi_borel_b: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_Itf__a_J,type,
    quasi_borel_a: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_Itf__b_J,type,
    sigma_measure_b: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_Itf__a_J,type,
    sigma_measure_a: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__b_J_J,type,
    set_set_b: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
    set_set_a: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_I_Eo_J,type,
    sigma_measure_o: $tType ).

thf(ty_n_t__Set__Oset_It__Complex__Ocomplex_J,type,
    set_complex: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__b_Mtf__b_J_J,type,
    set_b_b: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__b_Mtf__a_J_J,type,
    set_b_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__a_Mtf__b_J_J,type,
    set_a_b: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__a_Mtf__a_J_J,type,
    set_a_a: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
    set_set_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__a_M_Eo_J_J,type,
    set_a_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_Eo_Mtf__a_J_J,type,
    set_o_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_Eo_M_Eo_J_J,type,
    set_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
    set_real: $tType ).

thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
    set_nat: $tType ).

thf(ty_n_t__Set__Oset_Itf__b_J,type,
    set_b: $tType ).

thf(ty_n_t__Set__Oset_Itf__a_J,type,
    set_a: $tType ).

thf(ty_n_t__Complex__Ocomplex,type,
    complex: $tType ).

thf(ty_n_t__Set__Oset_I_Eo_J,type,
    set_o: $tType ).

thf(ty_n_t__Real__Oreal,type,
    real: $tType ).

thf(ty_n_t__Nat__Onat,type,
    nat: $tType ).

thf(ty_n_tf__b,type,
    b: $tType ).

thf(ty_n_tf__a,type,
    a: $tType ).

% Explicit typings (474)
thf(sy_c_Borel__Space_Ois__borel_001t__Real__Oreal_001t__Nat__Onat,type,
    borel_4557508243417129402al_nat: ( real > nat ) > sigma_measure_real > $o ).

thf(sy_c_Borel__Space_Ois__borel_001tf__a_001_Eo,type,
    borel_is_borel_a_o: ( a > $o ) > sigma_measure_a > $o ).

thf(sy_c_Borel__Space_Ois__borel_001tf__a_001t__Complex__Ocomplex,type,
    borel_8160143138670184560omplex: ( a > complex ) > sigma_measure_a > $o ).

thf(sy_c_Borel__Space_Ois__borel_001tf__a_001t__Nat__Onat,type,
    borel_is_borel_a_nat: ( a > nat ) > sigma_measure_a > $o ).

thf(sy_c_Borel__Space_Ois__borel_001tf__a_001t__Real__Oreal,type,
    borel_4993665998515044718a_real: ( a > real ) > sigma_measure_a > $o ).

thf(sy_c_Borel__Space_Otopological__space__class_Oborel_001_062_It__Real__Oreal_Mt__Nat__Onat_J,type,
    borel_1750461538259077885al_nat: sigma_6586288717683155060al_nat ).

thf(sy_c_Borel__Space_Otopological__space__class_Oborel_001_Eo,type,
    borel_5500255247093592246orel_o: sigma_measure_o ).

thf(sy_c_Borel__Space_Otopological__space__class_Oborel_001t__Complex__Ocomplex,type,
    borel_1392132677378845456omplex: sigma_3077487657436305159omplex ).

thf(sy_c_Borel__Space_Otopological__space__class_Oborel_001t__Extended____Nonnegative____Real__Oennreal,type,
    borel_6524799422816628122nnreal: sigma_7234349610311085201nnreal ).

thf(sy_c_Borel__Space_Otopological__space__class_Oborel_001t__Nat__Onat,type,
    borel_8449730974584783410el_nat: sigma_measure_nat ).

thf(sy_c_Borel__Space_Otopological__space__class_Oborel_001t__Real__Oreal,type,
    borel_5078946678739801102l_real: sigma_measure_real ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001_062_It__Real__Oreal_Mt__Nat__Onat_J,type,
    comple284232062038725972al_nat: set_real_nat > real > nat ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001_Eo,type,
    complete_Inf_Inf_o: set_o > $o ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Nat__Onat,type,
    complete_Inf_Inf_nat: set_nat > nat ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Real__Oreal,type,
    comple4887499456419720421f_real: set_real > real ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_I_062_It__Real__Oreal_Mt__Nat__Onat_J_J,type,
    comple8071895948329575818al_nat: set_set_real_nat > set_real_nat ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_I_062_It__Real__Oreal_Mtf__a_J_J,type,
    comple7650869245322889200real_a: set_set_real_a > set_real_a ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_I_062_It__Real__Oreal_Mtf__b_J_J,type,
    comple7721903285369235185real_b: set_set_real_b > set_real_b ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_I_062_Itf__a_M_Eo_J_J,type,
    comple8115264379980766446et_a_o: set_set_a_o > set_a_o ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_I_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
    comple987388759867256068omplex: set_set_a_complex > set_a_complex ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_I_062_Itf__a_Mt__Nat__Onat_J_J,type,
    comple4385993935590776358_a_nat: set_set_a_nat > set_a_nat ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_I_062_Itf__a_Mt__Real__Oreal_J_J,type,
    comple5242429829429470466a_real: set_set_a_real > set_a_real ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_I_062_Itf__a_Mtf__a_J_J,type,
    comple1050673676576882260et_a_a: set_set_a_a > set_a_a ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_I_Eo_J,type,
    comple3063163877087187839_set_o: set_set_o > set_o ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Complex__Ocomplex_J,type,
    comple2956690151646016541omplex: set_set_complex > set_complex ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Extended____Nonnegative____Real__Oennreal_J,type,
    comple5724520875574609319nnreal: set_se4580700918925141924nnreal > set_Ex3793607809372303086nnreal ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Nat__Onat_J,type,
    comple7806235888213564991et_nat: set_set_nat > set_nat ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Real__Oreal_J,type,
    comple8289635161444856091t_real: set_set_real > set_real ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_Itf__a_J,type,
    comple6135023378680113637_set_a: set_set_a > set_a ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_Itf__b_J,type,
    comple6135023382983342438_set_b: set_set_b > set_b ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001_062_I_062_Itf__a_Mt__Nat__Onat_J_M_Eo_J,type,
    comple4070330114094914769_nat_o: set_a_nat_o > ( a > nat ) > $o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001_062_I_062_Itf__a_Mtf__a_J_M_Eo_J,type,
    comple2105534466620790551_a_a_o: set_a_a_o > ( a > a ) > $o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001_062_It__Nat__Onat_M_Eo_J,type,
    comple8317665133742190828_nat_o: set_nat_o > nat > $o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001_062_It__Real__Oreal_Mt__Nat__Onat_J,type,
    comple5752178096987194350al_nat: set_real_nat > real > nat ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001_Eo,type,
    complete_Sup_Sup_o: set_o > $o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Extended____Nonnegative____Real__Oennreal,type,
    comple6814414086264997003nnreal: set_Ex3793607809372303086nnreal > extend8495563244428889912nnreal ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Nat__Onat,type,
    complete_Sup_Sup_nat: set_nat > nat ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Real__Oreal,type,
    comple1385675409528146559p_real: set_real > real ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_It__Real__Oreal_Mt__Nat__Onat_J_J,type,
    comple266511651042094116al_nat: set_set_real_nat > set_real_nat ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_It__Real__Oreal_Mtf__a_J_J,type,
    comple4225921873958597590real_a: set_set_real_a > set_real_a ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_It__Real__Oreal_Mtf__b_J_J,type,
    comple4296955914004943575real_b: set_set_real_b > set_real_b ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_Itf__a_M_Eo_J_J,type,
    comple3956969172160116872et_a_o: set_set_a_o > set_a_o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
    comple8696354750574632938omplex: set_set_a_complex > set_a_complex ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_Itf__a_Mt__Nat__Onat_J_J,type,
    comple4286861423968083212_a_nat: set_set_a_nat > set_a_nat ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_Itf__a_Mt__Real__Oreal_J_J,type,
    comple1817482458065178856a_real: set_set_a_real > set_a_real ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_Itf__a_Mtf__a_J_J,type,
    comple6518619711525350638et_a_a: set_set_a_a > set_a_a ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_Eo_J,type,
    comple90263536869209701_set_o: set_set_o > set_o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Complex__Ocomplex_J,type,
    comple8424636186594484919omplex: set_set_complex > set_complex ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Extended____Nonnegative____Real__Oennreal_J,type,
    comple4226387801268262977nnreal: set_se4580700918925141924nnreal > set_Ex3793607809372303086nnreal ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Nat__Onat_J,type,
    comple7399068483239264473et_nat: set_set_nat > set_nat ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Real__Oreal_J,type,
    comple3096694443085538997t_real: set_set_real > set_real ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_Itf__a_J,type,
    comple2307003609928055243_set_a: set_set_a > set_a ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_Itf__b_J,type,
    comple2307003614231284044_set_b: set_set_b > set_b ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Sigma____Algebra__Omeasure_I_Eo_J,type,
    comple8691778902212741480sure_o: set_Sigma_measure_o > sigma_measure_o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Sigma____Algebra__Omeasure_It__Extended____Nonnegative____Real__Oennreal_J,type,
    comple2394123286901040126nnreal: set_Si97717610131227249nnreal > sigma_7234349610311085201nnreal ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Sigma____Algebra__Omeasure_It__Nat__Onat_J,type,
    comple1344625017055687830re_nat: set_Si3048223896905877257re_nat > sigma_measure_nat ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Sigma____Algebra__Omeasure_It__Real__Oreal_J,type,
    comple1433435454551854066e_real: set_Si6059263944882162789e_real > sigma_measure_real ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Sigma____Algebra__Omeasure_Itf__a_J,type,
    comple2239804592135895886sure_a: set_Sigma_measure_a > sigma_measure_a ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Sigma____Algebra__Omeasure_Itf__b_J,type,
    comple2239804596439124687sure_b: set_Sigma_measure_b > sigma_measure_b ).

thf(sy_c_Conditionally__Complete__Lattices_Opreorder__class_Obdd__above_001t__Nat__Onat,type,
    condit2214826472909112428ve_nat: set_nat > $o ).

thf(sy_c_Countable__Set_Ocountable_001_062_It__Real__Oreal_Mt__Nat__Onat_J,type,
    counta7410736174393390496al_nat: set_real_nat > $o ).

thf(sy_c_Countable__Set_Ocountable_001_062_It__Real__Oreal_Mtf__a_J,type,
    counta6639396083684174020real_a: set_real_a > $o ).

thf(sy_c_Countable__Set_Ocountable_001_062_It__Real__Oreal_Mtf__b_J,type,
    counta6639396087987402821real_b: set_real_b > $o ).

thf(sy_c_Countable__Set_Ocountable_001_062_Itf__a_Mt__Complex__Ocomplex_J,type,
    counta599731762510375256omplex: set_a_complex > $o ).

thf(sy_c_Countable__Set_Ocountable_001_062_Itf__a_Mt__Real__Oreal_J,type,
    counta6122129581416836822a_real: set_a_real > $o ).

thf(sy_c_Countable__Set_Ocountable_001_Eo,type,
    counta5976203206615340371able_o: set_o > $o ).

thf(sy_c_Countable__Set_Ocountable_001t__Complex__Ocomplex,type,
    counta5113917769705169331omplex: set_complex > $o ).

thf(sy_c_Countable__Set_Ocountable_001t__Extended____Nonnegative____Real__Oennreal,type,
    counta8439243037236335165nnreal: set_Ex3793607809372303086nnreal > $o ).

thf(sy_c_Countable__Set_Ocountable_001t__Nat__Onat,type,
    counta1168086296615599829le_nat: set_nat > $o ).

thf(sy_c_Countable__Set_Ocountable_001t__Real__Oreal,type,
    counta7319604579010473777e_real: set_real > $o ).

thf(sy_c_Countable__Set_Ocountable_001tf__a,type,
    counta4098120917673242425able_a: set_a > $o ).

thf(sy_c_Countable__Set_Ocountable_001tf__b,type,
    counta4098120917673242426able_b: set_b > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
    finite_finite_nat: set_nat > $o ).

thf(sy_c_FuncSet_OPi_001_Eo_001t__Nat__Onat,type,
    pi_o_nat: set_o > ( $o > set_nat ) > set_o_nat ).

thf(sy_c_FuncSet_OPi_001_Eo_001t__Real__Oreal,type,
    pi_o_real: set_o > ( $o > set_real ) > set_o_real ).

thf(sy_c_FuncSet_OPi_001_Eo_001tf__a,type,
    pi_o_a: set_o > ( $o > set_a ) > set_o_a ).

thf(sy_c_FuncSet_OPi_001t__Extended____Nonnegative____Real__Oennreal_001tf__a,type,
    pi_Ext7789591913556194873real_a: set_Ex3793607809372303086nnreal > ( extend8495563244428889912nnreal > set_a ) > set_Ex2249781601450085341real_a ).

thf(sy_c_FuncSet_OPi_001t__Nat__Onat_001_Eo,type,
    pi_nat_o: set_nat > ( nat > set_o ) > set_nat_o ).

thf(sy_c_FuncSet_OPi_001t__Nat__Onat_001t__Extended____Nonnegative____Real__Oennreal,type,
    pi_nat6594671786139111381nnreal: set_nat > ( nat > set_Ex3793607809372303086nnreal ) > set_na7716847989478749277nnreal ).

thf(sy_c_FuncSet_OPi_001t__Nat__Onat_001t__Nat__Onat,type,
    pi_nat_nat: set_nat > ( nat > set_nat ) > set_nat_nat ).

thf(sy_c_FuncSet_OPi_001t__Nat__Onat_001t__Real__Oreal,type,
    pi_nat_real: set_nat > ( nat > set_real ) > set_nat_real ).

thf(sy_c_FuncSet_OPi_001t__Nat__Onat_001tf__a,type,
    pi_nat_a: set_nat > ( nat > set_a ) > set_nat_a ).

thf(sy_c_FuncSet_OPi_001t__Real__Oreal_001_Eo,type,
    pi_real_o: set_real > ( real > set_o ) > set_real_o ).

thf(sy_c_FuncSet_OPi_001t__Real__Oreal_001t__Extended____Nonnegative____Real__Oennreal,type,
    pi_rea7198910874028739761nnreal: set_real > ( real > set_Ex3793607809372303086nnreal ) > set_re5328672808648366137nnreal ).

thf(sy_c_FuncSet_OPi_001t__Real__Oreal_001t__Nat__Onat,type,
    pi_real_nat: set_real > ( real > set_nat ) > set_real_nat ).

thf(sy_c_FuncSet_OPi_001t__Real__Oreal_001t__Real__Oreal,type,
    pi_real_real: set_real > ( real > set_real ) > set_real_real ).

thf(sy_c_FuncSet_OPi_001t__Real__Oreal_001tf__a,type,
    pi_real_a: set_real > ( real > set_a ) > set_real_a ).

thf(sy_c_FuncSet_OPi_001t__Real__Oreal_001tf__b,type,
    pi_real_b: set_real > ( real > set_b ) > set_real_b ).

thf(sy_c_FuncSet_OPi_001tf__a_001_Eo,type,
    pi_a_o: set_a > ( a > set_o ) > set_a_o ).

thf(sy_c_FuncSet_OPi_001tf__a_001t__Complex__Ocomplex,type,
    pi_a_complex: set_a > ( a > set_complex ) > set_a_complex ).

thf(sy_c_FuncSet_OPi_001tf__a_001t__Extended____Nonnegative____Real__Oennreal,type,
    pi_a_E4973063519588424107nnreal: set_a > ( a > set_Ex3793607809372303086nnreal ) > set_a_7161065143582548615nnreal ).

thf(sy_c_FuncSet_OPi_001tf__a_001t__Nat__Onat,type,
    pi_a_nat: set_a > ( a > set_nat ) > set_a_nat ).

thf(sy_c_FuncSet_OPi_001tf__a_001t__Real__Oreal,type,
    pi_a_real: set_a > ( a > set_real ) > set_a_real ).

thf(sy_c_FuncSet_OPi_001tf__a_001tf__a,type,
    pi_a_a: set_a > ( a > set_a ) > set_a_a ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Extended____Nonnegative____Real__Oennreal,type,
    minus_8429688780609304081nnreal: extend8495563244428889912nnreal > extend8495563244428889912nnreal > extend8495563244428889912nnreal ).

thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
    uminus_uminus_real: real > real ).

thf(sy_c_HOL_OThe_001t__Real__Oreal,type,
    the_real: ( real > $o ) > real ).

thf(sy_c_HOL_OThe_001tf__a,type,
    the_a: ( a > $o ) > a ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Real__Oreal_Mt__Nat__Onat_J_M_Eo_J,type,
    inf_inf_real_nat_o: ( ( real > nat ) > $o ) > ( ( real > nat ) > $o ) > ( real > nat ) > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Real__Oreal_Mtf__a_J_M_Eo_J,type,
    inf_inf_real_a_o: ( ( real > a ) > $o ) > ( ( real > a ) > $o ) > ( real > a ) > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Real__Oreal_Mtf__b_J_M_Eo_J,type,
    inf_inf_real_b_o: ( ( real > b ) > $o ) > ( ( real > b ) > $o ) > ( real > b ) > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_Itf__a_M_Eo_J_M_Eo_J,type,
    inf_inf_a_o_o: ( ( a > $o ) > $o ) > ( ( a > $o ) > $o ) > ( a > $o ) > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_Itf__a_Mt__Complex__Ocomplex_J_M_Eo_J,type,
    inf_inf_a_complex_o: ( ( a > complex ) > $o ) > ( ( a > complex ) > $o ) > ( a > complex ) > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_Itf__a_Mt__Nat__Onat_J_M_Eo_J,type,
    inf_inf_a_nat_o: ( ( a > nat ) > $o ) > ( ( a > nat ) > $o ) > ( a > nat ) > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_Itf__a_Mt__Real__Oreal_J_M_Eo_J,type,
    inf_inf_a_real_o: ( ( a > real ) > $o ) > ( ( a > real ) > $o ) > ( a > real ) > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_Itf__a_Mtf__a_J_M_Eo_J,type,
    inf_inf_a_a_o: ( ( a > a ) > $o ) > ( ( a > a ) > $o ) > ( a > a ) > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Nat__Onat_M_Eo_J,type,
    inf_inf_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_Itf__a_M_Eo_J,type,
    inf_inf_a_o: ( a > $o ) > ( a > $o ) > a > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
    inf_inf_nat: nat > nat > nat ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Real__Oreal,type,
    inf_inf_real: real > real > real ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_It__Real__Oreal_Mt__Nat__Onat_J_J,type,
    inf_inf_set_real_nat: set_real_nat > set_real_nat > set_real_nat ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_It__Real__Oreal_Mtf__a_J_J,type,
    inf_inf_set_real_a: set_real_a > set_real_a > set_real_a ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_It__Real__Oreal_Mtf__b_J_J,type,
    inf_inf_set_real_b: set_real_b > set_real_b > set_real_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_Itf__a_M_Eo_J_J,type,
    inf_inf_set_a_o: set_a_o > set_a_o > set_a_o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
    inf_in3709910040937683179omplex: set_a_complex > set_a_complex > set_a_complex ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_Itf__a_Mt__Nat__Onat_J_J,type,
    inf_inf_set_a_nat: set_a_nat > set_a_nat > set_a_nat ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_Itf__a_Mt__Real__Oreal_J_J,type,
    inf_inf_set_a_real: set_a_real > set_a_real > set_a_real ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_Itf__a_Mtf__a_J_J,type,
    inf_inf_set_a_a: set_a_a > set_a_a > set_a_a ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_Eo_J,type,
    inf_inf_set_o: set_o > set_o > set_o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Complex__Ocomplex_J,type,
    inf_inf_set_complex: set_complex > set_complex > set_complex ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Extended____Nonnegative____Real__Oennreal_J,type,
    inf_in3368558534146122112nnreal: set_Ex3793607809372303086nnreal > set_Ex3793607809372303086nnreal > set_Ex3793607809372303086nnreal ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
    inf_inf_set_nat: set_nat > set_nat > set_nat ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Real__Oreal_J,type,
    inf_inf_set_real: set_real > set_real > set_real ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
    inf_inf_set_a: set_a > set_a > set_a ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__b_J,type,
    inf_inf_set_b: set_b > set_b > set_b ).

thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
    semiri5074537144036343181t_real: nat > real ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_Eo_J,type,
    bot_bot_set_o: set_o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Extended____Nonnegative____Real__Oennreal_J,type,
    bot_bo4854962954004695426nnreal: set_Ex3793607809372303086nnreal ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
    bot_bot_set_nat: set_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
    bot_bot_set_real: set_real ).

thf(sy_c_Orderings_Oord__class_OLeast_001t__Nat__Onat,type,
    ord_Least_nat: ( nat > $o ) > nat ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Extended____Nonnegative____Real__Oennreal,type,
    ord_le7381754540660121996nnreal: extend8495563244428889912nnreal > extend8495563244428889912nnreal > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
    ord_less_nat: nat > nat > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_It__Real__Oreal_Mt__Nat__Onat_J_M_Eo_J,type,
    top_top_real_nat_o: ( real > nat ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_It__Real__Oreal_Mtf__a_J_M_Eo_J,type,
    top_top_real_a_o: ( real > a ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_It__Real__Oreal_Mtf__b_J_M_Eo_J,type,
    top_top_real_b_o: ( real > b ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_Itf__a_M_Eo_J_M_Eo_J,type,
    top_top_a_o_o: ( a > $o ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_Itf__a_Mt__Complex__Ocomplex_J_M_Eo_J,type,
    top_top_a_complex_o: ( a > complex ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_Itf__a_Mt__Real__Oreal_J_M_Eo_J,type,
    top_top_a_real_o: ( a > real ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_Eo_M_Eo_J,type,
    top_top_o_o: $o > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Complex__Ocomplex_M_Eo_J,type,
    top_top_complex_o: complex > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Extended____Nonnegative____Real__Oennreal_M_Eo_J,type,
    top_to5118619752887738471real_o: extend8495563244428889912nnreal > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
    top_top_nat_o: nat > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Real__Oreal_M_Eo_J,type,
    top_top_real_o: real > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_Itf__a_M_Eo_J,type,
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thf(sy_c_Orderings_Otop__class_Otop_001_062_Itf__b_M_Eo_J,type,
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thf(sy_c_Orderings_Otop__class_Otop_001_Eo,type,
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thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
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thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
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thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
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thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_Itf__b_J_J,type,
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thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
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thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__b_J,type,
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thf(sy_c_QuasiBorel_Oqbs__Mx_001_062_It__Real__Oreal_Mt__Nat__Onat_J,type,
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thf(sy_c_QuasiBorel_Oqbs__Mx_001tf__a,type,
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thf(sy_c_QuasiBorel_Oqbs__Mx_001tf__b,type,
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thf(sy_c_QuasiBorel_Oqbs__space_001_062_It__Real__Oreal_Mt__Nat__Onat_J,type,
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thf(sy_c_QuasiBorel_Oqbs__space_001tf__a,type,
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thf(sy_c_QuasiBorel_Oqbs__space_001tf__b,type,
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    image_nat_set_real_b: ( nat > set_real_b ) > set_nat > set_set_real_b ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_I_062_Itf__a_M_Eo_J_J,type,
    image_nat_set_a_o: ( nat > set_a_o ) > set_nat > set_set_a_o ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_I_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
    image_3591888402735308390omplex: ( nat > set_a_complex ) > set_nat > set_set_a_complex ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_I_062_Itf__a_Mt__Nat__Onat_J_J,type,
    image_nat_set_a_nat: ( nat > set_a_nat ) > set_nat > set_set_a_nat ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_I_062_Itf__a_Mt__Real__Oreal_J_J,type,
    image_nat_set_a_real: ( nat > set_a_real ) > set_nat > set_set_a_real ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_I_062_Itf__a_Mtf__a_J_J,type,
    image_nat_set_a_a: ( nat > set_a_a ) > set_nat > set_set_a_a ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_I_Eo_J,type,
    image_nat_set_o: ( nat > set_o ) > set_nat > set_set_o ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Complex__Ocomplex_J,type,
    image_6594795319511438139omplex: ( nat > set_complex ) > set_nat > set_set_complex ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
    image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Real__Oreal_J,type,
    image_nat_set_real: ( nat > set_real ) > set_nat > set_set_real ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_Itf__a_J,type,
    image_nat_set_a: ( nat > set_a ) > set_nat > set_set_a ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Sigma____Algebra__Omeasure_It__Real__Oreal_J,type,
    image_4672691044420781678e_real: ( nat > sigma_measure_real ) > set_nat > set_Si6059263944882162789e_real ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Sigma____Algebra__Omeasure_Itf__a_J,type,
    image_1114366812419140050sure_a: ( nat > sigma_measure_a ) > set_nat > set_Sigma_measure_a ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001tf__a,type,
    image_nat_a: ( nat > a ) > set_nat > set_a ).

thf(sy_c_Set_Oimage_001t__Real__Oreal_001_Eo,type,
    image_real_o: ( real > $o ) > set_real > set_o ).

thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Complex__Ocomplex,type,
    image_real_complex: ( real > complex ) > set_real > set_complex ).

thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Nat__Onat,type,
    image_real_nat: ( real > nat ) > set_real > set_nat ).

thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
    image_real_real: ( real > real ) > set_real > set_real ).

thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Set__Oset_I_Eo_J,type,
    image_real_set_o: ( real > set_o ) > set_real > set_set_o ).

thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Set__Oset_It__Complex__Ocomplex_J,type,
    image_2129611632225307415omplex: ( real > set_complex ) > set_real > set_set_complex ).

thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Set__Oset_It__Nat__Onat_J,type,
    image_real_set_nat: ( real > set_nat ) > set_real > set_set_nat ).

thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Set__Oset_It__Real__Oreal_J,type,
    image_real_set_real: ( real > set_real ) > set_real > set_set_real ).

thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Set__Oset_Itf__a_J,type,
    image_real_set_a: ( real > set_a ) > set_real > set_set_a ).

thf(sy_c_Set_Oimage_001t__Real__Oreal_001tf__a,type,
    image_real_a: ( real > a ) > set_real > set_a ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_062_It__Real__Oreal_Mt__Nat__Onat_J_J_001_Eo,type,
    image_set_real_nat_o: ( set_real_nat > $o ) > set_set_real_nat > set_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_062_It__Real__Oreal_Mtf__a_J_J_001_Eo,type,
    image_set_real_a_o: ( set_real_a > $o ) > set_set_real_a > set_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_062_It__Real__Oreal_Mtf__b_J_J_001_Eo,type,
    image_set_real_b_o: ( set_real_b > $o ) > set_set_real_b > set_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_062_Itf__a_M_Eo_J_J_001_Eo,type,
    image_set_a_o_o: ( set_a_o > $o ) > set_set_a_o > set_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_062_Itf__a_Mt__Complex__Ocomplex_J_J_001_Eo,type,
    image_5240558645659804640plex_o: ( set_a_complex > $o ) > set_set_a_complex > set_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_062_Itf__a_Mt__Nat__Onat_J_J_001_Eo,type,
    image_set_a_nat_o: ( set_a_nat > $o ) > set_set_a_nat > set_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_062_Itf__a_Mt__Real__Oreal_J_J_001_Eo,type,
    image_set_a_real_o: ( set_a_real > $o ) > set_set_a_real > set_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_062_Itf__a_Mtf__a_J_J_001_Eo,type,
    image_set_a_a_o: ( set_a_a > $o ) > set_set_a_a > set_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Nat__Onat_J_001_Eo,type,
    image_set_nat_o: ( set_nat > $o ) > set_set_nat > set_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_Itf__a_J_001_Eo,type,
    image_set_a_o: ( set_a > $o ) > set_set_a > set_o ).

thf(sy_c_Set_Oimage_001t__Sigma____Algebra__Omeasure_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
    image_5027996441425795932_set_o: ( sigma_measure_o > set_o ) > set_Sigma_measure_o > set_set_o ).

thf(sy_c_Set_Oimage_001t__Sigma____Algebra__Omeasure_It__Extended____Nonnegative____Real__Oennreal_J_001t__Set__Oset_It__Extended____Nonnegative____Real__Oennreal_J,type,
    image_5045373228407281722nnreal: ( sigma_7234349610311085201nnreal > set_Ex3793607809372303086nnreal ) > set_Si97717610131227249nnreal > set_se4580700918925141924nnreal ).

thf(sy_c_Set_Oimage_001t__Sigma____Algebra__Omeasure_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    image_8842839924425425258et_nat: ( sigma_measure_nat > set_nat ) > set_Si3048223896905877257re_nat > set_set_nat ).

thf(sy_c_Set_Oimage_001t__Sigma____Algebra__Omeasure_It__Real__Oreal_J_001t__Set__Oset_It__Real__Oreal_J,type,
    image_494530498693788066t_real: ( sigma_measure_real > set_real ) > set_Si6059263944882162789e_real > set_set_real ).

thf(sy_c_Set_Oimage_001tf__a_001_062_It__Real__Oreal_Mt__Nat__Onat_J,type,
    image_a_real_nat: ( a > real > nat ) > set_a > set_real_nat ).

thf(sy_c_Set_Oimage_001tf__a_001_062_It__Real__Oreal_Mtf__a_J,type,
    image_a_real_a: ( a > real > a ) > set_a > set_real_a ).

thf(sy_c_Set_Oimage_001tf__a_001_062_It__Real__Oreal_Mtf__b_J,type,
    image_a_real_b: ( a > real > b ) > set_a > set_real_b ).

thf(sy_c_Set_Oimage_001tf__a_001_Eo,type,
    image_a_o: ( a > $o ) > set_a > set_o ).

thf(sy_c_Set_Oimage_001tf__a_001t__Nat__Onat,type,
    image_a_nat: ( a > nat ) > set_a > set_nat ).

thf(sy_c_Set_Oimage_001tf__a_001t__Real__Oreal,type,
    image_a_real: ( a > real ) > set_a > set_real ).

thf(sy_c_Set_Oimage_001tf__a_001t__Set__Oset_I_Eo_J,type,
    image_a_set_o: ( a > set_o ) > set_a > set_set_o ).

thf(sy_c_Set_Oimage_001tf__a_001t__Set__Oset_It__Complex__Ocomplex_J,type,
    image_a_set_complex: ( a > set_complex ) > set_a > set_set_complex ).

thf(sy_c_Set_Oimage_001tf__a_001t__Set__Oset_It__Nat__Onat_J,type,
    image_a_set_nat: ( a > set_nat ) > set_a > set_set_nat ).

thf(sy_c_Set_Oimage_001tf__a_001t__Set__Oset_It__Real__Oreal_J,type,
    image_a_set_real: ( a > set_real ) > set_a > set_set_real ).

thf(sy_c_Set_Oimage_001tf__a_001t__Set__Oset_Itf__a_J,type,
    image_a_set_a: ( a > set_a ) > set_a > set_set_a ).

thf(sy_c_Set_Oimage_001tf__a_001t__Sigma____Algebra__Omeasure_It__Real__Oreal_J,type,
    image_4051082315841709580e_real: ( a > sigma_measure_real ) > set_a > set_Si6059263944882162789e_real ).

thf(sy_c_Set_Oimage_001tf__a_001t__Sigma____Algebra__Omeasure_Itf__a_J,type,
    image_5550635671931946676sure_a: ( a > sigma_measure_a ) > set_a > set_Sigma_measure_a ).

thf(sy_c_Set_Oimage_001tf__a_001tf__a,type,
    image_a_a: ( a > a ) > set_a > set_a ).

thf(sy_c_Set_Oinsert_001_Eo,type,
    insert_o: $o > set_o > set_o ).

thf(sy_c_Set_Oinsert_001t__Extended____Nonnegative____Real__Oennreal,type,
    insert7407984058720857448nnreal: extend8495563244428889912nnreal > set_Ex3793607809372303086nnreal > set_Ex3793607809372303086nnreal ).

thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
    insert_nat: nat > set_nat > set_nat ).

thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
    insert_real: real > set_real > set_real ).

thf(sy_c_Set_Ovimage_001t__Real__Oreal_001t__Nat__Onat,type,
    vimage_real_nat: ( real > nat ) > set_nat > set_real ).

thf(sy_c_Sigma__Algebra_Ocount__space_001_Eo,type,
    sigma_count_space_o: set_o > sigma_measure_o ).

thf(sy_c_Sigma__Algebra_Ocount__space_001t__Complex__Ocomplex,type,
    sigma_3977070789342921045omplex: set_complex > sigma_3077487657436305159omplex ).

thf(sy_c_Sigma__Algebra_Ocount__space_001t__Extended____Nonnegative____Real__Oennreal,type,
    sigma_7204664791115113951nnreal: set_Ex3793607809372303086nnreal > sigma_7234349610311085201nnreal ).

thf(sy_c_Sigma__Algebra_Ocount__space_001t__Nat__Onat,type,
    sigma_7685844798829912695ce_nat: set_nat > sigma_measure_nat ).

thf(sy_c_Sigma__Algebra_Ocount__space_001t__Real__Oreal,type,
    sigma_8508918144308765139e_real: set_real > sigma_measure_real ).

thf(sy_c_Sigma__Algebra_Ocount__space_001tf__a,type,
    sigma_count_space_a: set_a > sigma_measure_a ).

thf(sy_c_Sigma__Algebra_Ocount__space_001tf__b,type,
    sigma_count_space_b: set_b > sigma_measure_b ).

thf(sy_c_Sigma__Algebra_Omeasurable_001_062_It__Real__Oreal_Mt__Nat__Onat_J_001_Eo,type,
    sigma_4110928884538380267_nat_o: sigma_6586288717683155060al_nat > sigma_measure_o > set_real_nat_o ).

thf(sy_c_Sigma__Algebra_Omeasurable_001_062_It__Real__Oreal_Mtf__a_J_001_Eo,type,
    sigma_902503387808413471al_a_o: sigma_measure_real_a > sigma_measure_o > set_real_a_o2 ).

thf(sy_c_Sigma__Algebra_Omeasurable_001_062_It__Real__Oreal_Mtf__b_J_001_Eo,type,
    sigma_7338419842690513246al_b_o: sigma_measure_real_b > sigma_measure_o > set_real_b_o ).

thf(sy_c_Sigma__Algebra_Omeasurable_001_062_Itf__a_M_Eo_J_001_Eo,type,
    sigma_1195952539894209287_a_o_o: sigma_measure_a_o > sigma_measure_o > set_a_o_o ).

thf(sy_c_Sigma__Algebra_Omeasurable_001_062_Itf__a_Mt__Complex__Ocomplex_J_001_Eo,type,
    sigma_2293258167702796171plex_o: sigma_2418697800065292186omplex > sigma_measure_o > set_a_complex_o ).

thf(sy_c_Sigma__Algebra_Omeasurable_001_062_Itf__a_Mt__Nat__Onat_J_001_Eo,type,
    sigma_128654050890844905_nat_o: sigma_measure_a_nat > sigma_measure_o > set_a_nat_o ).

thf(sy_c_Sigma__Algebra_Omeasurable_001_062_Itf__a_Mt__Real__Oreal_J_001_Eo,type,
    sigma_9085598459323199629real_o: sigma_measure_a_real > sigma_measure_o > set_a_real_o ).

thf(sy_c_Sigma__Algebra_Omeasurable_001_062_Itf__a_Mtf__a_J_001_Eo,type,
    sigma_7605542298065862561_a_a_o: sigma_measure_a_a > sigma_measure_o > set_a_a_o ).

thf(sy_c_Sigma__Algebra_Omeasurable_001_Eo_001_Eo,type,
    sigma_measurable_o_o: sigma_measure_o > sigma_measure_o > set_o_o ).

thf(sy_c_Sigma__Algebra_Omeasurable_001_Eo_001t__Nat__Onat,type,
    sigma_1999164137574644376_o_nat: sigma_measure_o > sigma_measure_nat > set_o_nat ).

thf(sy_c_Sigma__Algebra_Omeasurable_001_Eo_001t__Real__Oreal,type,
    sigma_2430008634441611636o_real: sigma_measure_o > sigma_measure_real > set_o_real ).

thf(sy_c_Sigma__Algebra_Omeasurable_001_Eo_001tf__a,type,
    sigma_measurable_o_a: sigma_measure_o > sigma_measure_a > set_o_a ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
    sigma_5867711785444923182omplex: sigma_3077487657436305159omplex > sigma_3077487657436305159omplex > set_complex_complex ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Complex__Ocomplex_001t__Real__Oreal,type,
    sigma_9165504702370893100x_real: sigma_3077487657436305159omplex > sigma_measure_real > set_complex_real ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Extended____Nonnegative____Real__Oennreal_001_Eo,type,
    sigma_6279906219187228174real_o: sigma_7234349610311085201nnreal > sigma_measure_o > set_Ex70502500924464887real_o ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Extended____Nonnegative____Real__Oennreal_001t__Nat__Onat,type,
    sigma_1856489715609627354al_nat: sigma_7234349610311085201nnreal > sigma_measure_nat > set_Ex1875306066257539165al_nat ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Extended____Nonnegative____Real__Oennreal_001t__Real__Oreal,type,
    sigma_7049758200512112822l_real: sigma_7234349610311085201nnreal > sigma_measure_real > set_Ex5658717452565810105l_real ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Extended____Nonnegative____Real__Oennreal_001tf__a,type,
    sigma_3031480723531659892real_a: sigma_7234349610311085201nnreal > sigma_measure_a > set_Ex2249781601450085341real_a ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Nat__Onat_001_Eo,type,
    sigma_5101835498682829686_nat_o: sigma_measure_nat > sigma_measure_o > set_nat_o ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Nat__Onat_001t__Extended____Nonnegative____Real__Oennreal,type,
    sigma_6306161311797543642nnreal: sigma_measure_nat > sigma_7234349610311085201nnreal > set_na7716847989478749277nnreal ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Nat__Onat_001t__Nat__Onat,type,
    sigma_4350458207664084850at_nat: sigma_measure_nat > sigma_measure_nat > set_nat_nat ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Nat__Onat_001t__Real__Oreal,type,
    sigma_1747752005702207822t_real: sigma_measure_nat > sigma_measure_real > set_nat_real ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Nat__Onat_001tf__a,type,
    sigma_4105081583803843548_nat_a: sigma_measure_nat > sigma_measure_a > set_nat_a ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Nat__Onat_001tf__b,type,
    sigma_4105081583803843549_nat_b: sigma_measure_nat > sigma_measure_b > set_nat_b ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Real__Oreal_001_Eo,type,
    sigma_3939073009482781210real_o: sigma_measure_real > sigma_measure_o > set_real_o ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Real__Oreal_001t__Complex__Ocomplex,type,
    sigma_9111916201866572460omplex: sigma_measure_real > sigma_3077487657436305159omplex > set_real_complex ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Real__Oreal_001t__Extended____Nonnegative____Real__Oennreal,type,
    sigma_9017504469962657078nnreal: sigma_measure_real > sigma_7234349610311085201nnreal > set_re5328672808648366137nnreal ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Real__Oreal_001t__Nat__Onat,type,
    sigma_6315060578831106510al_nat: sigma_measure_real > sigma_measure_nat > set_real_nat ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Real__Oreal_001t__Real__Oreal,type,
    sigma_5267869275261027754l_real: sigma_measure_real > sigma_measure_real > set_real_real ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Real__Oreal_001tf__a,type,
    sigma_523072396149930112real_a: sigma_measure_real > sigma_measure_a > set_real_a ).

thf(sy_c_Sigma__Algebra_Omeasurable_001t__Real__Oreal_001tf__b,type,
    sigma_523072396149930113real_b: sigma_measure_real > sigma_measure_b > set_real_b ).

thf(sy_c_Sigma__Algebra_Omeasurable_001tf__a_001_Eo,type,
    sigma_measurable_a_o: sigma_measure_a > sigma_measure_o > set_a_o ).

thf(sy_c_Sigma__Algebra_Omeasurable_001tf__a_001t__Complex__Ocomplex,type,
    sigma_852363994732143452omplex: sigma_measure_a > sigma_3077487657436305159omplex > set_a_complex ).

thf(sy_c_Sigma__Algebra_Omeasurable_001tf__a_001t__Extended____Nonnegative____Real__Oennreal,type,
    sigma_214952329563889126nnreal: sigma_measure_a > sigma_7234349610311085201nnreal > set_a_7161065143582548615nnreal ).

thf(sy_c_Sigma__Algebra_Omeasurable_001tf__a_001t__Nat__Onat,type,
    sigma_73150082625557118_a_nat: sigma_measure_a > sigma_measure_nat > set_a_nat ).

thf(sy_c_Sigma__Algebra_Omeasurable_001tf__a_001t__Real__Oreal,type,
    sigma_9116425665531756122a_real: sigma_measure_a > sigma_measure_real > set_a_real ).

thf(sy_c_Sigma__Algebra_Omeasurable_001tf__a_001tf__a,type,
    sigma_measurable_a_a: sigma_measure_a > sigma_measure_a > set_a_a ).

thf(sy_c_Sigma__Algebra_Omeasurable_001tf__a_001tf__b,type,
    sigma_measurable_a_b: sigma_measure_a > sigma_measure_b > set_a_b ).

thf(sy_c_Sigma__Algebra_Omeasurable_001tf__b_001t__Nat__Onat,type,
    sigma_1308594411581951615_b_nat: sigma_measure_b > sigma_measure_nat > set_b_nat ).

thf(sy_c_Sigma__Algebra_Omeasurable_001tf__b_001tf__a,type,
    sigma_measurable_b_a: sigma_measure_b > sigma_measure_a > set_b_a ).

thf(sy_c_Sigma__Algebra_Omeasurable_001tf__b_001tf__b,type,
    sigma_measurable_b_b: sigma_measure_b > sigma_measure_b > set_b_b ).

thf(sy_c_Sigma__Algebra_Orestrict__space_001_Eo,type,
    sigma_8520893325391096540pace_o: sigma_measure_o > set_o > sigma_measure_o ).

thf(sy_c_Sigma__Algebra_Orestrict__space_001t__Complex__Ocomplex,type,
    sigma_216592511309337194omplex: sigma_3077487657436305159omplex > set_complex > sigma_3077487657436305159omplex ).

thf(sy_c_Sigma__Algebra_Orestrict__space_001t__Extended____Nonnegative____Real__Oennreal,type,
    sigma_4884701650823297268nnreal: sigma_7234349610311085201nnreal > set_Ex3793607809372303086nnreal > sigma_7234349610311085201nnreal ).

thf(sy_c_Sigma__Algebra_Orestrict__space_001t__Nat__Onat,type,
    sigma_744083341818469772ce_nat: sigma_measure_nat > set_nat > sigma_measure_nat ).

thf(sy_c_Sigma__Algebra_Orestrict__space_001t__Real__Oreal,type,
    sigma_5414646170262037096e_real: sigma_measure_real > set_real > sigma_measure_real ).

thf(sy_c_Sigma__Algebra_Orestrict__space_001tf__a,type,
    sigma_8692839461743104066pace_a: sigma_measure_a > set_a > sigma_measure_a ).

thf(sy_c_Sigma__Algebra_Orestrict__space_001tf__b,type,
    sigma_8692839461743104067pace_b: sigma_measure_b > set_b > sigma_measure_b ).

thf(sy_c_Sigma__Algebra_Osets_001_Eo,type,
    sigma_sets_o: sigma_measure_o > set_set_o ).

thf(sy_c_Sigma__Algebra_Osets_001t__Extended____Nonnegative____Real__Oennreal,type,
    sigma_5465916536984168985nnreal: sigma_7234349610311085201nnreal > set_se4580700918925141924nnreal ).

thf(sy_c_Sigma__Algebra_Osets_001t__Nat__Onat,type,
    sigma_sets_nat: sigma_measure_nat > set_set_nat ).

thf(sy_c_Sigma__Algebra_Osets_001t__Real__Oreal,type,
    sigma_sets_real: sigma_measure_real > set_set_real ).

thf(sy_c_Sigma__Algebra_Ospace_001_062_It__Real__Oreal_Mt__Nat__Onat_J,type,
    sigma_space_real_nat: sigma_6586288717683155060al_nat > set_real_nat ).

thf(sy_c_Sigma__Algebra_Ospace_001_062_It__Real__Oreal_Mtf__a_J,type,
    sigma_space_real_a: sigma_measure_real_a > set_real_a ).

thf(sy_c_Sigma__Algebra_Ospace_001_062_It__Real__Oreal_Mtf__b_J,type,
    sigma_space_real_b: sigma_measure_real_b > set_real_b ).

thf(sy_c_Sigma__Algebra_Ospace_001_062_Itf__a_Mt__Complex__Ocomplex_J,type,
    sigma_2448487161356845349omplex: sigma_2418697800065292186omplex > set_a_complex ).

thf(sy_c_Sigma__Algebra_Ospace_001_062_Itf__a_Mt__Real__Oreal_J,type,
    sigma_space_a_real: sigma_measure_a_real > set_a_real ).

thf(sy_c_Sigma__Algebra_Ospace_001_Eo,type,
    sigma_space_o: sigma_measure_o > set_o ).

thf(sy_c_Sigma__Algebra_Ospace_001t__Complex__Ocomplex,type,
    sigma_space_complex: sigma_3077487657436305159omplex > set_complex ).

thf(sy_c_Sigma__Algebra_Ospace_001t__Extended____Nonnegative____Real__Oennreal,type,
    sigma_3147302497200244656nnreal: sigma_7234349610311085201nnreal > set_Ex3793607809372303086nnreal ).

thf(sy_c_Sigma__Algebra_Ospace_001t__Nat__Onat,type,
    sigma_space_nat: sigma_measure_nat > set_nat ).

thf(sy_c_Sigma__Algebra_Ospace_001t__Real__Oreal,type,
    sigma_space_real: sigma_measure_real > set_real ).

thf(sy_c_Sigma__Algebra_Ospace_001tf__a,type,
    sigma_space_a: sigma_measure_a > set_a ).

thf(sy_c_Sigma__Algebra_Ospace_001tf__b,type,
    sigma_space_b: sigma_measure_b > set_b ).

thf(sy_c_StandardBorel_Ostandard__borel__space__UNIV__axioms_001_062_It__Real__Oreal_Mt__Nat__Onat_J,type,
    standa1166615221086727615al_nat: sigma_6586288717683155060al_nat > $o ).

thf(sy_c_StandardBorel_Ostandard__borel__space__UNIV__axioms_001_062_It__Real__Oreal_Mtf__a_J,type,
    standa5303581020940319333real_a: sigma_measure_real_a > $o ).

thf(sy_c_StandardBorel_Ostandard__borel__space__UNIV__axioms_001_062_It__Real__Oreal_Mtf__b_J,type,
    standa5303581025243548134real_b: sigma_measure_real_b > $o ).

thf(sy_c_StandardBorel_Ostandard__borel__space__UNIV__axioms_001_Eo,type,
    standa4575222554423029108ioms_o: sigma_measure_o > $o ).

thf(sy_c_StandardBorel_Ostandard__borel__space__UNIV__axioms_001t__Complex__Ocomplex,type,
    standa483509463685453266omplex: sigma_3077487657436305159omplex > $o ).

thf(sy_c_StandardBorel_Ostandard__borel__space__UNIV__axioms_001t__Extended____Nonnegative____Real__Oennreal,type,
    standa602082540683807836nnreal: sigma_7234349610311085201nnreal > $o ).

thf(sy_c_StandardBorel_Ostandard__borel__space__UNIV__axioms_001t__Nat__Onat,type,
    standa4898135366436483316ms_nat: sigma_measure_nat > $o ).

thf(sy_c_StandardBorel_Ostandard__borel__space__UNIV__axioms_001t__Real__Oreal,type,
    standa1498722272452280784s_real: sigma_measure_real > $o ).

thf(sy_c_StandardBorel_Ostandard__borel__space__UNIV__axioms_001tf__a,type,
    standa2153564630574221018ioms_a: sigma_measure_a > $o ).

thf(sy_c_StandardBorel_Ostandard__borel__space__UNIV__axioms_001tf__b,type,
    standa2153564630574221019ioms_b: sigma_measure_b > $o ).

thf(sy_c_member_001_062_I_062_It__Real__Oreal_Mt__Nat__Onat_J_M_Eo_J,type,
    member_real_nat_o: ( ( real > nat ) > $o ) > set_real_nat_o > $o ).

thf(sy_c_member_001_062_I_062_It__Real__Oreal_Mtf__a_J_M_Eo_J,type,
    member_real_a_o: ( ( real > a ) > $o ) > set_real_a_o2 > $o ).

thf(sy_c_member_001_062_I_062_It__Real__Oreal_Mtf__b_J_M_Eo_J,type,
    member_real_b_o: ( ( real > b ) > $o ) > set_real_b_o > $o ).

thf(sy_c_member_001_062_I_062_Itf__a_M_Eo_J_M_Eo_J,type,
    member_a_o_o: ( ( a > $o ) > $o ) > set_a_o_o > $o ).

thf(sy_c_member_001_062_I_062_Itf__a_Mt__Complex__Ocomplex_J_M_Eo_J,type,
    member_a_complex_o: ( ( a > complex ) > $o ) > set_a_complex_o > $o ).

thf(sy_c_member_001_062_I_062_Itf__a_Mt__Nat__Onat_J_M_Eo_J,type,
    member_a_nat_o: ( ( a > nat ) > $o ) > set_a_nat_o > $o ).

thf(sy_c_member_001_062_I_062_Itf__a_Mt__Real__Oreal_J_M_Eo_J,type,
    member_a_real_o: ( ( a > real ) > $o ) > set_a_real_o > $o ).

thf(sy_c_member_001_062_I_062_Itf__a_Mtf__a_J_M_Eo_J,type,
    member_a_a_o: ( ( a > a ) > $o ) > set_a_a_o > $o ).

thf(sy_c_member_001_062_I_Eo_M_Eo_J,type,
    member_o_o: ( $o > $o ) > set_o_o > $o ).

thf(sy_c_member_001_062_I_Eo_Mt__Nat__Onat_J,type,
    member_o_nat: ( $o > nat ) > set_o_nat > $o ).

thf(sy_c_member_001_062_I_Eo_Mt__Real__Oreal_J,type,
    member_o_real: ( $o > real ) > set_o_real > $o ).

thf(sy_c_member_001_062_I_Eo_Mtf__a_J,type,
    member_o_a: ( $o > a ) > set_o_a > $o ).

thf(sy_c_member_001_062_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
    member5128974058612258834omplex: ( complex > complex ) > set_complex_complex > $o ).

thf(sy_c_member_001_062_It__Complex__Ocomplex_Mt__Real__Oreal_J,type,
    member_complex_real: ( complex > real ) > set_complex_real > $o ).

thf(sy_c_member_001_062_It__Extended____Nonnegative____Real__Oennreal_M_Eo_J,type,
    member8095236870201115968real_o: ( extend8495563244428889912nnreal > $o ) > set_Ex70502500924464887real_o > $o ).

thf(sy_c_member_001_062_It__Extended____Nonnegative____Real__Oennreal_Mt__Nat__Onat_J,type,
    member6436672275262627518al_nat: ( extend8495563244428889912nnreal > nat ) > set_Ex1875306066257539165al_nat > $o ).

thf(sy_c_member_001_062_It__Extended____Nonnegative____Real__Oennreal_Mt__Real__Oreal_J,type,
    member2874014351250825754l_real: ( extend8495563244428889912nnreal > real ) > set_Ex5658717452565810105l_real > $o ).

thf(sy_c_member_001_062_It__Extended____Nonnegative____Real__Oennreal_Mtf__a_J,type,
    member4924430693770431270real_a: ( extend8495563244428889912nnreal > a ) > set_Ex2249781601450085341real_a > $o ).

thf(sy_c_member_001_062_It__Nat__Onat_M_Eo_J,type,
    member_nat_o: ( nat > $o ) > set_nat_o > $o ).

thf(sy_c_member_001_062_It__Nat__Onat_Mt__Extended____Nonnegative____Real__Oennreal_J,type,
    member8283130129095025342nnreal: ( nat > extend8495563244428889912nnreal ) > set_na7716847989478749277nnreal > $o ).

thf(sy_c_member_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
    member_nat_nat: ( nat > nat ) > set_nat_nat > $o ).

thf(sy_c_member_001_062_It__Nat__Onat_Mt__Real__Oreal_J,type,
    member_nat_real: ( nat > real ) > set_nat_real > $o ).

thf(sy_c_member_001_062_It__Nat__Onat_Mtf__a_J,type,
    member_nat_a: ( nat > a ) > set_nat_a > $o ).

thf(sy_c_member_001_062_It__Nat__Onat_Mtf__b_J,type,
    member_nat_b: ( nat > b ) > set_nat_b > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_M_062_It__Real__Oreal_Mt__Nat__Onat_J_J,type,
    member_real_real_nat: ( real > real > nat ) > set_real_real_nat > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_M_062_It__Real__Oreal_Mtf__a_J_J,type,
    member_real_real_a: ( real > real > a ) > set_real_real_a > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_M_062_It__Real__Oreal_Mtf__b_J_J,type,
    member_real_real_b: ( real > real > b ) > set_real_real_b > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_M_062_Itf__a_M_Eo_J_J,type,
    member_real_a_o2: ( real > a > $o ) > set_real_a_o > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_M_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
    member8749487273670996305omplex: ( real > a > complex ) > set_real_a_complex > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_M_062_Itf__a_Mt__Nat__Onat_J_J,type,
    member_real_a_nat: ( real > a > nat ) > set_real_a_nat > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_M_062_Itf__a_Mt__Real__Oreal_J_J,type,
    member_real_a_real: ( real > a > real ) > set_real_a_real > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_M_Eo_J,type,
    member_real_o: ( real > $o ) > set_real_o > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Complex__Ocomplex_J,type,
    member_real_complex: ( real > complex ) > set_real_complex > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Extended____Nonnegative____Real__Oennreal_J,type,
    member2919562650594848410nnreal: ( real > extend8495563244428889912nnreal ) > set_re5328672808648366137nnreal > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Nat__Onat_J,type,
    member_real_nat: ( real > nat ) > set_real_nat > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Real__Oreal_J,type,
    member_real_real: ( real > real ) > set_real_real > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mtf__a_J,type,
    member_real_a: ( real > a ) > set_real_a > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mtf__b_J,type,
    member_real_b: ( real > b ) > set_real_b > $o ).

thf(sy_c_member_001_062_Itf__a_M_Eo_J,type,
    member_a_o: ( a > $o ) > set_a_o > $o ).

thf(sy_c_member_001_062_Itf__a_Mt__Complex__Ocomplex_J,type,
    member_a_complex: ( a > complex ) > set_a_complex > $o ).

thf(sy_c_member_001_062_Itf__a_Mt__Extended____Nonnegative____Real__Oennreal_J,type,
    member298456594901751504nnreal: ( a > extend8495563244428889912nnreal ) > set_a_7161065143582548615nnreal > $o ).

thf(sy_c_member_001_062_Itf__a_Mt__Nat__Onat_J,type,
    member_a_nat: ( a > nat ) > set_a_nat > $o ).

thf(sy_c_member_001_062_Itf__a_Mt__Real__Oreal_J,type,
    member_a_real: ( a > real ) > set_a_real > $o ).

thf(sy_c_member_001_062_Itf__a_Mtf__a_J,type,
    member_a_a: ( a > a ) > set_a_a > $o ).

thf(sy_c_member_001_062_Itf__a_Mtf__b_J,type,
    member_a_b: ( a > b ) > set_a_b > $o ).

thf(sy_c_member_001_062_Itf__b_Mt__Nat__Onat_J,type,
    member_b_nat: ( b > nat ) > set_b_nat > $o ).

thf(sy_c_member_001_062_Itf__b_Mtf__a_J,type,
    member_b_a: ( b > a ) > set_b_a > $o ).

thf(sy_c_member_001_062_Itf__b_Mtf__b_J,type,
    member_b_b: ( b > b ) > set_b_b > $o ).

thf(sy_c_member_001_Eo,type,
    member_o: $o > set_o > $o ).

thf(sy_c_member_001t__Complex__Ocomplex,type,
    member_complex: complex > set_complex > $o ).

thf(sy_c_member_001t__Extended____Nonnegative____Real__Oennreal,type,
    member7908768830364227535nnreal: extend8495563244428889912nnreal > set_Ex3793607809372303086nnreal > $o ).

thf(sy_c_member_001t__Nat__Onat,type,
    member_nat: nat > set_nat > $o ).

thf(sy_c_member_001t__Real__Oreal,type,
    member_real: real > set_real > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_It__Real__Oreal_Mt__Nat__Onat_J_J,type,
    member_set_real_nat: set_real_nat > set_set_real_nat > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_It__Real__Oreal_Mtf__a_J_J,type,
    member_set_real_a: set_real_a > set_set_real_a > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_It__Real__Oreal_Mtf__b_J_J,type,
    member_set_real_b: set_real_b > set_set_real_b > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_Itf__a_M_Eo_J_J,type,
    member_set_a_o: set_a_o > set_set_a_o > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_Itf__a_Mt__Complex__Ocomplex_J_J,type,
    member_set_a_complex: set_a_complex > set_set_a_complex > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_Itf__a_Mt__Nat__Onat_J_J,type,
    member_set_a_nat: set_a_nat > set_set_a_nat > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_Itf__a_Mt__Real__Oreal_J_J,type,
    member_set_a_real: set_a_real > set_set_a_real > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_Itf__a_Mtf__a_J_J,type,
    member_set_a_a: set_a_a > set_set_a_a > $o ).

thf(sy_c_member_001t__Set__Oset_I_Eo_J,type,
    member_set_o: set_o > set_set_o > $o ).

thf(sy_c_member_001t__Set__Oset_It__Complex__Ocomplex_J,type,
    member_set_complex: set_complex > set_set_complex > $o ).

thf(sy_c_member_001t__Set__Oset_It__Extended____Nonnegative____Real__Oennreal_J,type,
    member603777416030116741nnreal: set_Ex3793607809372303086nnreal > set_se4580700918925141924nnreal > $o ).

thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
    member_set_nat: set_nat > set_set_nat > $o ).

thf(sy_c_member_001t__Set__Oset_It__Real__Oreal_J,type,
    member_set_real: set_real > set_set_real > $o ).

thf(sy_c_member_001t__Set__Oset_Itf__a_J,type,
    member_set_a: set_a > set_set_a > $o ).

thf(sy_c_member_001t__Set__Oset_Itf__b_J,type,
    member_set_b: set_b > set_set_b > $o ).

thf(sy_c_member_001t__Sigma____Algebra__Omeasure_It__Real__Oreal_J,type,
    member4553183543495551918e_real: sigma_measure_real > set_Si6059263944882162789e_real > $o ).

thf(sy_c_member_001t__Sigma____Algebra__Omeasure_Itf__a_J,type,
    member3534519376729797778sure_a: sigma_measure_a > set_Sigma_measure_a > $o ).

thf(sy_c_member_001tf__a,type,
    member_a: a > set_a > $o ).

thf(sy_c_member_001tf__b,type,
    member_b: b > set_b > $o ).

thf(sy_v_Fi,type,
    fi: a > real > b ).

thf(sy_v_I,type,
    i: set_a ).

thf(sy_v_P,type,
    p: real > a ).

thf(sy_v_X,type,
    x: quasi_borel_b ).

% Relevant facts (1276)
thf(fact_0__092_060open_062restrict__space_A_Icount__space_AI_J_A_Irange_AP_J_A_061_Acount__space_A_Irange_AP_A_092_060inter_062_AI_J_092_060close_062,axiom,
    ( ( sigma_8692839461743104066pace_a @ ( sigma_count_space_a @ i ) @ ( image_real_a @ p @ top_top_set_real ) )
    = ( sigma_count_space_a @ ( inf_inf_set_a @ ( image_real_a @ p @ top_top_set_real ) @ i ) ) ) ).

% \<open>restrict_space (count_space I) (range P) = count_space (range P \<inter> I)\<close>
thf(fact_1_assms_I2_J,axiom,
    member_real_a @ p @ ( sigma_523072396149930112real_a @ borel_5078946678739801102l_real @ ( sigma_count_space_a @ i ) ) ).

% assms(2)
thf(fact_2__C0_C,axiom,
    ( ( inf_inf_set_a @ ( image_real_a @ p @ top_top_set_real ) @ i )
    = ( image_real_a @ p @ top_top_set_real ) ) ).

% "0"
thf(fact_3_borel__measurable__count__space,axiom,
    ! [F: a > real,S: set_a] : ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ ( sigma_count_space_a @ S ) @ borel_5078946678739801102l_real ) ) ).

% borel_measurable_count_space
thf(fact_4_borel__measurable__count__space,axiom,
    ! [F: real > real,S: set_real] : ( member_real_real @ F @ ( sigma_5267869275261027754l_real @ ( sigma_8508918144308765139e_real @ S ) @ borel_5078946678739801102l_real ) ) ).

% borel_measurable_count_space
thf(fact_5_borel__measurable__count__space,axiom,
    ! [F: $o > real,S: set_o] : ( member_o_real @ F @ ( sigma_2430008634441611636o_real @ ( sigma_count_space_o @ S ) @ borel_5078946678739801102l_real ) ) ).

% borel_measurable_count_space
thf(fact_6_borel__measurable__count__space,axiom,
    ! [F: nat > real,S: set_nat] : ( member_nat_real @ F @ ( sigma_1747752005702207822t_real @ ( sigma_7685844798829912695ce_nat @ S ) @ borel_5078946678739801102l_real ) ) ).

% borel_measurable_count_space
thf(fact_7_borel__measurable__count__space,axiom,
    ! [F: extend8495563244428889912nnreal > real,S: set_Ex3793607809372303086nnreal] : ( member2874014351250825754l_real @ F @ ( sigma_7049758200512112822l_real @ ( sigma_7204664791115113951nnreal @ S ) @ borel_5078946678739801102l_real ) ) ).

% borel_measurable_count_space
thf(fact_8_borel__measurable__count__space,axiom,
    ! [F: a > nat,S: set_a] : ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ ( sigma_count_space_a @ S ) @ borel_8449730974584783410el_nat ) ) ).

% borel_measurable_count_space
thf(fact_9_borel__measurable__count__space,axiom,
    ! [F: real > nat,S: set_real] : ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ ( sigma_8508918144308765139e_real @ S ) @ borel_8449730974584783410el_nat ) ) ).

% borel_measurable_count_space
thf(fact_10_borel__measurable__count__space,axiom,
    ! [F: $o > nat,S: set_o] : ( member_o_nat @ F @ ( sigma_1999164137574644376_o_nat @ ( sigma_count_space_o @ S ) @ borel_8449730974584783410el_nat ) ) ).

% borel_measurable_count_space
thf(fact_11_borel__measurable__count__space,axiom,
    ! [F: nat > nat,S: set_nat] : ( member_nat_nat @ F @ ( sigma_4350458207664084850at_nat @ ( sigma_7685844798829912695ce_nat @ S ) @ borel_8449730974584783410el_nat ) ) ).

% borel_measurable_count_space
thf(fact_12_borel__measurable__count__space,axiom,
    ! [F: extend8495563244428889912nnreal > nat,S: set_Ex3793607809372303086nnreal] : ( member6436672275262627518al_nat @ F @ ( sigma_1856489715609627354al_nat @ ( sigma_7204664791115113951nnreal @ S ) @ borel_8449730974584783410el_nat ) ) ).

% borel_measurable_count_space
thf(fact_13_measurable__count__space,axiom,
    ! [F: a > complex,A: set_a] : ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ ( sigma_count_space_a @ A ) @ ( sigma_3977070789342921045omplex @ top_top_set_complex ) ) ) ).

% measurable_count_space
thf(fact_14_measurable__count__space,axiom,
    ! [F: a > a,A: set_a] : ( member_a_a @ F @ ( sigma_measurable_a_a @ ( sigma_count_space_a @ A ) @ ( sigma_count_space_a @ top_top_set_a ) ) ) ).

% measurable_count_space
thf(fact_15_measurable__count__space,axiom,
    ! [F: a > real,A: set_a] : ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ ( sigma_count_space_a @ A ) @ ( sigma_8508918144308765139e_real @ top_top_set_real ) ) ) ).

% measurable_count_space
thf(fact_16_measurable__count__space,axiom,
    ! [F: a > $o,A: set_a] : ( member_a_o @ F @ ( sigma_measurable_a_o @ ( sigma_count_space_a @ A ) @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% measurable_count_space
thf(fact_17_measurable__count__space,axiom,
    ! [F: a > nat,A: set_a] : ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ ( sigma_count_space_a @ A ) @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) ) ).

% measurable_count_space
thf(fact_18_measurable__count__space,axiom,
    ! [F: a > extend8495563244428889912nnreal,A: set_a] : ( member298456594901751504nnreal @ F @ ( sigma_214952329563889126nnreal @ ( sigma_count_space_a @ A ) @ ( sigma_7204664791115113951nnreal @ top_to7994903218803871134nnreal ) ) ) ).

% measurable_count_space
thf(fact_19_measurable__count__space,axiom,
    ! [F: real > b,A: set_real] : ( member_real_b @ F @ ( sigma_523072396149930113real_b @ ( sigma_8508918144308765139e_real @ A ) @ ( sigma_count_space_b @ top_top_set_b ) ) ) ).

% measurable_count_space
thf(fact_20_measurable__count__space,axiom,
    ! [F: real > complex,A: set_real] : ( member_real_complex @ F @ ( sigma_9111916201866572460omplex @ ( sigma_8508918144308765139e_real @ A ) @ ( sigma_3977070789342921045omplex @ top_top_set_complex ) ) ) ).

% measurable_count_space
thf(fact_21_measurable__count__space,axiom,
    ! [F: real > a,A: set_real] : ( member_real_a @ F @ ( sigma_523072396149930112real_a @ ( sigma_8508918144308765139e_real @ A ) @ ( sigma_count_space_a @ top_top_set_a ) ) ) ).

% measurable_count_space
thf(fact_22_measurable__count__space,axiom,
    ! [F: real > real,A: set_real] : ( member_real_real @ F @ ( sigma_5267869275261027754l_real @ ( sigma_8508918144308765139e_real @ A ) @ ( sigma_8508918144308765139e_real @ top_top_set_real ) ) ) ).

% measurable_count_space
thf(fact_23_assms_I1_J,axiom,
    counta4098120917673242425able_a @ i ).

% assms(1)
thf(fact_24_assms_I3_J,axiom,
    ! [I: a] :
      ( ( member_a @ I @ ( image_real_a @ p @ top_top_set_real ) )
     => ( member_real_b @ ( fi @ I ) @ ( qbs_Mx_b @ x ) ) ) ).

% assms(3)
thf(fact_25_image__eqI,axiom,
    ! [B: real,F: real > real,X: real,A: set_real] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_real @ X @ A )
       => ( member_real @ B @ ( image_real_real @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_26_image__eqI,axiom,
    ! [B: a,F: real > a,X: real,A: set_real] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_real @ X @ A )
       => ( member_a @ B @ ( image_real_a @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_27_image__eqI,axiom,
    ! [B: real,F: nat > real,X: nat,A: set_nat] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_nat @ X @ A )
       => ( member_real @ B @ ( image_nat_real @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_28_image__eqI,axiom,
    ! [B: complex,F: nat > complex,X: nat,A: set_nat] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_nat @ X @ A )
       => ( member_complex @ B @ ( image_nat_complex @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_29_image__eqI,axiom,
    ! [B: nat,F: nat > nat,X: nat,A: set_nat] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_nat @ X @ A )
       => ( member_nat @ B @ ( image_nat_nat @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_30_image__eqI,axiom,
    ! [B: a,F: nat > a,X: nat,A: set_nat] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_nat @ X @ A )
       => ( member_a @ B @ ( image_nat_a @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_31_image__eqI,axiom,
    ! [B: nat,F: a > nat,X: a,A: set_a] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_a @ X @ A )
       => ( member_nat @ B @ ( image_a_nat @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_32_image__eqI,axiom,
    ! [B: a,F: a > a,X: a,A: set_a] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_a @ X @ A )
       => ( member_a @ B @ ( image_a_a @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_33_image__eqI,axiom,
    ! [B: real > nat,F: nat > real > nat,X: nat,A: set_nat] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_nat @ X @ A )
       => ( member_real_nat @ B @ ( image_nat_real_nat @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_34_image__eqI,axiom,
    ! [B: real > b,F: nat > real > b,X: nat,A: set_nat] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_nat @ X @ A )
       => ( member_real_b @ B @ ( image_nat_real_b @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_35_UNIV__I,axiom,
    ! [X: a] : ( member_a @ X @ top_top_set_a ) ).

% UNIV_I
thf(fact_36_UNIV__I,axiom,
    ! [X: extend8495563244428889912nnreal] : ( member7908768830364227535nnreal @ X @ top_to7994903218803871134nnreal ) ).

% UNIV_I
thf(fact_37_UNIV__I,axiom,
    ! [X: complex] : ( member_complex @ X @ top_top_set_complex ) ).

% UNIV_I
thf(fact_38_UNIV__I,axiom,
    ! [X: real] : ( member_real @ X @ top_top_set_real ) ).

% UNIV_I
thf(fact_39_UNIV__I,axiom,
    ! [X: $o] : ( member_o @ X @ top_top_set_o ) ).

% UNIV_I
thf(fact_40_UNIV__I,axiom,
    ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).

% UNIV_I
thf(fact_41_UNIV__I,axiom,
    ! [X: real > nat] : ( member_real_nat @ X @ top_top_set_real_nat ) ).

% UNIV_I
thf(fact_42_UNIV__I,axiom,
    ! [X: real > b] : ( member_real_b @ X @ top_top_set_real_b ) ).

% UNIV_I
thf(fact_43_UNIV__I,axiom,
    ! [X: real > a] : ( member_real_a @ X @ top_top_set_real_a ) ).

% UNIV_I
thf(fact_44_UNIV__I,axiom,
    ! [X: b] : ( member_b @ X @ top_top_set_b ) ).

% UNIV_I
thf(fact_45_iso__tuple__UNIV__I,axiom,
    ! [X: a] : ( member_a @ X @ top_top_set_a ) ).

% iso_tuple_UNIV_I
thf(fact_46_iso__tuple__UNIV__I,axiom,
    ! [X: extend8495563244428889912nnreal] : ( member7908768830364227535nnreal @ X @ top_to7994903218803871134nnreal ) ).

% iso_tuple_UNIV_I
thf(fact_47_iso__tuple__UNIV__I,axiom,
    ! [X: complex] : ( member_complex @ X @ top_top_set_complex ) ).

% iso_tuple_UNIV_I
thf(fact_48_iso__tuple__UNIV__I,axiom,
    ! [X: real] : ( member_real @ X @ top_top_set_real ) ).

% iso_tuple_UNIV_I
thf(fact_49_iso__tuple__UNIV__I,axiom,
    ! [X: $o] : ( member_o @ X @ top_top_set_o ) ).

% iso_tuple_UNIV_I
thf(fact_50_iso__tuple__UNIV__I,axiom,
    ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).

% iso_tuple_UNIV_I
thf(fact_51_iso__tuple__UNIV__I,axiom,
    ! [X: real > nat] : ( member_real_nat @ X @ top_top_set_real_nat ) ).

% iso_tuple_UNIV_I
thf(fact_52_iso__tuple__UNIV__I,axiom,
    ! [X: real > b] : ( member_real_b @ X @ top_top_set_real_b ) ).

% iso_tuple_UNIV_I
thf(fact_53_iso__tuple__UNIV__I,axiom,
    ! [X: real > a] : ( member_real_a @ X @ top_top_set_real_a ) ).

% iso_tuple_UNIV_I
thf(fact_54_iso__tuple__UNIV__I,axiom,
    ! [X: b] : ( member_b @ X @ top_top_set_b ) ).

% iso_tuple_UNIV_I
thf(fact_55_surjD,axiom,
    ! [F: extend8495563244428889912nnreal > extend8495563244428889912nnreal,Y: extend8495563244428889912nnreal] :
      ( ( ( image_8394674774369097847nnreal @ F @ top_to7994903218803871134nnreal )
        = top_to7994903218803871134nnreal )
     => ? [X2: extend8495563244428889912nnreal] :
          ( Y
          = ( F @ X2 ) ) ) ).

% surjD
thf(fact_56_surjD,axiom,
    ! [F: extend8495563244428889912nnreal > complex,Y: complex] :
      ( ( ( image_3781532184644764653omplex @ F @ top_to7994903218803871134nnreal )
        = top_top_set_complex )
     => ? [X2: extend8495563244428889912nnreal] :
          ( Y
          = ( F @ X2 ) ) ) ).

% surjD
thf(fact_57_surjD,axiom,
    ! [F: extend8495563244428889912nnreal > real,Y: real] :
      ( ( ( image_5648444867695151211l_real @ F @ top_to7994903218803871134nnreal )
        = top_top_set_real )
     => ? [X2: extend8495563244428889912nnreal] :
          ( Y
          = ( F @ X2 ) ) ) ).

% surjD
thf(fact_58_surjD,axiom,
    ! [F: extend8495563244428889912nnreal > $o,Y: $o] :
      ( ( ( image_3162942742313426073real_o @ F @ top_to7994903218803871134nnreal )
        = top_top_set_o )
     => ? [X2: extend8495563244428889912nnreal] :
          ( Y
          = ( F @ X2 ) ) ) ).

% surjD
thf(fact_59_surjD,axiom,
    ! [F: extend8495563244428889912nnreal > nat,Y: nat] :
      ( ( ( image_4010189972324537615al_nat @ F @ top_to7994903218803871134nnreal )
        = top_top_set_nat )
     => ? [X2: extend8495563244428889912nnreal] :
          ( Y
          = ( F @ X2 ) ) ) ).

% surjD
thf(fact_60_surjD,axiom,
    ! [F: extend8495563244428889912nnreal > a,Y: a] :
      ( ( ( image_7862617044475835263real_a @ F @ top_to7994903218803871134nnreal )
        = top_top_set_a )
     => ? [X2: extend8495563244428889912nnreal] :
          ( Y
          = ( F @ X2 ) ) ) ).

% surjD
thf(fact_61_surjD,axiom,
    ! [F: extend8495563244428889912nnreal > b,Y: b] :
      ( ( ( image_7862617044475835264real_b @ F @ top_to7994903218803871134nnreal )
        = top_top_set_b )
     => ? [X2: extend8495563244428889912nnreal] :
          ( Y
          = ( F @ X2 ) ) ) ).

% surjD
thf(fact_62_surjD,axiom,
    ! [F: complex > extend8495563244428889912nnreal,Y: extend8495563244428889912nnreal] :
      ( ( ( image_4927658817219388909nnreal @ F @ top_top_set_complex )
        = top_to7994903218803871134nnreal )
     => ? [X2: complex] :
          ( Y
          = ( F @ X2 ) ) ) ).

% surjD
thf(fact_63_surjD,axiom,
    ! [F: complex > complex,Y: complex] :
      ( ( ( image_1468599708987790691omplex @ F @ top_top_set_complex )
        = top_top_set_complex )
     => ? [X2: complex] :
          ( Y
          = ( F @ X2 ) ) ) ).

% surjD
thf(fact_64_surjD,axiom,
    ! [F: complex > real,Y: real] :
      ( ( ( image_complex_real @ F @ top_top_set_complex )
        = top_top_set_real )
     => ? [X2: complex] :
          ( Y
          = ( F @ X2 ) ) ) ).

% surjD
thf(fact_65_surjE,axiom,
    ! [F: extend8495563244428889912nnreal > extend8495563244428889912nnreal,Y: extend8495563244428889912nnreal] :
      ( ( ( image_8394674774369097847nnreal @ F @ top_to7994903218803871134nnreal )
        = top_to7994903218803871134nnreal )
     => ~ ! [X2: extend8495563244428889912nnreal] :
            ( Y
           != ( F @ X2 ) ) ) ).

% surjE
thf(fact_66_surjE,axiom,
    ! [F: extend8495563244428889912nnreal > complex,Y: complex] :
      ( ( ( image_3781532184644764653omplex @ F @ top_to7994903218803871134nnreal )
        = top_top_set_complex )
     => ~ ! [X2: extend8495563244428889912nnreal] :
            ( Y
           != ( F @ X2 ) ) ) ).

% surjE
thf(fact_67_surjE,axiom,
    ! [F: extend8495563244428889912nnreal > real,Y: real] :
      ( ( ( image_5648444867695151211l_real @ F @ top_to7994903218803871134nnreal )
        = top_top_set_real )
     => ~ ! [X2: extend8495563244428889912nnreal] :
            ( Y
           != ( F @ X2 ) ) ) ).

% surjE
thf(fact_68_surjE,axiom,
    ! [F: extend8495563244428889912nnreal > $o,Y: $o] :
      ( ( ( image_3162942742313426073real_o @ F @ top_to7994903218803871134nnreal )
        = top_top_set_o )
     => ~ ! [X2: extend8495563244428889912nnreal] :
            ( Y
            = ( ~ ( F @ X2 ) ) ) ) ).

% surjE
thf(fact_69_surjE,axiom,
    ! [F: extend8495563244428889912nnreal > nat,Y: nat] :
      ( ( ( image_4010189972324537615al_nat @ F @ top_to7994903218803871134nnreal )
        = top_top_set_nat )
     => ~ ! [X2: extend8495563244428889912nnreal] :
            ( Y
           != ( F @ X2 ) ) ) ).

% surjE
thf(fact_70_surjE,axiom,
    ! [F: extend8495563244428889912nnreal > a,Y: a] :
      ( ( ( image_7862617044475835263real_a @ F @ top_to7994903218803871134nnreal )
        = top_top_set_a )
     => ~ ! [X2: extend8495563244428889912nnreal] :
            ( Y
           != ( F @ X2 ) ) ) ).

% surjE
thf(fact_71_surjE,axiom,
    ! [F: extend8495563244428889912nnreal > b,Y: b] :
      ( ( ( image_7862617044475835264real_b @ F @ top_to7994903218803871134nnreal )
        = top_top_set_b )
     => ~ ! [X2: extend8495563244428889912nnreal] :
            ( Y
           != ( F @ X2 ) ) ) ).

% surjE
thf(fact_72_surjE,axiom,
    ! [F: complex > extend8495563244428889912nnreal,Y: extend8495563244428889912nnreal] :
      ( ( ( image_4927658817219388909nnreal @ F @ top_top_set_complex )
        = top_to7994903218803871134nnreal )
     => ~ ! [X2: complex] :
            ( Y
           != ( F @ X2 ) ) ) ).

% surjE
thf(fact_73_surjE,axiom,
    ! [F: complex > complex,Y: complex] :
      ( ( ( image_1468599708987790691omplex @ F @ top_top_set_complex )
        = top_top_set_complex )
     => ~ ! [X2: complex] :
            ( Y
           != ( F @ X2 ) ) ) ).

% surjE
thf(fact_74_surjE,axiom,
    ! [F: complex > real,Y: real] :
      ( ( ( image_complex_real @ F @ top_top_set_complex )
        = top_top_set_real )
     => ~ ! [X2: complex] :
            ( Y
           != ( F @ X2 ) ) ) ).

% surjE
thf(fact_75_surjI,axiom,
    ! [G: extend8495563244428889912nnreal > extend8495563244428889912nnreal,F: extend8495563244428889912nnreal > extend8495563244428889912nnreal] :
      ( ! [X2: extend8495563244428889912nnreal] :
          ( ( G @ ( F @ X2 ) )
          = X2 )
     => ( ( image_8394674774369097847nnreal @ G @ top_to7994903218803871134nnreal )
        = top_to7994903218803871134nnreal ) ) ).

% surjI
thf(fact_76_surjI,axiom,
    ! [G: extend8495563244428889912nnreal > complex,F: complex > extend8495563244428889912nnreal] :
      ( ! [X2: complex] :
          ( ( G @ ( F @ X2 ) )
          = X2 )
     => ( ( image_3781532184644764653omplex @ G @ top_to7994903218803871134nnreal )
        = top_top_set_complex ) ) ).

% surjI
thf(fact_77_surjI,axiom,
    ! [G: extend8495563244428889912nnreal > real,F: real > extend8495563244428889912nnreal] :
      ( ! [X2: real] :
          ( ( G @ ( F @ X2 ) )
          = X2 )
     => ( ( image_5648444867695151211l_real @ G @ top_to7994903218803871134nnreal )
        = top_top_set_real ) ) ).

% surjI
thf(fact_78_surjI,axiom,
    ! [G: extend8495563244428889912nnreal > $o,F: $o > extend8495563244428889912nnreal] :
      ( ! [X2: $o] :
          ( ( G @ ( F @ X2 ) )
          = X2 )
     => ( ( image_3162942742313426073real_o @ G @ top_to7994903218803871134nnreal )
        = top_top_set_o ) ) ).

% surjI
thf(fact_79_surjI,axiom,
    ! [G: extend8495563244428889912nnreal > nat,F: nat > extend8495563244428889912nnreal] :
      ( ! [X2: nat] :
          ( ( G @ ( F @ X2 ) )
          = X2 )
     => ( ( image_4010189972324537615al_nat @ G @ top_to7994903218803871134nnreal )
        = top_top_set_nat ) ) ).

% surjI
thf(fact_80_surjI,axiom,
    ! [G: extend8495563244428889912nnreal > a,F: a > extend8495563244428889912nnreal] :
      ( ! [X2: a] :
          ( ( G @ ( F @ X2 ) )
          = X2 )
     => ( ( image_7862617044475835263real_a @ G @ top_to7994903218803871134nnreal )
        = top_top_set_a ) ) ).

% surjI
thf(fact_81_surjI,axiom,
    ! [G: extend8495563244428889912nnreal > b,F: b > extend8495563244428889912nnreal] :
      ( ! [X2: b] :
          ( ( G @ ( F @ X2 ) )
          = X2 )
     => ( ( image_7862617044475835264real_b @ G @ top_to7994903218803871134nnreal )
        = top_top_set_b ) ) ).

% surjI
thf(fact_82_surjI,axiom,
    ! [G: complex > extend8495563244428889912nnreal,F: extend8495563244428889912nnreal > complex] :
      ( ! [X2: extend8495563244428889912nnreal] :
          ( ( G @ ( F @ X2 ) )
          = X2 )
     => ( ( image_4927658817219388909nnreal @ G @ top_top_set_complex )
        = top_to7994903218803871134nnreal ) ) ).

% surjI
thf(fact_83_surjI,axiom,
    ! [G: complex > complex,F: complex > complex] :
      ( ! [X2: complex] :
          ( ( G @ ( F @ X2 ) )
          = X2 )
     => ( ( image_1468599708987790691omplex @ G @ top_top_set_complex )
        = top_top_set_complex ) ) ).

% surjI
thf(fact_84_surjI,axiom,
    ! [G: complex > real,F: real > complex] :
      ( ! [X2: real] :
          ( ( G @ ( F @ X2 ) )
          = X2 )
     => ( ( image_complex_real @ G @ top_top_set_complex )
        = top_top_set_real ) ) ).

% surjI
thf(fact_85_rangeI,axiom,
    ! [F: extend8495563244428889912nnreal > nat,X: extend8495563244428889912nnreal] : ( member_nat @ ( F @ X ) @ ( image_4010189972324537615al_nat @ F @ top_to7994903218803871134nnreal ) ) ).

% rangeI
thf(fact_86_rangeI,axiom,
    ! [F: extend8495563244428889912nnreal > a,X: extend8495563244428889912nnreal] : ( member_a @ ( F @ X ) @ ( image_7862617044475835263real_a @ F @ top_to7994903218803871134nnreal ) ) ).

% rangeI
thf(fact_87_rangeI,axiom,
    ! [F: complex > nat,X: complex] : ( member_nat @ ( F @ X ) @ ( image_complex_nat @ F @ top_top_set_complex ) ) ).

% rangeI
thf(fact_88_rangeI,axiom,
    ! [F: complex > a,X: complex] : ( member_a @ ( F @ X ) @ ( image_complex_a @ F @ top_top_set_complex ) ) ).

% rangeI
thf(fact_89_rangeI,axiom,
    ! [F: real > real,X: real] : ( member_real @ ( F @ X ) @ ( image_real_real @ F @ top_top_set_real ) ) ).

% rangeI
thf(fact_90_rangeI,axiom,
    ! [F: real > nat,X: real] : ( member_nat @ ( F @ X ) @ ( image_real_nat @ F @ top_top_set_real ) ) ).

% rangeI
thf(fact_91_rangeI,axiom,
    ! [F: real > a,X: real] : ( member_a @ ( F @ X ) @ ( image_real_a @ F @ top_top_set_real ) ) ).

% rangeI
thf(fact_92_rangeI,axiom,
    ! [F: $o > nat,X: $o] : ( member_nat @ ( F @ X ) @ ( image_o_nat @ F @ top_top_set_o ) ) ).

% rangeI
thf(fact_93_rangeI,axiom,
    ! [F: $o > a,X: $o] : ( member_a @ ( F @ X ) @ ( image_o_a @ F @ top_top_set_o ) ) ).

% rangeI
thf(fact_94_rangeI,axiom,
    ! [F: nat > real,X: nat] : ( member_real @ ( F @ X ) @ ( image_nat_real @ F @ top_top_set_nat ) ) ).

% rangeI
thf(fact_95_IntI,axiom,
    ! [C: nat,A: set_nat,B2: set_nat] :
      ( ( member_nat @ C @ A )
     => ( ( member_nat @ C @ B2 )
       => ( member_nat @ C @ ( inf_inf_set_nat @ A @ B2 ) ) ) ) ).

% IntI
thf(fact_96_IntI,axiom,
    ! [C: real > nat,A: set_real_nat,B2: set_real_nat] :
      ( ( member_real_nat @ C @ A )
     => ( ( member_real_nat @ C @ B2 )
       => ( member_real_nat @ C @ ( inf_inf_set_real_nat @ A @ B2 ) ) ) ) ).

% IntI
thf(fact_97_IntI,axiom,
    ! [C: real > b,A: set_real_b,B2: set_real_b] :
      ( ( member_real_b @ C @ A )
     => ( ( member_real_b @ C @ B2 )
       => ( member_real_b @ C @ ( inf_inf_set_real_b @ A @ B2 ) ) ) ) ).

% IntI
thf(fact_98_IntI,axiom,
    ! [C: real > a,A: set_real_a,B2: set_real_a] :
      ( ( member_real_a @ C @ A )
     => ( ( member_real_a @ C @ B2 )
       => ( member_real_a @ C @ ( inf_inf_set_real_a @ A @ B2 ) ) ) ) ).

% IntI
thf(fact_99_IntI,axiom,
    ! [C: a > complex,A: set_a_complex,B2: set_a_complex] :
      ( ( member_a_complex @ C @ A )
     => ( ( member_a_complex @ C @ B2 )
       => ( member_a_complex @ C @ ( inf_in3709910040937683179omplex @ A @ B2 ) ) ) ) ).

% IntI
thf(fact_100_IntI,axiom,
    ! [C: a > real,A: set_a_real,B2: set_a_real] :
      ( ( member_a_real @ C @ A )
     => ( ( member_a_real @ C @ B2 )
       => ( member_a_real @ C @ ( inf_inf_set_a_real @ A @ B2 ) ) ) ) ).

% IntI
thf(fact_101_IntI,axiom,
    ! [C: a > $o,A: set_a_o,B2: set_a_o] :
      ( ( member_a_o @ C @ A )
     => ( ( member_a_o @ C @ B2 )
       => ( member_a_o @ C @ ( inf_inf_set_a_o @ A @ B2 ) ) ) ) ).

% IntI
thf(fact_102_IntI,axiom,
    ! [C: a > nat,A: set_a_nat,B2: set_a_nat] :
      ( ( member_a_nat @ C @ A )
     => ( ( member_a_nat @ C @ B2 )
       => ( member_a_nat @ C @ ( inf_inf_set_a_nat @ A @ B2 ) ) ) ) ).

% IntI
thf(fact_103_IntI,axiom,
    ! [C: a > a,A: set_a_a,B2: set_a_a] :
      ( ( member_a_a @ C @ A )
     => ( ( member_a_a @ C @ B2 )
       => ( member_a_a @ C @ ( inf_inf_set_a_a @ A @ B2 ) ) ) ) ).

% IntI
thf(fact_104_IntI,axiom,
    ! [C: a,A: set_a,B2: set_a] :
      ( ( member_a @ C @ A )
     => ( ( member_a @ C @ B2 )
       => ( member_a @ C @ ( inf_inf_set_a @ A @ B2 ) ) ) ) ).

% IntI
thf(fact_105_Int__iff,axiom,
    ! [C: nat,A: set_nat,B2: set_nat] :
      ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B2 ) )
      = ( ( member_nat @ C @ A )
        & ( member_nat @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_106_Int__iff,axiom,
    ! [C: real > nat,A: set_real_nat,B2: set_real_nat] :
      ( ( member_real_nat @ C @ ( inf_inf_set_real_nat @ A @ B2 ) )
      = ( ( member_real_nat @ C @ A )
        & ( member_real_nat @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_107_Int__iff,axiom,
    ! [C: real > b,A: set_real_b,B2: set_real_b] :
      ( ( member_real_b @ C @ ( inf_inf_set_real_b @ A @ B2 ) )
      = ( ( member_real_b @ C @ A )
        & ( member_real_b @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_108_Int__iff,axiom,
    ! [C: real > a,A: set_real_a,B2: set_real_a] :
      ( ( member_real_a @ C @ ( inf_inf_set_real_a @ A @ B2 ) )
      = ( ( member_real_a @ C @ A )
        & ( member_real_a @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_109_Int__iff,axiom,
    ! [C: a > complex,A: set_a_complex,B2: set_a_complex] :
      ( ( member_a_complex @ C @ ( inf_in3709910040937683179omplex @ A @ B2 ) )
      = ( ( member_a_complex @ C @ A )
        & ( member_a_complex @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_110_Int__iff,axiom,
    ! [C: a > real,A: set_a_real,B2: set_a_real] :
      ( ( member_a_real @ C @ ( inf_inf_set_a_real @ A @ B2 ) )
      = ( ( member_a_real @ C @ A )
        & ( member_a_real @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_111_Int__iff,axiom,
    ! [C: a > $o,A: set_a_o,B2: set_a_o] :
      ( ( member_a_o @ C @ ( inf_inf_set_a_o @ A @ B2 ) )
      = ( ( member_a_o @ C @ A )
        & ( member_a_o @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_112_Int__iff,axiom,
    ! [C: a > nat,A: set_a_nat,B2: set_a_nat] :
      ( ( member_a_nat @ C @ ( inf_inf_set_a_nat @ A @ B2 ) )
      = ( ( member_a_nat @ C @ A )
        & ( member_a_nat @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_113_Int__iff,axiom,
    ! [C: a > a,A: set_a_a,B2: set_a_a] :
      ( ( member_a_a @ C @ ( inf_inf_set_a_a @ A @ B2 ) )
      = ( ( member_a_a @ C @ A )
        & ( member_a_a @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_114_Int__iff,axiom,
    ! [C: a,A: set_a,B2: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A @ B2 ) )
      = ( ( member_a @ C @ A )
        & ( member_a @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_115_Int__UNIV,axiom,
    ! [A: set_Ex3793607809372303086nnreal,B2: set_Ex3793607809372303086nnreal] :
      ( ( ( inf_in3368558534146122112nnreal @ A @ B2 )
        = top_to7994903218803871134nnreal )
      = ( ( A = top_to7994903218803871134nnreal )
        & ( B2 = top_to7994903218803871134nnreal ) ) ) ).

% Int_UNIV
thf(fact_116_Int__UNIV,axiom,
    ! [A: set_complex,B2: set_complex] :
      ( ( ( inf_inf_set_complex @ A @ B2 )
        = top_top_set_complex )
      = ( ( A = top_top_set_complex )
        & ( B2 = top_top_set_complex ) ) ) ).

% Int_UNIV
thf(fact_117_Int__UNIV,axiom,
    ! [A: set_real,B2: set_real] :
      ( ( ( inf_inf_set_real @ A @ B2 )
        = top_top_set_real )
      = ( ( A = top_top_set_real )
        & ( B2 = top_top_set_real ) ) ) ).

% Int_UNIV
thf(fact_118_Int__UNIV,axiom,
    ! [A: set_o,B2: set_o] :
      ( ( ( inf_inf_set_o @ A @ B2 )
        = top_top_set_o )
      = ( ( A = top_top_set_o )
        & ( B2 = top_top_set_o ) ) ) ).

% Int_UNIV
thf(fact_119_Int__UNIV,axiom,
    ! [A: set_nat,B2: set_nat] :
      ( ( ( inf_inf_set_nat @ A @ B2 )
        = top_top_set_nat )
      = ( ( A = top_top_set_nat )
        & ( B2 = top_top_set_nat ) ) ) ).

% Int_UNIV
thf(fact_120_Int__UNIV,axiom,
    ! [A: set_a,B2: set_a] :
      ( ( ( inf_inf_set_a @ A @ B2 )
        = top_top_set_a )
      = ( ( A = top_top_set_a )
        & ( B2 = top_top_set_a ) ) ) ).

% Int_UNIV
thf(fact_121_Int__UNIV,axiom,
    ! [A: set_b,B2: set_b] :
      ( ( ( inf_inf_set_b @ A @ B2 )
        = top_top_set_b )
      = ( ( A = top_top_set_b )
        & ( B2 = top_top_set_b ) ) ) ).

% Int_UNIV
thf(fact_122_Int__UNIV,axiom,
    ! [A: set_real_a,B2: set_real_a] :
      ( ( ( inf_inf_set_real_a @ A @ B2 )
        = top_top_set_real_a )
      = ( ( A = top_top_set_real_a )
        & ( B2 = top_top_set_real_a ) ) ) ).

% Int_UNIV
thf(fact_123_Int__UNIV,axiom,
    ! [A: set_real_b,B2: set_real_b] :
      ( ( ( inf_inf_set_real_b @ A @ B2 )
        = top_top_set_real_b )
      = ( ( A = top_top_set_real_b )
        & ( B2 = top_top_set_real_b ) ) ) ).

% Int_UNIV
thf(fact_124_Int__UNIV,axiom,
    ! [A: set_real_nat,B2: set_real_nat] :
      ( ( ( inf_inf_set_real_nat @ A @ B2 )
        = top_top_set_real_nat )
      = ( ( A = top_top_set_real_nat )
        & ( B2 = top_top_set_real_nat ) ) ) ).

% Int_UNIV
thf(fact_125_IntE,axiom,
    ! [C: nat,A: set_nat,B2: set_nat] :
      ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B2 ) )
     => ~ ( ( member_nat @ C @ A )
         => ~ ( member_nat @ C @ B2 ) ) ) ).

% IntE
thf(fact_126_IntE,axiom,
    ! [C: real > nat,A: set_real_nat,B2: set_real_nat] :
      ( ( member_real_nat @ C @ ( inf_inf_set_real_nat @ A @ B2 ) )
     => ~ ( ( member_real_nat @ C @ A )
         => ~ ( member_real_nat @ C @ B2 ) ) ) ).

% IntE
thf(fact_127_IntE,axiom,
    ! [C: real > b,A: set_real_b,B2: set_real_b] :
      ( ( member_real_b @ C @ ( inf_inf_set_real_b @ A @ B2 ) )
     => ~ ( ( member_real_b @ C @ A )
         => ~ ( member_real_b @ C @ B2 ) ) ) ).

% IntE
thf(fact_128_IntE,axiom,
    ! [C: real > a,A: set_real_a,B2: set_real_a] :
      ( ( member_real_a @ C @ ( inf_inf_set_real_a @ A @ B2 ) )
     => ~ ( ( member_real_a @ C @ A )
         => ~ ( member_real_a @ C @ B2 ) ) ) ).

% IntE
thf(fact_129_IntE,axiom,
    ! [C: a > complex,A: set_a_complex,B2: set_a_complex] :
      ( ( member_a_complex @ C @ ( inf_in3709910040937683179omplex @ A @ B2 ) )
     => ~ ( ( member_a_complex @ C @ A )
         => ~ ( member_a_complex @ C @ B2 ) ) ) ).

% IntE
thf(fact_130_IntE,axiom,
    ! [C: a > real,A: set_a_real,B2: set_a_real] :
      ( ( member_a_real @ C @ ( inf_inf_set_a_real @ A @ B2 ) )
     => ~ ( ( member_a_real @ C @ A )
         => ~ ( member_a_real @ C @ B2 ) ) ) ).

% IntE
thf(fact_131_IntE,axiom,
    ! [C: a > $o,A: set_a_o,B2: set_a_o] :
      ( ( member_a_o @ C @ ( inf_inf_set_a_o @ A @ B2 ) )
     => ~ ( ( member_a_o @ C @ A )
         => ~ ( member_a_o @ C @ B2 ) ) ) ).

% IntE
thf(fact_132_IntE,axiom,
    ! [C: a > nat,A: set_a_nat,B2: set_a_nat] :
      ( ( member_a_nat @ C @ ( inf_inf_set_a_nat @ A @ B2 ) )
     => ~ ( ( member_a_nat @ C @ A )
         => ~ ( member_a_nat @ C @ B2 ) ) ) ).

% IntE
thf(fact_133_IntE,axiom,
    ! [C: a > a,A: set_a_a,B2: set_a_a] :
      ( ( member_a_a @ C @ ( inf_inf_set_a_a @ A @ B2 ) )
     => ~ ( ( member_a_a @ C @ A )
         => ~ ( member_a_a @ C @ B2 ) ) ) ).

% IntE
thf(fact_134_IntE,axiom,
    ! [C: a,A: set_a,B2: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A @ B2 ) )
     => ~ ( ( member_a @ C @ A )
         => ~ ( member_a @ C @ B2 ) ) ) ).

% IntE
thf(fact_135_IntD1,axiom,
    ! [C: nat,A: set_nat,B2: set_nat] :
      ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B2 ) )
     => ( member_nat @ C @ A ) ) ).

% IntD1
thf(fact_136_IntD1,axiom,
    ! [C: real > nat,A: set_real_nat,B2: set_real_nat] :
      ( ( member_real_nat @ C @ ( inf_inf_set_real_nat @ A @ B2 ) )
     => ( member_real_nat @ C @ A ) ) ).

% IntD1
thf(fact_137_IntD1,axiom,
    ! [C: real > b,A: set_real_b,B2: set_real_b] :
      ( ( member_real_b @ C @ ( inf_inf_set_real_b @ A @ B2 ) )
     => ( member_real_b @ C @ A ) ) ).

% IntD1
thf(fact_138_IntD1,axiom,
    ! [C: real > a,A: set_real_a,B2: set_real_a] :
      ( ( member_real_a @ C @ ( inf_inf_set_real_a @ A @ B2 ) )
     => ( member_real_a @ C @ A ) ) ).

% IntD1
thf(fact_139_IntD1,axiom,
    ! [C: a > complex,A: set_a_complex,B2: set_a_complex] :
      ( ( member_a_complex @ C @ ( inf_in3709910040937683179omplex @ A @ B2 ) )
     => ( member_a_complex @ C @ A ) ) ).

% IntD1
thf(fact_140_IntD1,axiom,
    ! [C: a > real,A: set_a_real,B2: set_a_real] :
      ( ( member_a_real @ C @ ( inf_inf_set_a_real @ A @ B2 ) )
     => ( member_a_real @ C @ A ) ) ).

% IntD1
thf(fact_141_IntD1,axiom,
    ! [C: a > $o,A: set_a_o,B2: set_a_o] :
      ( ( member_a_o @ C @ ( inf_inf_set_a_o @ A @ B2 ) )
     => ( member_a_o @ C @ A ) ) ).

% IntD1
thf(fact_142_IntD1,axiom,
    ! [C: a > nat,A: set_a_nat,B2: set_a_nat] :
      ( ( member_a_nat @ C @ ( inf_inf_set_a_nat @ A @ B2 ) )
     => ( member_a_nat @ C @ A ) ) ).

% IntD1
thf(fact_143_IntD1,axiom,
    ! [C: a > a,A: set_a_a,B2: set_a_a] :
      ( ( member_a_a @ C @ ( inf_inf_set_a_a @ A @ B2 ) )
     => ( member_a_a @ C @ A ) ) ).

% IntD1
thf(fact_144_IntD1,axiom,
    ! [C: a,A: set_a,B2: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A @ B2 ) )
     => ( member_a @ C @ A ) ) ).

% IntD1
thf(fact_145_IntD2,axiom,
    ! [C: nat,A: set_nat,B2: set_nat] :
      ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B2 ) )
     => ( member_nat @ C @ B2 ) ) ).

% IntD2
thf(fact_146_IntD2,axiom,
    ! [C: real > nat,A: set_real_nat,B2: set_real_nat] :
      ( ( member_real_nat @ C @ ( inf_inf_set_real_nat @ A @ B2 ) )
     => ( member_real_nat @ C @ B2 ) ) ).

% IntD2
thf(fact_147_IntD2,axiom,
    ! [C: real > b,A: set_real_b,B2: set_real_b] :
      ( ( member_real_b @ C @ ( inf_inf_set_real_b @ A @ B2 ) )
     => ( member_real_b @ C @ B2 ) ) ).

% IntD2
thf(fact_148_IntD2,axiom,
    ! [C: real > a,A: set_real_a,B2: set_real_a] :
      ( ( member_real_a @ C @ ( inf_inf_set_real_a @ A @ B2 ) )
     => ( member_real_a @ C @ B2 ) ) ).

% IntD2
thf(fact_149_IntD2,axiom,
    ! [C: a > complex,A: set_a_complex,B2: set_a_complex] :
      ( ( member_a_complex @ C @ ( inf_in3709910040937683179omplex @ A @ B2 ) )
     => ( member_a_complex @ C @ B2 ) ) ).

% IntD2
thf(fact_150_IntD2,axiom,
    ! [C: a > real,A: set_a_real,B2: set_a_real] :
      ( ( member_a_real @ C @ ( inf_inf_set_a_real @ A @ B2 ) )
     => ( member_a_real @ C @ B2 ) ) ).

% IntD2
thf(fact_151_IntD2,axiom,
    ! [C: a > $o,A: set_a_o,B2: set_a_o] :
      ( ( member_a_o @ C @ ( inf_inf_set_a_o @ A @ B2 ) )
     => ( member_a_o @ C @ B2 ) ) ).

% IntD2
thf(fact_152_IntD2,axiom,
    ! [C: a > nat,A: set_a_nat,B2: set_a_nat] :
      ( ( member_a_nat @ C @ ( inf_inf_set_a_nat @ A @ B2 ) )
     => ( member_a_nat @ C @ B2 ) ) ).

% IntD2
thf(fact_153_IntD2,axiom,
    ! [C: a > a,A: set_a_a,B2: set_a_a] :
      ( ( member_a_a @ C @ ( inf_inf_set_a_a @ A @ B2 ) )
     => ( member_a_a @ C @ B2 ) ) ).

% IntD2
thf(fact_154_IntD2,axiom,
    ! [C: a,A: set_a,B2: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A @ B2 ) )
     => ( member_a @ C @ B2 ) ) ).

% IntD2
thf(fact_155_Int__assoc,axiom,
    ! [A: set_a,B2: set_a,C2: set_a] :
      ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B2 ) @ C2 )
      = ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B2 @ C2 ) ) ) ).

% Int_assoc
thf(fact_156_Int__absorb,axiom,
    ! [A: set_a] :
      ( ( inf_inf_set_a @ A @ A )
      = A ) ).

% Int_absorb
thf(fact_157_Int__commute,axiom,
    ( inf_inf_set_a
    = ( ^ [A2: set_a,B3: set_a] : ( inf_inf_set_a @ B3 @ A2 ) ) ) ).

% Int_commute
thf(fact_158_Int__left__absorb,axiom,
    ! [A: set_a,B2: set_a] :
      ( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B2 ) )
      = ( inf_inf_set_a @ A @ B2 ) ) ).

% Int_left_absorb
thf(fact_159_Int__left__commute,axiom,
    ! [A: set_a,B2: set_a,C2: set_a] :
      ( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B2 @ C2 ) )
      = ( inf_inf_set_a @ B2 @ ( inf_inf_set_a @ A @ C2 ) ) ) ).

% Int_left_commute
thf(fact_160_top__set__def,axiom,
    ( top_to7994903218803871134nnreal
    = ( collec6648975593938027277nnreal @ top_to5118619752887738471real_o ) ) ).

% top_set_def
thf(fact_161_top__set__def,axiom,
    ( top_top_set_complex
    = ( collect_complex @ top_top_complex_o ) ) ).

% top_set_def
thf(fact_162_top__set__def,axiom,
    ( top_top_set_real
    = ( collect_real @ top_top_real_o ) ) ).

% top_set_def
thf(fact_163_top__set__def,axiom,
    ( top_top_set_o
    = ( collect_o @ top_top_o_o ) ) ).

% top_set_def
thf(fact_164_top__set__def,axiom,
    ( top_top_set_nat
    = ( collect_nat @ top_top_nat_o ) ) ).

% top_set_def
thf(fact_165_top__set__def,axiom,
    ( top_top_set_a
    = ( collect_a @ top_top_a_o ) ) ).

% top_set_def
thf(fact_166_top__set__def,axiom,
    ( top_top_set_b
    = ( collect_b @ top_top_b_o ) ) ).

% top_set_def
thf(fact_167_top__set__def,axiom,
    ( top_top_set_real_a
    = ( collect_real_a @ top_top_real_a_o ) ) ).

% top_set_def
thf(fact_168_top__set__def,axiom,
    ( top_top_set_real_b
    = ( collect_real_b @ top_top_real_b_o ) ) ).

% top_set_def
thf(fact_169_top__set__def,axiom,
    ( top_top_set_real_nat
    = ( collect_real_nat @ top_top_real_nat_o ) ) ).

% top_set_def
thf(fact_170_measurable__restrict__space1,axiom,
    ! [F: real > b,M: sigma_measure_real,N: sigma_measure_b,Omega: set_real] :
      ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ N ) )
     => ( member_real_b @ F @ ( sigma_523072396149930113real_b @ ( sigma_5414646170262037096e_real @ M @ Omega ) @ N ) ) ) ).

% measurable_restrict_space1
thf(fact_171_measurable__restrict__space1,axiom,
    ! [F: real > a,M: sigma_measure_real,N: sigma_measure_a,Omega: set_real] :
      ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ N ) )
     => ( member_real_a @ F @ ( sigma_523072396149930112real_a @ ( sigma_5414646170262037096e_real @ M @ Omega ) @ N ) ) ) ).

% measurable_restrict_space1
thf(fact_172_measurable__restrict__space1,axiom,
    ! [F: real > nat,M: sigma_measure_real,N: sigma_measure_nat,Omega: set_real] :
      ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M @ N ) )
     => ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ ( sigma_5414646170262037096e_real @ M @ Omega ) @ N ) ) ) ).

% measurable_restrict_space1
thf(fact_173_measurable__restrict__space1,axiom,
    ! [F: a > complex,M: sigma_measure_a,N: sigma_3077487657436305159omplex,Omega: set_a] :
      ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ M @ N ) )
     => ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ ( sigma_8692839461743104066pace_a @ M @ Omega ) @ N ) ) ) ).

% measurable_restrict_space1
thf(fact_174_measurable__restrict__space1,axiom,
    ! [F: a > real,M: sigma_measure_a,N: sigma_measure_real,Omega: set_a] :
      ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M @ N ) )
     => ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ ( sigma_8692839461743104066pace_a @ M @ Omega ) @ N ) ) ) ).

% measurable_restrict_space1
thf(fact_175_measurable__restrict__space1,axiom,
    ! [F: a > $o,M: sigma_measure_a,N: sigma_measure_o,Omega: set_a] :
      ( ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ N ) )
     => ( member_a_o @ F @ ( sigma_measurable_a_o @ ( sigma_8692839461743104066pace_a @ M @ Omega ) @ N ) ) ) ).

% measurable_restrict_space1
thf(fact_176_measurable__restrict__space1,axiom,
    ! [F: a > nat,M: sigma_measure_a,N: sigma_measure_nat,Omega: set_a] :
      ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M @ N ) )
     => ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ ( sigma_8692839461743104066pace_a @ M @ Omega ) @ N ) ) ) ).

% measurable_restrict_space1
thf(fact_177_measurable__restrict__space1,axiom,
    ! [F: a > a,M: sigma_measure_a,N: sigma_measure_a,Omega: set_a] :
      ( ( member_a_a @ F @ ( sigma_measurable_a_a @ M @ N ) )
     => ( member_a_a @ F @ ( sigma_measurable_a_a @ ( sigma_8692839461743104066pace_a @ M @ Omega ) @ N ) ) ) ).

% measurable_restrict_space1
thf(fact_178_Int__UNIV__right,axiom,
    ! [A: set_Ex3793607809372303086nnreal] :
      ( ( inf_in3368558534146122112nnreal @ A @ top_to7994903218803871134nnreal )
      = A ) ).

% Int_UNIV_right
thf(fact_179_Int__UNIV__right,axiom,
    ! [A: set_complex] :
      ( ( inf_inf_set_complex @ A @ top_top_set_complex )
      = A ) ).

% Int_UNIV_right
thf(fact_180_Int__UNIV__right,axiom,
    ! [A: set_real] :
      ( ( inf_inf_set_real @ A @ top_top_set_real )
      = A ) ).

% Int_UNIV_right
thf(fact_181_Int__UNIV__right,axiom,
    ! [A: set_o] :
      ( ( inf_inf_set_o @ A @ top_top_set_o )
      = A ) ).

% Int_UNIV_right
thf(fact_182_Int__UNIV__right,axiom,
    ! [A: set_nat] :
      ( ( inf_inf_set_nat @ A @ top_top_set_nat )
      = A ) ).

% Int_UNIV_right
thf(fact_183_Int__UNIV__right,axiom,
    ! [A: set_a] :
      ( ( inf_inf_set_a @ A @ top_top_set_a )
      = A ) ).

% Int_UNIV_right
thf(fact_184_Int__UNIV__right,axiom,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ top_top_set_b )
      = A ) ).

% Int_UNIV_right
thf(fact_185_Int__UNIV__right,axiom,
    ! [A: set_real_a] :
      ( ( inf_inf_set_real_a @ A @ top_top_set_real_a )
      = A ) ).

% Int_UNIV_right
thf(fact_186_Int__UNIV__right,axiom,
    ! [A: set_real_b] :
      ( ( inf_inf_set_real_b @ A @ top_top_set_real_b )
      = A ) ).

% Int_UNIV_right
thf(fact_187_Int__UNIV__right,axiom,
    ! [A: set_real_nat] :
      ( ( inf_inf_set_real_nat @ A @ top_top_set_real_nat )
      = A ) ).

% Int_UNIV_right
thf(fact_188_Int__UNIV__left,axiom,
    ! [B2: set_Ex3793607809372303086nnreal] :
      ( ( inf_in3368558534146122112nnreal @ top_to7994903218803871134nnreal @ B2 )
      = B2 ) ).

% Int_UNIV_left
thf(fact_189_Int__UNIV__left,axiom,
    ! [B2: set_complex] :
      ( ( inf_inf_set_complex @ top_top_set_complex @ B2 )
      = B2 ) ).

% Int_UNIV_left
thf(fact_190_Int__UNIV__left,axiom,
    ! [B2: set_real] :
      ( ( inf_inf_set_real @ top_top_set_real @ B2 )
      = B2 ) ).

% Int_UNIV_left
thf(fact_191_Int__UNIV__left,axiom,
    ! [B2: set_o] :
      ( ( inf_inf_set_o @ top_top_set_o @ B2 )
      = B2 ) ).

% Int_UNIV_left
thf(fact_192_Int__UNIV__left,axiom,
    ! [B2: set_nat] :
      ( ( inf_inf_set_nat @ top_top_set_nat @ B2 )
      = B2 ) ).

% Int_UNIV_left
thf(fact_193_Int__UNIV__left,axiom,
    ! [B2: set_a] :
      ( ( inf_inf_set_a @ top_top_set_a @ B2 )
      = B2 ) ).

% Int_UNIV_left
thf(fact_194_Int__UNIV__left,axiom,
    ! [B2: set_b] :
      ( ( inf_inf_set_b @ top_top_set_b @ B2 )
      = B2 ) ).

% Int_UNIV_left
thf(fact_195_Int__UNIV__left,axiom,
    ! [B2: set_real_a] :
      ( ( inf_inf_set_real_a @ top_top_set_real_a @ B2 )
      = B2 ) ).

% Int_UNIV_left
thf(fact_196_Int__UNIV__left,axiom,
    ! [B2: set_real_b] :
      ( ( inf_inf_set_real_b @ top_top_set_real_b @ B2 )
      = B2 ) ).

% Int_UNIV_left
thf(fact_197_Int__UNIV__left,axiom,
    ! [B2: set_real_nat] :
      ( ( inf_inf_set_real_nat @ top_top_set_real_nat @ B2 )
      = B2 ) ).

% Int_UNIV_left
thf(fact_198_UNIV__witness,axiom,
    ? [X2: extend8495563244428889912nnreal] : ( member7908768830364227535nnreal @ X2 @ top_to7994903218803871134nnreal ) ).

% UNIV_witness
thf(fact_199_UNIV__witness,axiom,
    ? [X2: complex] : ( member_complex @ X2 @ top_top_set_complex ) ).

% UNIV_witness
thf(fact_200_UNIV__witness,axiom,
    ? [X2: real] : ( member_real @ X2 @ top_top_set_real ) ).

% UNIV_witness
thf(fact_201_UNIV__witness,axiom,
    ? [X2: $o] : ( member_o @ X2 @ top_top_set_o ) ).

% UNIV_witness
thf(fact_202_UNIV__witness,axiom,
    ? [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ).

% UNIV_witness
thf(fact_203_UNIV__witness,axiom,
    ? [X2: a] : ( member_a @ X2 @ top_top_set_a ) ).

% UNIV_witness
thf(fact_204_UNIV__witness,axiom,
    ? [X2: b] : ( member_b @ X2 @ top_top_set_b ) ).

% UNIV_witness
thf(fact_205_UNIV__witness,axiom,
    ? [X2: a > complex] : ( member_a_complex @ X2 @ top_to8623610131301960013omplex ) ).

% UNIV_witness
thf(fact_206_UNIV__witness,axiom,
    ? [X2: a > real] : ( member_a_real @ X2 @ top_top_set_a_real ) ).

% UNIV_witness
thf(fact_207_UNIV__witness,axiom,
    ? [X2: a > $o] : ( member_a_o @ X2 @ top_top_set_a_o ) ).

% UNIV_witness
thf(fact_208_UNIV__eq__I,axiom,
    ! [A: set_Ex3793607809372303086nnreal] :
      ( ! [X2: extend8495563244428889912nnreal] : ( member7908768830364227535nnreal @ X2 @ A )
     => ( top_to7994903218803871134nnreal = A ) ) ).

% UNIV_eq_I
thf(fact_209_UNIV__eq__I,axiom,
    ! [A: set_complex] :
      ( ! [X2: complex] : ( member_complex @ X2 @ A )
     => ( top_top_set_complex = A ) ) ).

% UNIV_eq_I
thf(fact_210_UNIV__eq__I,axiom,
    ! [A: set_real] :
      ( ! [X2: real] : ( member_real @ X2 @ A )
     => ( top_top_set_real = A ) ) ).

% UNIV_eq_I
thf(fact_211_UNIV__eq__I,axiom,
    ! [A: set_o] :
      ( ! [X2: $o] : ( member_o @ X2 @ A )
     => ( top_top_set_o = A ) ) ).

% UNIV_eq_I
thf(fact_212_UNIV__eq__I,axiom,
    ! [A: set_nat] :
      ( ! [X2: nat] : ( member_nat @ X2 @ A )
     => ( top_top_set_nat = A ) ) ).

% UNIV_eq_I
thf(fact_213_UNIV__eq__I,axiom,
    ! [A: set_a] :
      ( ! [X2: a] : ( member_a @ X2 @ A )
     => ( top_top_set_a = A ) ) ).

% UNIV_eq_I
thf(fact_214_UNIV__eq__I,axiom,
    ! [A: set_b] :
      ( ! [X2: b] : ( member_b @ X2 @ A )
     => ( top_top_set_b = A ) ) ).

% UNIV_eq_I
thf(fact_215_UNIV__eq__I,axiom,
    ! [A: set_a_complex] :
      ( ! [X2: a > complex] : ( member_a_complex @ X2 @ A )
     => ( top_to8623610131301960013omplex = A ) ) ).

% UNIV_eq_I
thf(fact_216_UNIV__eq__I,axiom,
    ! [A: set_a_real] :
      ( ! [X2: a > real] : ( member_a_real @ X2 @ A )
     => ( top_top_set_a_real = A ) ) ).

% UNIV_eq_I
thf(fact_217_UNIV__eq__I,axiom,
    ! [A: set_a_o] :
      ( ! [X2: a > $o] : ( member_a_o @ X2 @ A )
     => ( top_top_set_a_o = A ) ) ).

% UNIV_eq_I
thf(fact_218_rev__image__eqI,axiom,
    ! [X: real,A: set_real,B: real,F: real > real] :
      ( ( member_real @ X @ A )
     => ( ( B
          = ( F @ X ) )
       => ( member_real @ B @ ( image_real_real @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_219_rev__image__eqI,axiom,
    ! [X: real,A: set_real,B: a,F: real > a] :
      ( ( member_real @ X @ A )
     => ( ( B
          = ( F @ X ) )
       => ( member_a @ B @ ( image_real_a @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_220_rev__image__eqI,axiom,
    ! [X: nat,A: set_nat,B: real,F: nat > real] :
      ( ( member_nat @ X @ A )
     => ( ( B
          = ( F @ X ) )
       => ( member_real @ B @ ( image_nat_real @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_221_rev__image__eqI,axiom,
    ! [X: nat,A: set_nat,B: complex,F: nat > complex] :
      ( ( member_nat @ X @ A )
     => ( ( B
          = ( F @ X ) )
       => ( member_complex @ B @ ( image_nat_complex @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_222_rev__image__eqI,axiom,
    ! [X: nat,A: set_nat,B: nat,F: nat > nat] :
      ( ( member_nat @ X @ A )
     => ( ( B
          = ( F @ X ) )
       => ( member_nat @ B @ ( image_nat_nat @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_223_rev__image__eqI,axiom,
    ! [X: nat,A: set_nat,B: a,F: nat > a] :
      ( ( member_nat @ X @ A )
     => ( ( B
          = ( F @ X ) )
       => ( member_a @ B @ ( image_nat_a @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_224_rev__image__eqI,axiom,
    ! [X: a,A: set_a,B: nat,F: a > nat] :
      ( ( member_a @ X @ A )
     => ( ( B
          = ( F @ X ) )
       => ( member_nat @ B @ ( image_a_nat @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_225_rev__image__eqI,axiom,
    ! [X: a,A: set_a,B: a,F: a > a] :
      ( ( member_a @ X @ A )
     => ( ( B
          = ( F @ X ) )
       => ( member_a @ B @ ( image_a_a @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_226_rev__image__eqI,axiom,
    ! [X: nat,A: set_nat,B: real > nat,F: nat > real > nat] :
      ( ( member_nat @ X @ A )
     => ( ( B
          = ( F @ X ) )
       => ( member_real_nat @ B @ ( image_nat_real_nat @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_227_rev__image__eqI,axiom,
    ! [X: nat,A: set_nat,B: real > b,F: nat > real > b] :
      ( ( member_nat @ X @ A )
     => ( ( B
          = ( F @ X ) )
       => ( member_real_b @ B @ ( image_nat_real_b @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_228_ball__imageD,axiom,
    ! [F: real > a,A: set_real,P: a > $o] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ ( image_real_a @ F @ A ) )
         => ( P @ X2 ) )
     => ! [X3: real] :
          ( ( member_real @ X3 @ A )
         => ( P @ ( F @ X3 ) ) ) ) ).

% ball_imageD
thf(fact_229_ball__imageD,axiom,
    ! [F: nat > real,A: set_nat,P: real > $o] :
      ( ! [X2: real] :
          ( ( member_real @ X2 @ ( image_nat_real @ F @ A ) )
         => ( P @ X2 ) )
     => ! [X3: nat] :
          ( ( member_nat @ X3 @ A )
         => ( P @ ( F @ X3 ) ) ) ) ).

% ball_imageD
thf(fact_230_ball__imageD,axiom,
    ! [F: nat > complex,A: set_nat,P: complex > $o] :
      ( ! [X2: complex] :
          ( ( member_complex @ X2 @ ( image_nat_complex @ F @ A ) )
         => ( P @ X2 ) )
     => ! [X3: nat] :
          ( ( member_nat @ X3 @ A )
         => ( P @ ( F @ X3 ) ) ) ) ).

% ball_imageD
thf(fact_231_ball__imageD,axiom,
    ! [F: real > real,A: set_real,P: real > $o] :
      ( ! [X2: real] :
          ( ( member_real @ X2 @ ( image_real_real @ F @ A ) )
         => ( P @ X2 ) )
     => ! [X3: real] :
          ( ( member_real @ X3 @ A )
         => ( P @ ( F @ X3 ) ) ) ) ).

% ball_imageD
thf(fact_232_ball__imageD,axiom,
    ! [F: a > nat,A: set_a,P: nat > $o] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ ( image_a_nat @ F @ A ) )
         => ( P @ X2 ) )
     => ! [X3: a] :
          ( ( member_a @ X3 @ A )
         => ( P @ ( F @ X3 ) ) ) ) ).

% ball_imageD
thf(fact_233_ball__imageD,axiom,
    ! [F: a > real > nat,A: set_a,P: ( real > nat ) > $o] :
      ( ! [X2: real > nat] :
          ( ( member_real_nat @ X2 @ ( image_a_real_nat @ F @ A ) )
         => ( P @ X2 ) )
     => ! [X3: a] :
          ( ( member_a @ X3 @ A )
         => ( P @ ( F @ X3 ) ) ) ) ).

% ball_imageD
thf(fact_234_ball__imageD,axiom,
    ! [F: a > real > b,A: set_a,P: ( real > b ) > $o] :
      ( ! [X2: real > b] :
          ( ( member_real_b @ X2 @ ( image_a_real_b @ F @ A ) )
         => ( P @ X2 ) )
     => ! [X3: a] :
          ( ( member_a @ X3 @ A )
         => ( P @ ( F @ X3 ) ) ) ) ).

% ball_imageD
thf(fact_235_ball__imageD,axiom,
    ! [F: a > real > a,A: set_a,P: ( real > a ) > $o] :
      ( ! [X2: real > a] :
          ( ( member_real_a @ X2 @ ( image_a_real_a @ F @ A ) )
         => ( P @ X2 ) )
     => ! [X3: a] :
          ( ( member_a @ X3 @ A )
         => ( P @ ( F @ X3 ) ) ) ) ).

% ball_imageD
thf(fact_236_ball__imageD,axiom,
    ! [F: a > a,A: set_a,P: a > $o] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ ( image_a_a @ F @ A ) )
         => ( P @ X2 ) )
     => ! [X3: a] :
          ( ( member_a @ X3 @ A )
         => ( P @ ( F @ X3 ) ) ) ) ).

% ball_imageD
thf(fact_237_image__cong,axiom,
    ! [M: set_real,N: set_real,F: real > a,G: real > a] :
      ( ( M = N )
     => ( ! [X2: real] :
            ( ( member_real @ X2 @ N )
           => ( ( F @ X2 )
              = ( G @ X2 ) ) )
       => ( ( image_real_a @ F @ M )
          = ( image_real_a @ G @ N ) ) ) ) ).

% image_cong
thf(fact_238_image__cong,axiom,
    ! [M: set_real,N: set_real,F: real > real,G: real > real] :
      ( ( M = N )
     => ( ! [X2: real] :
            ( ( member_real @ X2 @ N )
           => ( ( F @ X2 )
              = ( G @ X2 ) ) )
       => ( ( image_real_real @ F @ M )
          = ( image_real_real @ G @ N ) ) ) ) ).

% image_cong
thf(fact_239_image__cong,axiom,
    ! [M: set_nat,N: set_nat,F: nat > real,G: nat > real] :
      ( ( M = N )
     => ( ! [X2: nat] :
            ( ( member_nat @ X2 @ N )
           => ( ( F @ X2 )
              = ( G @ X2 ) ) )
       => ( ( image_nat_real @ F @ M )
          = ( image_nat_real @ G @ N ) ) ) ) ).

% image_cong
thf(fact_240_image__cong,axiom,
    ! [M: set_nat,N: set_nat,F: nat > complex,G: nat > complex] :
      ( ( M = N )
     => ( ! [X2: nat] :
            ( ( member_nat @ X2 @ N )
           => ( ( F @ X2 )
              = ( G @ X2 ) ) )
       => ( ( image_nat_complex @ F @ M )
          = ( image_nat_complex @ G @ N ) ) ) ) ).

% image_cong
thf(fact_241_image__cong,axiom,
    ! [M: set_a,N: set_a,F: a > nat,G: a > nat] :
      ( ( M = N )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ N )
           => ( ( F @ X2 )
              = ( G @ X2 ) ) )
       => ( ( image_a_nat @ F @ M )
          = ( image_a_nat @ G @ N ) ) ) ) ).

% image_cong
thf(fact_242_image__cong,axiom,
    ! [M: set_a,N: set_a,F: a > real > nat,G: a > real > nat] :
      ( ( M = N )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ N )
           => ( ( F @ X2 )
              = ( G @ X2 ) ) )
       => ( ( image_a_real_nat @ F @ M )
          = ( image_a_real_nat @ G @ N ) ) ) ) ).

% image_cong
thf(fact_243_image__cong,axiom,
    ! [M: set_a,N: set_a,F: a > real > b,G: a > real > b] :
      ( ( M = N )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ N )
           => ( ( F @ X2 )
              = ( G @ X2 ) ) )
       => ( ( image_a_real_b @ F @ M )
          = ( image_a_real_b @ G @ N ) ) ) ) ).

% image_cong
thf(fact_244_image__cong,axiom,
    ! [M: set_a,N: set_a,F: a > real > a,G: a > real > a] :
      ( ( M = N )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ N )
           => ( ( F @ X2 )
              = ( G @ X2 ) ) )
       => ( ( image_a_real_a @ F @ M )
          = ( image_a_real_a @ G @ N ) ) ) ) ).

% image_cong
thf(fact_245_image__cong,axiom,
    ! [M: set_a,N: set_a,F: a > a,G: a > a] :
      ( ( M = N )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ N )
           => ( ( F @ X2 )
              = ( G @ X2 ) ) )
       => ( ( image_a_a @ F @ M )
          = ( image_a_a @ G @ N ) ) ) ) ).

% image_cong
thf(fact_246_bex__imageD,axiom,
    ! [F: real > a,A: set_real,P: a > $o] :
      ( ? [X3: a] :
          ( ( member_a @ X3 @ ( image_real_a @ F @ A ) )
          & ( P @ X3 ) )
     => ? [X2: real] :
          ( ( member_real @ X2 @ A )
          & ( P @ ( F @ X2 ) ) ) ) ).

% bex_imageD
thf(fact_247_bex__imageD,axiom,
    ! [F: nat > real,A: set_nat,P: real > $o] :
      ( ? [X3: real] :
          ( ( member_real @ X3 @ ( image_nat_real @ F @ A ) )
          & ( P @ X3 ) )
     => ? [X2: nat] :
          ( ( member_nat @ X2 @ A )
          & ( P @ ( F @ X2 ) ) ) ) ).

% bex_imageD
thf(fact_248_bex__imageD,axiom,
    ! [F: nat > complex,A: set_nat,P: complex > $o] :
      ( ? [X3: complex] :
          ( ( member_complex @ X3 @ ( image_nat_complex @ F @ A ) )
          & ( P @ X3 ) )
     => ? [X2: nat] :
          ( ( member_nat @ X2 @ A )
          & ( P @ ( F @ X2 ) ) ) ) ).

% bex_imageD
thf(fact_249_bex__imageD,axiom,
    ! [F: real > real,A: set_real,P: real > $o] :
      ( ? [X3: real] :
          ( ( member_real @ X3 @ ( image_real_real @ F @ A ) )
          & ( P @ X3 ) )
     => ? [X2: real] :
          ( ( member_real @ X2 @ A )
          & ( P @ ( F @ X2 ) ) ) ) ).

% bex_imageD
thf(fact_250_bex__imageD,axiom,
    ! [F: a > nat,A: set_a,P: nat > $o] :
      ( ? [X3: nat] :
          ( ( member_nat @ X3 @ ( image_a_nat @ F @ A ) )
          & ( P @ X3 ) )
     => ? [X2: a] :
          ( ( member_a @ X2 @ A )
          & ( P @ ( F @ X2 ) ) ) ) ).

% bex_imageD
thf(fact_251_bex__imageD,axiom,
    ! [F: a > real > nat,A: set_a,P: ( real > nat ) > $o] :
      ( ? [X3: real > nat] :
          ( ( member_real_nat @ X3 @ ( image_a_real_nat @ F @ A ) )
          & ( P @ X3 ) )
     => ? [X2: a] :
          ( ( member_a @ X2 @ A )
          & ( P @ ( F @ X2 ) ) ) ) ).

% bex_imageD
thf(fact_252_bex__imageD,axiom,
    ! [F: a > real > b,A: set_a,P: ( real > b ) > $o] :
      ( ? [X3: real > b] :
          ( ( member_real_b @ X3 @ ( image_a_real_b @ F @ A ) )
          & ( P @ X3 ) )
     => ? [X2: a] :
          ( ( member_a @ X2 @ A )
          & ( P @ ( F @ X2 ) ) ) ) ).

% bex_imageD
thf(fact_253_bex__imageD,axiom,
    ! [F: a > real > a,A: set_a,P: ( real > a ) > $o] :
      ( ? [X3: real > a] :
          ( ( member_real_a @ X3 @ ( image_a_real_a @ F @ A ) )
          & ( P @ X3 ) )
     => ? [X2: a] :
          ( ( member_a @ X2 @ A )
          & ( P @ ( F @ X2 ) ) ) ) ).

% bex_imageD
thf(fact_254_bex__imageD,axiom,
    ! [F: a > a,A: set_a,P: a > $o] :
      ( ? [X3: a] :
          ( ( member_a @ X3 @ ( image_a_a @ F @ A ) )
          & ( P @ X3 ) )
     => ? [X2: a] :
          ( ( member_a @ X2 @ A )
          & ( P @ ( F @ X2 ) ) ) ) ).

% bex_imageD
thf(fact_255_image__iff,axiom,
    ! [Z: real,F: nat > real,A: set_nat] :
      ( ( member_real @ Z @ ( image_nat_real @ F @ A ) )
      = ( ? [X4: nat] :
            ( ( member_nat @ X4 @ A )
            & ( Z
              = ( F @ X4 ) ) ) ) ) ).

% image_iff
thf(fact_256_image__iff,axiom,
    ! [Z: complex,F: nat > complex,A: set_nat] :
      ( ( member_complex @ Z @ ( image_nat_complex @ F @ A ) )
      = ( ? [X4: nat] :
            ( ( member_nat @ X4 @ A )
            & ( Z
              = ( F @ X4 ) ) ) ) ) ).

% image_iff
thf(fact_257_image__iff,axiom,
    ! [Z: real,F: real > real,A: set_real] :
      ( ( member_real @ Z @ ( image_real_real @ F @ A ) )
      = ( ? [X4: real] :
            ( ( member_real @ X4 @ A )
            & ( Z
              = ( F @ X4 ) ) ) ) ) ).

% image_iff
thf(fact_258_image__iff,axiom,
    ! [Z: nat,F: a > nat,A: set_a] :
      ( ( member_nat @ Z @ ( image_a_nat @ F @ A ) )
      = ( ? [X4: a] :
            ( ( member_a @ X4 @ A )
            & ( Z
              = ( F @ X4 ) ) ) ) ) ).

% image_iff
thf(fact_259_image__iff,axiom,
    ! [Z: real > nat,F: a > real > nat,A: set_a] :
      ( ( member_real_nat @ Z @ ( image_a_real_nat @ F @ A ) )
      = ( ? [X4: a] :
            ( ( member_a @ X4 @ A )
            & ( Z
              = ( F @ X4 ) ) ) ) ) ).

% image_iff
thf(fact_260_image__iff,axiom,
    ! [Z: real > b,F: a > real > b,A: set_a] :
      ( ( member_real_b @ Z @ ( image_a_real_b @ F @ A ) )
      = ( ? [X4: a] :
            ( ( member_a @ X4 @ A )
            & ( Z
              = ( F @ X4 ) ) ) ) ) ).

% image_iff
thf(fact_261_image__iff,axiom,
    ! [Z: real > a,F: a > real > a,A: set_a] :
      ( ( member_real_a @ Z @ ( image_a_real_a @ F @ A ) )
      = ( ? [X4: a] :
            ( ( member_a @ X4 @ A )
            & ( Z
              = ( F @ X4 ) ) ) ) ) ).

% image_iff
thf(fact_262_image__iff,axiom,
    ! [Z: a,F: real > a,A: set_real] :
      ( ( member_a @ Z @ ( image_real_a @ F @ A ) )
      = ( ? [X4: real] :
            ( ( member_real @ X4 @ A )
            & ( Z
              = ( F @ X4 ) ) ) ) ) ).

% image_iff
thf(fact_263_image__iff,axiom,
    ! [Z: a,F: a > a,A: set_a] :
      ( ( member_a @ Z @ ( image_a_a @ F @ A ) )
      = ( ? [X4: a] :
            ( ( member_a @ X4 @ A )
            & ( Z
              = ( F @ X4 ) ) ) ) ) ).

% image_iff
thf(fact_264_imageI,axiom,
    ! [X: real,A: set_real,F: real > real] :
      ( ( member_real @ X @ A )
     => ( member_real @ ( F @ X ) @ ( image_real_real @ F @ A ) ) ) ).

% imageI
thf(fact_265_imageI,axiom,
    ! [X: real,A: set_real,F: real > a] :
      ( ( member_real @ X @ A )
     => ( member_a @ ( F @ X ) @ ( image_real_a @ F @ A ) ) ) ).

% imageI
thf(fact_266_imageI,axiom,
    ! [X: nat,A: set_nat,F: nat > real] :
      ( ( member_nat @ X @ A )
     => ( member_real @ ( F @ X ) @ ( image_nat_real @ F @ A ) ) ) ).

% imageI
thf(fact_267_imageI,axiom,
    ! [X: nat,A: set_nat,F: nat > complex] :
      ( ( member_nat @ X @ A )
     => ( member_complex @ ( F @ X ) @ ( image_nat_complex @ F @ A ) ) ) ).

% imageI
thf(fact_268_imageI,axiom,
    ! [X: nat,A: set_nat,F: nat > nat] :
      ( ( member_nat @ X @ A )
     => ( member_nat @ ( F @ X ) @ ( image_nat_nat @ F @ A ) ) ) ).

% imageI
thf(fact_269_imageI,axiom,
    ! [X: nat,A: set_nat,F: nat > a] :
      ( ( member_nat @ X @ A )
     => ( member_a @ ( F @ X ) @ ( image_nat_a @ F @ A ) ) ) ).

% imageI
thf(fact_270_imageI,axiom,
    ! [X: a,A: set_a,F: a > nat] :
      ( ( member_a @ X @ A )
     => ( member_nat @ ( F @ X ) @ ( image_a_nat @ F @ A ) ) ) ).

% imageI
thf(fact_271_imageI,axiom,
    ! [X: a,A: set_a,F: a > a] :
      ( ( member_a @ X @ A )
     => ( member_a @ ( F @ X ) @ ( image_a_a @ F @ A ) ) ) ).

% imageI
thf(fact_272_imageI,axiom,
    ! [X: nat,A: set_nat,F: nat > real > nat] :
      ( ( member_nat @ X @ A )
     => ( member_real_nat @ ( F @ X ) @ ( image_nat_real_nat @ F @ A ) ) ) ).

% imageI
thf(fact_273_imageI,axiom,
    ! [X: nat,A: set_nat,F: nat > real > b] :
      ( ( member_nat @ X @ A )
     => ( member_real_b @ ( F @ X ) @ ( image_nat_real_b @ F @ A ) ) ) ).

% imageI
thf(fact_274_range__eqI,axiom,
    ! [B: nat,F: extend8495563244428889912nnreal > nat,X: extend8495563244428889912nnreal] :
      ( ( B
        = ( F @ X ) )
     => ( member_nat @ B @ ( image_4010189972324537615al_nat @ F @ top_to7994903218803871134nnreal ) ) ) ).

% range_eqI
thf(fact_275_range__eqI,axiom,
    ! [B: a,F: extend8495563244428889912nnreal > a,X: extend8495563244428889912nnreal] :
      ( ( B
        = ( F @ X ) )
     => ( member_a @ B @ ( image_7862617044475835263real_a @ F @ top_to7994903218803871134nnreal ) ) ) ).

% range_eqI
thf(fact_276_range__eqI,axiom,
    ! [B: nat,F: complex > nat,X: complex] :
      ( ( B
        = ( F @ X ) )
     => ( member_nat @ B @ ( image_complex_nat @ F @ top_top_set_complex ) ) ) ).

% range_eqI
thf(fact_277_range__eqI,axiom,
    ! [B: a,F: complex > a,X: complex] :
      ( ( B
        = ( F @ X ) )
     => ( member_a @ B @ ( image_complex_a @ F @ top_top_set_complex ) ) ) ).

% range_eqI
thf(fact_278_range__eqI,axiom,
    ! [B: real,F: real > real,X: real] :
      ( ( B
        = ( F @ X ) )
     => ( member_real @ B @ ( image_real_real @ F @ top_top_set_real ) ) ) ).

% range_eqI
thf(fact_279_range__eqI,axiom,
    ! [B: nat,F: real > nat,X: real] :
      ( ( B
        = ( F @ X ) )
     => ( member_nat @ B @ ( image_real_nat @ F @ top_top_set_real ) ) ) ).

% range_eqI
thf(fact_280_range__eqI,axiom,
    ! [B: a,F: real > a,X: real] :
      ( ( B
        = ( F @ X ) )
     => ( member_a @ B @ ( image_real_a @ F @ top_top_set_real ) ) ) ).

% range_eqI
thf(fact_281_range__eqI,axiom,
    ! [B: nat,F: $o > nat,X: $o] :
      ( ( B
        = ( F @ X ) )
     => ( member_nat @ B @ ( image_o_nat @ F @ top_top_set_o ) ) ) ).

% range_eqI
thf(fact_282_range__eqI,axiom,
    ! [B: a,F: $o > a,X: $o] :
      ( ( B
        = ( F @ X ) )
     => ( member_a @ B @ ( image_o_a @ F @ top_top_set_o ) ) ) ).

% range_eqI
thf(fact_283_range__eqI,axiom,
    ! [B: real,F: nat > real,X: nat] :
      ( ( B
        = ( F @ X ) )
     => ( member_real @ B @ ( image_nat_real @ F @ top_top_set_nat ) ) ) ).

% range_eqI
thf(fact_284_surj__def,axiom,
    ! [F: extend8495563244428889912nnreal > extend8495563244428889912nnreal] :
      ( ( ( image_8394674774369097847nnreal @ F @ top_to7994903218803871134nnreal )
        = top_to7994903218803871134nnreal )
      = ( ! [Y2: extend8495563244428889912nnreal] :
          ? [X4: extend8495563244428889912nnreal] :
            ( Y2
            = ( F @ X4 ) ) ) ) ).

% surj_def
thf(fact_285_surj__def,axiom,
    ! [F: extend8495563244428889912nnreal > complex] :
      ( ( ( image_3781532184644764653omplex @ F @ top_to7994903218803871134nnreal )
        = top_top_set_complex )
      = ( ! [Y2: complex] :
          ? [X4: extend8495563244428889912nnreal] :
            ( Y2
            = ( F @ X4 ) ) ) ) ).

% surj_def
thf(fact_286_surj__def,axiom,
    ! [F: extend8495563244428889912nnreal > real] :
      ( ( ( image_5648444867695151211l_real @ F @ top_to7994903218803871134nnreal )
        = top_top_set_real )
      = ( ! [Y2: real] :
          ? [X4: extend8495563244428889912nnreal] :
            ( Y2
            = ( F @ X4 ) ) ) ) ).

% surj_def
thf(fact_287_surj__def,axiom,
    ! [F: extend8495563244428889912nnreal > $o] :
      ( ( ( image_3162942742313426073real_o @ F @ top_to7994903218803871134nnreal )
        = top_top_set_o )
      = ( ! [Y2: $o] :
          ? [X4: extend8495563244428889912nnreal] :
            ( Y2
            = ( F @ X4 ) ) ) ) ).

% surj_def
thf(fact_288_surj__def,axiom,
    ! [F: extend8495563244428889912nnreal > nat] :
      ( ( ( image_4010189972324537615al_nat @ F @ top_to7994903218803871134nnreal )
        = top_top_set_nat )
      = ( ! [Y2: nat] :
          ? [X4: extend8495563244428889912nnreal] :
            ( Y2
            = ( F @ X4 ) ) ) ) ).

% surj_def
thf(fact_289_surj__def,axiom,
    ! [F: extend8495563244428889912nnreal > a] :
      ( ( ( image_7862617044475835263real_a @ F @ top_to7994903218803871134nnreal )
        = top_top_set_a )
      = ( ! [Y2: a] :
          ? [X4: extend8495563244428889912nnreal] :
            ( Y2
            = ( F @ X4 ) ) ) ) ).

% surj_def
thf(fact_290_surj__def,axiom,
    ! [F: extend8495563244428889912nnreal > b] :
      ( ( ( image_7862617044475835264real_b @ F @ top_to7994903218803871134nnreal )
        = top_top_set_b )
      = ( ! [Y2: b] :
          ? [X4: extend8495563244428889912nnreal] :
            ( Y2
            = ( F @ X4 ) ) ) ) ).

% surj_def
thf(fact_291_surj__def,axiom,
    ! [F: complex > extend8495563244428889912nnreal] :
      ( ( ( image_4927658817219388909nnreal @ F @ top_top_set_complex )
        = top_to7994903218803871134nnreal )
      = ( ! [Y2: extend8495563244428889912nnreal] :
          ? [X4: complex] :
            ( Y2
            = ( F @ X4 ) ) ) ) ).

% surj_def
thf(fact_292_surj__def,axiom,
    ! [F: complex > complex] :
      ( ( ( image_1468599708987790691omplex @ F @ top_top_set_complex )
        = top_top_set_complex )
      = ( ! [Y2: complex] :
          ? [X4: complex] :
            ( Y2
            = ( F @ X4 ) ) ) ) ).

% surj_def
thf(fact_293_surj__def,axiom,
    ! [F: complex > real] :
      ( ( ( image_complex_real @ F @ top_top_set_complex )
        = top_top_set_real )
      = ( ! [Y2: real] :
          ? [X4: complex] :
            ( Y2
            = ( F @ X4 ) ) ) ) ).

% surj_def
thf(fact_294_space__borel,axiom,
    ( ( sigma_space_complex @ borel_1392132677378845456omplex )
    = top_top_set_complex ) ).

% space_borel
thf(fact_295_space__borel,axiom,
    ( ( sigma_space_real_nat @ borel_1750461538259077885al_nat )
    = top_top_set_real_nat ) ).

% space_borel
thf(fact_296_space__borel,axiom,
    ( ( sigma_space_real @ borel_5078946678739801102l_real )
    = top_top_set_real ) ).

% space_borel
thf(fact_297_space__borel,axiom,
    ( ( sigma_space_nat @ borel_8449730974584783410el_nat )
    = top_top_set_nat ) ).

% space_borel
thf(fact_298_space__borel,axiom,
    ( ( sigma_space_o @ borel_5500255247093592246orel_o )
    = top_top_set_o ) ).

% space_borel
thf(fact_299_space__borel,axiom,
    ( ( sigma_3147302497200244656nnreal @ borel_6524799422816628122nnreal )
    = top_to7994903218803871134nnreal ) ).

% space_borel
thf(fact_300_countable__Int1,axiom,
    ! [A: set_complex,B2: set_complex] :
      ( ( counta5113917769705169331omplex @ A )
     => ( counta5113917769705169331omplex @ ( inf_inf_set_complex @ A @ B2 ) ) ) ).

% countable_Int1
thf(fact_301_countable__Int1,axiom,
    ! [A: set_real,B2: set_real] :
      ( ( counta7319604579010473777e_real @ A )
     => ( counta7319604579010473777e_real @ ( inf_inf_set_real @ A @ B2 ) ) ) ).

% countable_Int1
thf(fact_302_countable__Int1,axiom,
    ! [A: set_o,B2: set_o] :
      ( ( counta5976203206615340371able_o @ A )
     => ( counta5976203206615340371able_o @ ( inf_inf_set_o @ A @ B2 ) ) ) ).

% countable_Int1
thf(fact_303_countable__Int1,axiom,
    ! [A: set_nat,B2: set_nat] :
      ( ( counta1168086296615599829le_nat @ A )
     => ( counta1168086296615599829le_nat @ ( inf_inf_set_nat @ A @ B2 ) ) ) ).

% countable_Int1
thf(fact_304_countable__Int1,axiom,
    ! [A: set_a,B2: set_a] :
      ( ( counta4098120917673242425able_a @ A )
     => ( counta4098120917673242425able_a @ ( inf_inf_set_a @ A @ B2 ) ) ) ).

% countable_Int1
thf(fact_305_countable__Int2,axiom,
    ! [B2: set_complex,A: set_complex] :
      ( ( counta5113917769705169331omplex @ B2 )
     => ( counta5113917769705169331omplex @ ( inf_inf_set_complex @ A @ B2 ) ) ) ).

% countable_Int2
thf(fact_306_countable__Int2,axiom,
    ! [B2: set_real,A: set_real] :
      ( ( counta7319604579010473777e_real @ B2 )
     => ( counta7319604579010473777e_real @ ( inf_inf_set_real @ A @ B2 ) ) ) ).

% countable_Int2
thf(fact_307_countable__Int2,axiom,
    ! [B2: set_o,A: set_o] :
      ( ( counta5976203206615340371able_o @ B2 )
     => ( counta5976203206615340371able_o @ ( inf_inf_set_o @ A @ B2 ) ) ) ).

% countable_Int2
thf(fact_308_countable__Int2,axiom,
    ! [B2: set_nat,A: set_nat] :
      ( ( counta1168086296615599829le_nat @ B2 )
     => ( counta1168086296615599829le_nat @ ( inf_inf_set_nat @ A @ B2 ) ) ) ).

% countable_Int2
thf(fact_309_countable__Int2,axiom,
    ! [B2: set_a,A: set_a] :
      ( ( counta4098120917673242425able_a @ B2 )
     => ( counta4098120917673242425able_a @ ( inf_inf_set_a @ A @ B2 ) ) ) ).

% countable_Int2
thf(fact_310_countable__image,axiom,
    ! [A: set_complex,F: complex > complex] :
      ( ( counta5113917769705169331omplex @ A )
     => ( counta5113917769705169331omplex @ ( image_1468599708987790691omplex @ F @ A ) ) ) ).

% countable_image
thf(fact_311_countable__image,axiom,
    ! [A: set_complex,F: complex > real] :
      ( ( counta5113917769705169331omplex @ A )
     => ( counta7319604579010473777e_real @ ( image_complex_real @ F @ A ) ) ) ).

% countable_image
thf(fact_312_countable__image,axiom,
    ! [A: set_complex,F: complex > $o] :
      ( ( counta5113917769705169331omplex @ A )
     => ( counta5976203206615340371able_o @ ( image_complex_o @ F @ A ) ) ) ).

% countable_image
thf(fact_313_countable__image,axiom,
    ! [A: set_complex,F: complex > nat] :
      ( ( counta5113917769705169331omplex @ A )
     => ( counta1168086296615599829le_nat @ ( image_complex_nat @ F @ A ) ) ) ).

% countable_image
thf(fact_314_countable__image,axiom,
    ! [A: set_complex,F: complex > a] :
      ( ( counta5113917769705169331omplex @ A )
     => ( counta4098120917673242425able_a @ ( image_complex_a @ F @ A ) ) ) ).

% countable_image
thf(fact_315_countable__image,axiom,
    ! [A: set_real,F: real > complex] :
      ( ( counta7319604579010473777e_real @ A )
     => ( counta5113917769705169331omplex @ ( image_real_complex @ F @ A ) ) ) ).

% countable_image
thf(fact_316_countable__image,axiom,
    ! [A: set_real,F: real > real] :
      ( ( counta7319604579010473777e_real @ A )
     => ( counta7319604579010473777e_real @ ( image_real_real @ F @ A ) ) ) ).

% countable_image
thf(fact_317_countable__image,axiom,
    ! [A: set_real,F: real > $o] :
      ( ( counta7319604579010473777e_real @ A )
     => ( counta5976203206615340371able_o @ ( image_real_o @ F @ A ) ) ) ).

% countable_image
thf(fact_318_countable__image,axiom,
    ! [A: set_real,F: real > nat] :
      ( ( counta7319604579010473777e_real @ A )
     => ( counta1168086296615599829le_nat @ ( image_real_nat @ F @ A ) ) ) ).

% countable_image
thf(fact_319_countable__image,axiom,
    ! [A: set_real,F: real > a] :
      ( ( counta7319604579010473777e_real @ A )
     => ( counta4098120917673242425able_a @ ( image_real_a @ F @ A ) ) ) ).

% countable_image
thf(fact_320_space__count__space,axiom,
    ! [Omega: set_a] :
      ( ( sigma_space_a @ ( sigma_count_space_a @ Omega ) )
      = Omega ) ).

% space_count_space
thf(fact_321_space__count__space,axiom,
    ! [Omega: set_real] :
      ( ( sigma_space_real @ ( sigma_8508918144308765139e_real @ Omega ) )
      = Omega ) ).

% space_count_space
thf(fact_322_space__count__space,axiom,
    ! [Omega: set_o] :
      ( ( sigma_space_o @ ( sigma_count_space_o @ Omega ) )
      = Omega ) ).

% space_count_space
thf(fact_323_space__count__space,axiom,
    ! [Omega: set_nat] :
      ( ( sigma_space_nat @ ( sigma_7685844798829912695ce_nat @ Omega ) )
      = Omega ) ).

% space_count_space
thf(fact_324_space__count__space,axiom,
    ! [Omega: set_Ex3793607809372303086nnreal] :
      ( ( sigma_3147302497200244656nnreal @ ( sigma_7204664791115113951nnreal @ Omega ) )
      = Omega ) ).

% space_count_space
thf(fact_325_space__count__space,axiom,
    ! [Omega: set_complex] :
      ( ( sigma_space_complex @ ( sigma_3977070789342921045omplex @ Omega ) )
      = Omega ) ).

% space_count_space
thf(fact_326_space__count__space,axiom,
    ! [Omega: set_b] :
      ( ( sigma_space_b @ ( sigma_count_space_b @ Omega ) )
      = Omega ) ).

% space_count_space
thf(fact_327_mem__Collect__eq,axiom,
    ! [A3: real > nat,P: ( real > nat ) > $o] :
      ( ( member_real_nat @ A3 @ ( collect_real_nat @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_328_mem__Collect__eq,axiom,
    ! [A3: real > b,P: ( real > b ) > $o] :
      ( ( member_real_b @ A3 @ ( collect_real_b @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_329_mem__Collect__eq,axiom,
    ! [A3: real > a,P: ( real > a ) > $o] :
      ( ( member_real_a @ A3 @ ( collect_real_a @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_330_mem__Collect__eq,axiom,
    ! [A3: a,P: a > $o] :
      ( ( member_a @ A3 @ ( collect_a @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_331_mem__Collect__eq,axiom,
    ! [A3: a > complex,P: ( a > complex ) > $o] :
      ( ( member_a_complex @ A3 @ ( collect_a_complex @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_332_mem__Collect__eq,axiom,
    ! [A3: a > real,P: ( a > real ) > $o] :
      ( ( member_a_real @ A3 @ ( collect_a_real @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_333_mem__Collect__eq,axiom,
    ! [A3: a > $o,P: ( a > $o ) > $o] :
      ( ( member_a_o @ A3 @ ( collect_a_o @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_334_mem__Collect__eq,axiom,
    ! [A3: a > nat,P: ( a > nat ) > $o] :
      ( ( member_a_nat @ A3 @ ( collect_a_nat @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_335_mem__Collect__eq,axiom,
    ! [A3: a > a,P: ( a > a ) > $o] :
      ( ( member_a_a @ A3 @ ( collect_a_a @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_336_mem__Collect__eq,axiom,
    ! [A3: nat,P: nat > $o] :
      ( ( member_nat @ A3 @ ( collect_nat @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_337_Collect__mem__eq,axiom,
    ! [A: set_real_nat] :
      ( ( collect_real_nat
        @ ^ [X4: real > nat] : ( member_real_nat @ X4 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_338_Collect__mem__eq,axiom,
    ! [A: set_real_b] :
      ( ( collect_real_b
        @ ^ [X4: real > b] : ( member_real_b @ X4 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_339_Collect__mem__eq,axiom,
    ! [A: set_real_a] :
      ( ( collect_real_a
        @ ^ [X4: real > a] : ( member_real_a @ X4 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_340_Collect__mem__eq,axiom,
    ! [A: set_a] :
      ( ( collect_a
        @ ^ [X4: a] : ( member_a @ X4 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_341_Collect__mem__eq,axiom,
    ! [A: set_a_complex] :
      ( ( collect_a_complex
        @ ^ [X4: a > complex] : ( member_a_complex @ X4 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_342_Collect__mem__eq,axiom,
    ! [A: set_a_real] :
      ( ( collect_a_real
        @ ^ [X4: a > real] : ( member_a_real @ X4 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_343_Collect__mem__eq,axiom,
    ! [A: set_a_o] :
      ( ( collect_a_o
        @ ^ [X4: a > $o] : ( member_a_o @ X4 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_344_Collect__mem__eq,axiom,
    ! [A: set_a_nat] :
      ( ( collect_a_nat
        @ ^ [X4: a > nat] : ( member_a_nat @ X4 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_345_Collect__mem__eq,axiom,
    ! [A: set_a_a] :
      ( ( collect_a_a
        @ ^ [X4: a > a] : ( member_a_a @ X4 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_346_Collect__mem__eq,axiom,
    ! [A: set_nat] :
      ( ( collect_nat
        @ ^ [X4: nat] : ( member_nat @ X4 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_347_Collect__cong,axiom,
    ! [P: nat > $o,Q: nat > $o] :
      ( ! [X2: nat] :
          ( ( P @ X2 )
          = ( Q @ X2 ) )
     => ( ( collect_nat @ P )
        = ( collect_nat @ Q ) ) ) ).

% Collect_cong
thf(fact_348_inf__top_Oright__neutral,axiom,
    ! [A3: set_Ex3793607809372303086nnreal] :
      ( ( inf_in3368558534146122112nnreal @ A3 @ top_to7994903218803871134nnreal )
      = A3 ) ).

% inf_top.right_neutral
thf(fact_349_inf__top_Oright__neutral,axiom,
    ! [A3: set_complex] :
      ( ( inf_inf_set_complex @ A3 @ top_top_set_complex )
      = A3 ) ).

% inf_top.right_neutral
thf(fact_350_inf__top_Oright__neutral,axiom,
    ! [A3: set_real] :
      ( ( inf_inf_set_real @ A3 @ top_top_set_real )
      = A3 ) ).

% inf_top.right_neutral
thf(fact_351_inf__top_Oright__neutral,axiom,
    ! [A3: set_o] :
      ( ( inf_inf_set_o @ A3 @ top_top_set_o )
      = A3 ) ).

% inf_top.right_neutral
thf(fact_352_inf__top_Oright__neutral,axiom,
    ! [A3: set_nat] :
      ( ( inf_inf_set_nat @ A3 @ top_top_set_nat )
      = A3 ) ).

% inf_top.right_neutral
thf(fact_353_inf__top_Oright__neutral,axiom,
    ! [A3: set_a] :
      ( ( inf_inf_set_a @ A3 @ top_top_set_a )
      = A3 ) ).

% inf_top.right_neutral
thf(fact_354_inf__top_Oright__neutral,axiom,
    ! [A3: set_b] :
      ( ( inf_inf_set_b @ A3 @ top_top_set_b )
      = A3 ) ).

% inf_top.right_neutral
thf(fact_355_inf__top_Oright__neutral,axiom,
    ! [A3: set_real_a] :
      ( ( inf_inf_set_real_a @ A3 @ top_top_set_real_a )
      = A3 ) ).

% inf_top.right_neutral
thf(fact_356_inf__top_Oright__neutral,axiom,
    ! [A3: set_real_b] :
      ( ( inf_inf_set_real_b @ A3 @ top_top_set_real_b )
      = A3 ) ).

% inf_top.right_neutral
thf(fact_357_inf__top_Oright__neutral,axiom,
    ! [A3: set_real_nat] :
      ( ( inf_inf_set_real_nat @ A3 @ top_top_set_real_nat )
      = A3 ) ).

% inf_top.right_neutral
thf(fact_358_inf__top_Oneutr__eq__iff,axiom,
    ! [A3: set_Ex3793607809372303086nnreal,B: set_Ex3793607809372303086nnreal] :
      ( ( top_to7994903218803871134nnreal
        = ( inf_in3368558534146122112nnreal @ A3 @ B ) )
      = ( ( A3 = top_to7994903218803871134nnreal )
        & ( B = top_to7994903218803871134nnreal ) ) ) ).

% inf_top.neutr_eq_iff
thf(fact_359_inf__top_Oneutr__eq__iff,axiom,
    ! [A3: set_complex,B: set_complex] :
      ( ( top_top_set_complex
        = ( inf_inf_set_complex @ A3 @ B ) )
      = ( ( A3 = top_top_set_complex )
        & ( B = top_top_set_complex ) ) ) ).

% inf_top.neutr_eq_iff
thf(fact_360_inf__top_Oneutr__eq__iff,axiom,
    ! [A3: set_real,B: set_real] :
      ( ( top_top_set_real
        = ( inf_inf_set_real @ A3 @ B ) )
      = ( ( A3 = top_top_set_real )
        & ( B = top_top_set_real ) ) ) ).

% inf_top.neutr_eq_iff
thf(fact_361_inf__top_Oneutr__eq__iff,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( top_top_set_o
        = ( inf_inf_set_o @ A3 @ B ) )
      = ( ( A3 = top_top_set_o )
        & ( B = top_top_set_o ) ) ) ).

% inf_top.neutr_eq_iff
thf(fact_362_inf__top_Oneutr__eq__iff,axiom,
    ! [A3: set_nat,B: set_nat] :
      ( ( top_top_set_nat
        = ( inf_inf_set_nat @ A3 @ B ) )
      = ( ( A3 = top_top_set_nat )
        & ( B = top_top_set_nat ) ) ) ).

% inf_top.neutr_eq_iff
thf(fact_363_inf__top_Oneutr__eq__iff,axiom,
    ! [A3: set_a,B: set_a] :
      ( ( top_top_set_a
        = ( inf_inf_set_a @ A3 @ B ) )
      = ( ( A3 = top_top_set_a )
        & ( B = top_top_set_a ) ) ) ).

% inf_top.neutr_eq_iff
thf(fact_364_inf__top_Oneutr__eq__iff,axiom,
    ! [A3: set_b,B: set_b] :
      ( ( top_top_set_b
        = ( inf_inf_set_b @ A3 @ B ) )
      = ( ( A3 = top_top_set_b )
        & ( B = top_top_set_b ) ) ) ).

% inf_top.neutr_eq_iff
thf(fact_365_inf__top_Oneutr__eq__iff,axiom,
    ! [A3: set_real_a,B: set_real_a] :
      ( ( top_top_set_real_a
        = ( inf_inf_set_real_a @ A3 @ B ) )
      = ( ( A3 = top_top_set_real_a )
        & ( B = top_top_set_real_a ) ) ) ).

% inf_top.neutr_eq_iff
thf(fact_366_inf__top_Oneutr__eq__iff,axiom,
    ! [A3: set_real_b,B: set_real_b] :
      ( ( top_top_set_real_b
        = ( inf_inf_set_real_b @ A3 @ B ) )
      = ( ( A3 = top_top_set_real_b )
        & ( B = top_top_set_real_b ) ) ) ).

% inf_top.neutr_eq_iff
thf(fact_367_inf__top_Oneutr__eq__iff,axiom,
    ! [A3: set_real_nat,B: set_real_nat] :
      ( ( top_top_set_real_nat
        = ( inf_inf_set_real_nat @ A3 @ B ) )
      = ( ( A3 = top_top_set_real_nat )
        & ( B = top_top_set_real_nat ) ) ) ).

% inf_top.neutr_eq_iff
thf(fact_368_inf__top_Oleft__neutral,axiom,
    ! [A3: set_Ex3793607809372303086nnreal] :
      ( ( inf_in3368558534146122112nnreal @ top_to7994903218803871134nnreal @ A3 )
      = A3 ) ).

% inf_top.left_neutral
thf(fact_369_inf__top_Oleft__neutral,axiom,
    ! [A3: set_complex] :
      ( ( inf_inf_set_complex @ top_top_set_complex @ A3 )
      = A3 ) ).

% inf_top.left_neutral
thf(fact_370_inf__top_Oleft__neutral,axiom,
    ! [A3: set_real] :
      ( ( inf_inf_set_real @ top_top_set_real @ A3 )
      = A3 ) ).

% inf_top.left_neutral
thf(fact_371_inf__top_Oleft__neutral,axiom,
    ! [A3: set_o] :
      ( ( inf_inf_set_o @ top_top_set_o @ A3 )
      = A3 ) ).

% inf_top.left_neutral
thf(fact_372_inf__top_Oleft__neutral,axiom,
    ! [A3: set_nat] :
      ( ( inf_inf_set_nat @ top_top_set_nat @ A3 )
      = A3 ) ).

% inf_top.left_neutral
thf(fact_373_inf__top_Oleft__neutral,axiom,
    ! [A3: set_a] :
      ( ( inf_inf_set_a @ top_top_set_a @ A3 )
      = A3 ) ).

% inf_top.left_neutral
thf(fact_374_inf__top_Oleft__neutral,axiom,
    ! [A3: set_b] :
      ( ( inf_inf_set_b @ top_top_set_b @ A3 )
      = A3 ) ).

% inf_top.left_neutral
thf(fact_375_inf__top_Oleft__neutral,axiom,
    ! [A3: set_real_a] :
      ( ( inf_inf_set_real_a @ top_top_set_real_a @ A3 )
      = A3 ) ).

% inf_top.left_neutral
thf(fact_376_inf__top_Oleft__neutral,axiom,
    ! [A3: set_real_b] :
      ( ( inf_inf_set_real_b @ top_top_set_real_b @ A3 )
      = A3 ) ).

% inf_top.left_neutral
thf(fact_377_inf__top_Oleft__neutral,axiom,
    ! [A3: set_real_nat] :
      ( ( inf_inf_set_real_nat @ top_top_set_real_nat @ A3 )
      = A3 ) ).

% inf_top.left_neutral
thf(fact_378_inf__top_Oeq__neutr__iff,axiom,
    ! [A3: set_Ex3793607809372303086nnreal,B: set_Ex3793607809372303086nnreal] :
      ( ( ( inf_in3368558534146122112nnreal @ A3 @ B )
        = top_to7994903218803871134nnreal )
      = ( ( A3 = top_to7994903218803871134nnreal )
        & ( B = top_to7994903218803871134nnreal ) ) ) ).

% inf_top.eq_neutr_iff
thf(fact_379_inf__top_Oeq__neutr__iff,axiom,
    ! [A3: set_complex,B: set_complex] :
      ( ( ( inf_inf_set_complex @ A3 @ B )
        = top_top_set_complex )
      = ( ( A3 = top_top_set_complex )
        & ( B = top_top_set_complex ) ) ) ).

% inf_top.eq_neutr_iff
thf(fact_380_inf__top_Oeq__neutr__iff,axiom,
    ! [A3: set_real,B: set_real] :
      ( ( ( inf_inf_set_real @ A3 @ B )
        = top_top_set_real )
      = ( ( A3 = top_top_set_real )
        & ( B = top_top_set_real ) ) ) ).

% inf_top.eq_neutr_iff
thf(fact_381_inf__top_Oeq__neutr__iff,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( ( inf_inf_set_o @ A3 @ B )
        = top_top_set_o )
      = ( ( A3 = top_top_set_o )
        & ( B = top_top_set_o ) ) ) ).

% inf_top.eq_neutr_iff
thf(fact_382_inf__top_Oeq__neutr__iff,axiom,
    ! [A3: set_nat,B: set_nat] :
      ( ( ( inf_inf_set_nat @ A3 @ B )
        = top_top_set_nat )
      = ( ( A3 = top_top_set_nat )
        & ( B = top_top_set_nat ) ) ) ).

% inf_top.eq_neutr_iff
thf(fact_383_inf__top_Oeq__neutr__iff,axiom,
    ! [A3: set_a,B: set_a] :
      ( ( ( inf_inf_set_a @ A3 @ B )
        = top_top_set_a )
      = ( ( A3 = top_top_set_a )
        & ( B = top_top_set_a ) ) ) ).

% inf_top.eq_neutr_iff
thf(fact_384_inf__top_Oeq__neutr__iff,axiom,
    ! [A3: set_b,B: set_b] :
      ( ( ( inf_inf_set_b @ A3 @ B )
        = top_top_set_b )
      = ( ( A3 = top_top_set_b )
        & ( B = top_top_set_b ) ) ) ).

% inf_top.eq_neutr_iff
thf(fact_385_inf__top_Oeq__neutr__iff,axiom,
    ! [A3: set_real_a,B: set_real_a] :
      ( ( ( inf_inf_set_real_a @ A3 @ B )
        = top_top_set_real_a )
      = ( ( A3 = top_top_set_real_a )
        & ( B = top_top_set_real_a ) ) ) ).

% inf_top.eq_neutr_iff
thf(fact_386_inf__top_Oeq__neutr__iff,axiom,
    ! [A3: set_real_b,B: set_real_b] :
      ( ( ( inf_inf_set_real_b @ A3 @ B )
        = top_top_set_real_b )
      = ( ( A3 = top_top_set_real_b )
        & ( B = top_top_set_real_b ) ) ) ).

% inf_top.eq_neutr_iff
thf(fact_387_inf__top_Oeq__neutr__iff,axiom,
    ! [A3: set_real_nat,B: set_real_nat] :
      ( ( ( inf_inf_set_real_nat @ A3 @ B )
        = top_top_set_real_nat )
      = ( ( A3 = top_top_set_real_nat )
        & ( B = top_top_set_real_nat ) ) ) ).

% inf_top.eq_neutr_iff
thf(fact_388_top__eq__inf__iff,axiom,
    ! [X: set_Ex3793607809372303086nnreal,Y: set_Ex3793607809372303086nnreal] :
      ( ( top_to7994903218803871134nnreal
        = ( inf_in3368558534146122112nnreal @ X @ Y ) )
      = ( ( X = top_to7994903218803871134nnreal )
        & ( Y = top_to7994903218803871134nnreal ) ) ) ).

% top_eq_inf_iff
thf(fact_389_top__eq__inf__iff,axiom,
    ! [X: set_complex,Y: set_complex] :
      ( ( top_top_set_complex
        = ( inf_inf_set_complex @ X @ Y ) )
      = ( ( X = top_top_set_complex )
        & ( Y = top_top_set_complex ) ) ) ).

% top_eq_inf_iff
thf(fact_390_top__eq__inf__iff,axiom,
    ! [X: set_real,Y: set_real] :
      ( ( top_top_set_real
        = ( inf_inf_set_real @ X @ Y ) )
      = ( ( X = top_top_set_real )
        & ( Y = top_top_set_real ) ) ) ).

% top_eq_inf_iff
thf(fact_391_top__eq__inf__iff,axiom,
    ! [X: set_o,Y: set_o] :
      ( ( top_top_set_o
        = ( inf_inf_set_o @ X @ Y ) )
      = ( ( X = top_top_set_o )
        & ( Y = top_top_set_o ) ) ) ).

% top_eq_inf_iff
thf(fact_392_top__eq__inf__iff,axiom,
    ! [X: set_nat,Y: set_nat] :
      ( ( top_top_set_nat
        = ( inf_inf_set_nat @ X @ Y ) )
      = ( ( X = top_top_set_nat )
        & ( Y = top_top_set_nat ) ) ) ).

% top_eq_inf_iff
thf(fact_393_top__eq__inf__iff,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( top_top_set_a
        = ( inf_inf_set_a @ X @ Y ) )
      = ( ( X = top_top_set_a )
        & ( Y = top_top_set_a ) ) ) ).

% top_eq_inf_iff
thf(fact_394_top__eq__inf__iff,axiom,
    ! [X: set_b,Y: set_b] :
      ( ( top_top_set_b
        = ( inf_inf_set_b @ X @ Y ) )
      = ( ( X = top_top_set_b )
        & ( Y = top_top_set_b ) ) ) ).

% top_eq_inf_iff
thf(fact_395_top__eq__inf__iff,axiom,
    ! [X: set_real_a,Y: set_real_a] :
      ( ( top_top_set_real_a
        = ( inf_inf_set_real_a @ X @ Y ) )
      = ( ( X = top_top_set_real_a )
        & ( Y = top_top_set_real_a ) ) ) ).

% top_eq_inf_iff
thf(fact_396_top__eq__inf__iff,axiom,
    ! [X: set_real_b,Y: set_real_b] :
      ( ( top_top_set_real_b
        = ( inf_inf_set_real_b @ X @ Y ) )
      = ( ( X = top_top_set_real_b )
        & ( Y = top_top_set_real_b ) ) ) ).

% top_eq_inf_iff
thf(fact_397_top__eq__inf__iff,axiom,
    ! [X: set_real_nat,Y: set_real_nat] :
      ( ( top_top_set_real_nat
        = ( inf_inf_set_real_nat @ X @ Y ) )
      = ( ( X = top_top_set_real_nat )
        & ( Y = top_top_set_real_nat ) ) ) ).

% top_eq_inf_iff
thf(fact_398_inf__eq__top__iff,axiom,
    ! [X: set_Ex3793607809372303086nnreal,Y: set_Ex3793607809372303086nnreal] :
      ( ( ( inf_in3368558534146122112nnreal @ X @ Y )
        = top_to7994903218803871134nnreal )
      = ( ( X = top_to7994903218803871134nnreal )
        & ( Y = top_to7994903218803871134nnreal ) ) ) ).

% inf_eq_top_iff
thf(fact_399_inf__eq__top__iff,axiom,
    ! [X: set_complex,Y: set_complex] :
      ( ( ( inf_inf_set_complex @ X @ Y )
        = top_top_set_complex )
      = ( ( X = top_top_set_complex )
        & ( Y = top_top_set_complex ) ) ) ).

% inf_eq_top_iff
thf(fact_400_inf__eq__top__iff,axiom,
    ! [X: set_real,Y: set_real] :
      ( ( ( inf_inf_set_real @ X @ Y )
        = top_top_set_real )
      = ( ( X = top_top_set_real )
        & ( Y = top_top_set_real ) ) ) ).

% inf_eq_top_iff
thf(fact_401_inf__eq__top__iff,axiom,
    ! [X: set_o,Y: set_o] :
      ( ( ( inf_inf_set_o @ X @ Y )
        = top_top_set_o )
      = ( ( X = top_top_set_o )
        & ( Y = top_top_set_o ) ) ) ).

% inf_eq_top_iff
thf(fact_402_inf__eq__top__iff,axiom,
    ! [X: set_nat,Y: set_nat] :
      ( ( ( inf_inf_set_nat @ X @ Y )
        = top_top_set_nat )
      = ( ( X = top_top_set_nat )
        & ( Y = top_top_set_nat ) ) ) ).

% inf_eq_top_iff
thf(fact_403_inf__eq__top__iff,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( ( inf_inf_set_a @ X @ Y )
        = top_top_set_a )
      = ( ( X = top_top_set_a )
        & ( Y = top_top_set_a ) ) ) ).

% inf_eq_top_iff
thf(fact_404_inf__eq__top__iff,axiom,
    ! [X: set_b,Y: set_b] :
      ( ( ( inf_inf_set_b @ X @ Y )
        = top_top_set_b )
      = ( ( X = top_top_set_b )
        & ( Y = top_top_set_b ) ) ) ).

% inf_eq_top_iff
thf(fact_405_inf__eq__top__iff,axiom,
    ! [X: set_real_a,Y: set_real_a] :
      ( ( ( inf_inf_set_real_a @ X @ Y )
        = top_top_set_real_a )
      = ( ( X = top_top_set_real_a )
        & ( Y = top_top_set_real_a ) ) ) ).

% inf_eq_top_iff
thf(fact_406_inf__eq__top__iff,axiom,
    ! [X: set_real_b,Y: set_real_b] :
      ( ( ( inf_inf_set_real_b @ X @ Y )
        = top_top_set_real_b )
      = ( ( X = top_top_set_real_b )
        & ( Y = top_top_set_real_b ) ) ) ).

% inf_eq_top_iff
thf(fact_407_inf__eq__top__iff,axiom,
    ! [X: set_real_nat,Y: set_real_nat] :
      ( ( ( inf_inf_set_real_nat @ X @ Y )
        = top_top_set_real_nat )
      = ( ( X = top_top_set_real_nat )
        & ( Y = top_top_set_real_nat ) ) ) ).

% inf_eq_top_iff
thf(fact_408_inf__top__right,axiom,
    ! [X: set_Ex3793607809372303086nnreal] :
      ( ( inf_in3368558534146122112nnreal @ X @ top_to7994903218803871134nnreal )
      = X ) ).

% inf_top_right
thf(fact_409_inf__top__right,axiom,
    ! [X: set_complex] :
      ( ( inf_inf_set_complex @ X @ top_top_set_complex )
      = X ) ).

% inf_top_right
thf(fact_410_inf__top__right,axiom,
    ! [X: set_real] :
      ( ( inf_inf_set_real @ X @ top_top_set_real )
      = X ) ).

% inf_top_right
thf(fact_411_inf__top__right,axiom,
    ! [X: set_o] :
      ( ( inf_inf_set_o @ X @ top_top_set_o )
      = X ) ).

% inf_top_right
thf(fact_412_inf__top__right,axiom,
    ! [X: set_nat] :
      ( ( inf_inf_set_nat @ X @ top_top_set_nat )
      = X ) ).

% inf_top_right
thf(fact_413_inf__top__right,axiom,
    ! [X: set_a] :
      ( ( inf_inf_set_a @ X @ top_top_set_a )
      = X ) ).

% inf_top_right
thf(fact_414_inf__top__right,axiom,
    ! [X: set_b] :
      ( ( inf_inf_set_b @ X @ top_top_set_b )
      = X ) ).

% inf_top_right
thf(fact_415_inf__top__right,axiom,
    ! [X: set_real_a] :
      ( ( inf_inf_set_real_a @ X @ top_top_set_real_a )
      = X ) ).

% inf_top_right
thf(fact_416_inf__top__right,axiom,
    ! [X: set_real_b] :
      ( ( inf_inf_set_real_b @ X @ top_top_set_real_b )
      = X ) ).

% inf_top_right
thf(fact_417_inf__top__right,axiom,
    ! [X: set_real_nat] :
      ( ( inf_inf_set_real_nat @ X @ top_top_set_real_nat )
      = X ) ).

% inf_top_right
thf(fact_418_inf__right__idem,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( inf_inf_set_a @ ( inf_inf_set_a @ X @ Y ) @ Y )
      = ( inf_inf_set_a @ X @ Y ) ) ).

% inf_right_idem
thf(fact_419_inf_Oright__idem,axiom,
    ! [A3: set_a,B: set_a] :
      ( ( inf_inf_set_a @ ( inf_inf_set_a @ A3 @ B ) @ B )
      = ( inf_inf_set_a @ A3 @ B ) ) ).

% inf.right_idem
thf(fact_420_inf__left__idem,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( inf_inf_set_a @ X @ ( inf_inf_set_a @ X @ Y ) )
      = ( inf_inf_set_a @ X @ Y ) ) ).

% inf_left_idem
thf(fact_421_inf_Oleft__idem,axiom,
    ! [A3: set_a,B: set_a] :
      ( ( inf_inf_set_a @ A3 @ ( inf_inf_set_a @ A3 @ B ) )
      = ( inf_inf_set_a @ A3 @ B ) ) ).

% inf.left_idem
thf(fact_422_inf__idem,axiom,
    ! [X: set_a] :
      ( ( inf_inf_set_a @ X @ X )
      = X ) ).

% inf_idem
thf(fact_423_inf_Oidem,axiom,
    ! [A3: set_a] :
      ( ( inf_inf_set_a @ A3 @ A3 )
      = A3 ) ).

% inf.idem
thf(fact_424_countableI__type,axiom,
    ! [A: set_o] : ( counta5976203206615340371able_o @ A ) ).

% countableI_type
thf(fact_425_countableI__type,axiom,
    ! [A: set_nat] : ( counta1168086296615599829le_nat @ A ) ).

% countableI_type
thf(fact_426_inf__top__left,axiom,
    ! [X: set_Ex3793607809372303086nnreal] :
      ( ( inf_in3368558534146122112nnreal @ top_to7994903218803871134nnreal @ X )
      = X ) ).

% inf_top_left
thf(fact_427_inf__top__left,axiom,
    ! [X: set_complex] :
      ( ( inf_inf_set_complex @ top_top_set_complex @ X )
      = X ) ).

% inf_top_left
thf(fact_428_inf__top__left,axiom,
    ! [X: set_real] :
      ( ( inf_inf_set_real @ top_top_set_real @ X )
      = X ) ).

% inf_top_left
thf(fact_429_inf__top__left,axiom,
    ! [X: set_o] :
      ( ( inf_inf_set_o @ top_top_set_o @ X )
      = X ) ).

% inf_top_left
thf(fact_430_inf__top__left,axiom,
    ! [X: set_nat] :
      ( ( inf_inf_set_nat @ top_top_set_nat @ X )
      = X ) ).

% inf_top_left
thf(fact_431_inf__top__left,axiom,
    ! [X: set_a] :
      ( ( inf_inf_set_a @ top_top_set_a @ X )
      = X ) ).

% inf_top_left
thf(fact_432_inf__top__left,axiom,
    ! [X: set_b] :
      ( ( inf_inf_set_b @ top_top_set_b @ X )
      = X ) ).

% inf_top_left
thf(fact_433_inf__top__left,axiom,
    ! [X: set_real_a] :
      ( ( inf_inf_set_real_a @ top_top_set_real_a @ X )
      = X ) ).

% inf_top_left
thf(fact_434_inf__top__left,axiom,
    ! [X: set_real_b] :
      ( ( inf_inf_set_real_b @ top_top_set_real_b @ X )
      = X ) ).

% inf_top_left
thf(fact_435_inf__top__left,axiom,
    ! [X: set_real_nat] :
      ( ( inf_inf_set_real_nat @ top_top_set_real_nat @ X )
      = X ) ).

% inf_top_left
thf(fact_436_inf__left__commute,axiom,
    ! [X: set_a,Y: set_a,Z: set_a] :
      ( ( inf_inf_set_a @ X @ ( inf_inf_set_a @ Y @ Z ) )
      = ( inf_inf_set_a @ Y @ ( inf_inf_set_a @ X @ Z ) ) ) ).

% inf_left_commute
thf(fact_437_inf_Oleft__commute,axiom,
    ! [B: set_a,A3: set_a,C: set_a] :
      ( ( inf_inf_set_a @ B @ ( inf_inf_set_a @ A3 @ C ) )
      = ( inf_inf_set_a @ A3 @ ( inf_inf_set_a @ B @ C ) ) ) ).

% inf.left_commute
thf(fact_438_inf__commute,axiom,
    ( inf_inf_set_a
    = ( ^ [X4: set_a,Y2: set_a] : ( inf_inf_set_a @ Y2 @ X4 ) ) ) ).

% inf_commute
thf(fact_439_inf_Ocommute,axiom,
    ( inf_inf_set_a
    = ( ^ [A4: set_a,B4: set_a] : ( inf_inf_set_a @ B4 @ A4 ) ) ) ).

% inf.commute
thf(fact_440_inf__assoc,axiom,
    ! [X: set_a,Y: set_a,Z: set_a] :
      ( ( inf_inf_set_a @ ( inf_inf_set_a @ X @ Y ) @ Z )
      = ( inf_inf_set_a @ X @ ( inf_inf_set_a @ Y @ Z ) ) ) ).

% inf_assoc
thf(fact_441_inf_Oassoc,axiom,
    ! [A3: set_a,B: set_a,C: set_a] :
      ( ( inf_inf_set_a @ ( inf_inf_set_a @ A3 @ B ) @ C )
      = ( inf_inf_set_a @ A3 @ ( inf_inf_set_a @ B @ C ) ) ) ).

% inf.assoc
thf(fact_442_inf__sup__aci_I1_J,axiom,
    ( inf_inf_set_a
    = ( ^ [X4: set_a,Y2: set_a] : ( inf_inf_set_a @ Y2 @ X4 ) ) ) ).

% inf_sup_aci(1)
thf(fact_443_inf__sup__aci_I2_J,axiom,
    ! [X: set_a,Y: set_a,Z: set_a] :
      ( ( inf_inf_set_a @ ( inf_inf_set_a @ X @ Y ) @ Z )
      = ( inf_inf_set_a @ X @ ( inf_inf_set_a @ Y @ Z ) ) ) ).

% inf_sup_aci(2)
thf(fact_444_inf__sup__aci_I3_J,axiom,
    ! [X: set_a,Y: set_a,Z: set_a] :
      ( ( inf_inf_set_a @ X @ ( inf_inf_set_a @ Y @ Z ) )
      = ( inf_inf_set_a @ Y @ ( inf_inf_set_a @ X @ Z ) ) ) ).

% inf_sup_aci(3)
thf(fact_445_inf__sup__aci_I4_J,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( inf_inf_set_a @ X @ ( inf_inf_set_a @ X @ Y ) )
      = ( inf_inf_set_a @ X @ Y ) ) ).

% inf_sup_aci(4)
thf(fact_446_measurable__cong,axiom,
    ! [M: sigma_measure_real,F: real > b,G: real > b,M2: sigma_measure_b] :
      ( ! [W: real] :
          ( ( member_real @ W @ ( sigma_space_real @ M ) )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ M2 ) )
        = ( member_real_b @ G @ ( sigma_523072396149930113real_b @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_447_measurable__cong,axiom,
    ! [M: sigma_measure_real,F: real > a,G: real > a,M2: sigma_measure_a] :
      ( ! [W: real] :
          ( ( member_real @ W @ ( sigma_space_real @ M ) )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ M2 ) )
        = ( member_real_a @ G @ ( sigma_523072396149930112real_a @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_448_measurable__cong,axiom,
    ! [M: sigma_measure_real,F: real > nat,G: real > nat,M2: sigma_measure_nat] :
      ( ! [W: real] :
          ( ( member_real @ W @ ( sigma_space_real @ M ) )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M @ M2 ) )
        = ( member_real_nat @ G @ ( sigma_6315060578831106510al_nat @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_449_measurable__cong,axiom,
    ! [M: sigma_measure_a,F: a > complex,G: a > complex,M2: sigma_3077487657436305159omplex] :
      ( ! [W: a] :
          ( ( member_a @ W @ ( sigma_space_a @ M ) )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ M @ M2 ) )
        = ( member_a_complex @ G @ ( sigma_852363994732143452omplex @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_450_measurable__cong,axiom,
    ! [M: sigma_measure_a,F: a > real,G: a > real,M2: sigma_measure_real] :
      ( ! [W: a] :
          ( ( member_a @ W @ ( sigma_space_a @ M ) )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M @ M2 ) )
        = ( member_a_real @ G @ ( sigma_9116425665531756122a_real @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_451_measurable__cong,axiom,
    ! [M: sigma_measure_a,F: a > $o,G: a > $o,M2: sigma_measure_o] :
      ( ! [W: a] :
          ( ( member_a @ W @ ( sigma_space_a @ M ) )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ M2 ) )
        = ( member_a_o @ G @ ( sigma_measurable_a_o @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_452_measurable__cong,axiom,
    ! [M: sigma_measure_a,F: a > nat,G: a > nat,M2: sigma_measure_nat] :
      ( ! [W: a] :
          ( ( member_a @ W @ ( sigma_space_a @ M ) )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M @ M2 ) )
        = ( member_a_nat @ G @ ( sigma_73150082625557118_a_nat @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_453_measurable__cong,axiom,
    ! [M: sigma_measure_a,F: a > a,G: a > a,M2: sigma_measure_a] :
      ( ! [W: a] :
          ( ( member_a @ W @ ( sigma_space_a @ M ) )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_a_a @ F @ ( sigma_measurable_a_a @ M @ M2 ) )
        = ( member_a_a @ G @ ( sigma_measurable_a_a @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_454_measurable__space,axiom,
    ! [F: a > extend8495563244428889912nnreal,M: sigma_measure_a,A: sigma_7234349610311085201nnreal,X: a] :
      ( ( member298456594901751504nnreal @ F @ ( sigma_214952329563889126nnreal @ M @ A ) )
     => ( ( member_a @ X @ ( sigma_space_a @ M ) )
       => ( member7908768830364227535nnreal @ ( F @ X ) @ ( sigma_3147302497200244656nnreal @ A ) ) ) ) ).

% measurable_space
thf(fact_455_measurable__space,axiom,
    ! [F: real > b,M: sigma_measure_real,A: sigma_measure_b,X: real] :
      ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ A ) )
     => ( ( member_real @ X @ ( sigma_space_real @ M ) )
       => ( member_b @ ( F @ X ) @ ( sigma_space_b @ A ) ) ) ) ).

% measurable_space
thf(fact_456_measurable__space,axiom,
    ! [F: real > real,M: sigma_measure_real,A: sigma_measure_real,X: real] :
      ( ( member_real_real @ F @ ( sigma_5267869275261027754l_real @ M @ A ) )
     => ( ( member_real @ X @ ( sigma_space_real @ M ) )
       => ( member_real @ ( F @ X ) @ ( sigma_space_real @ A ) ) ) ) ).

% measurable_space
thf(fact_457_measurable__space,axiom,
    ! [F: real > $o,M: sigma_measure_real,A: sigma_measure_o,X: real] :
      ( ( member_real_o @ F @ ( sigma_3939073009482781210real_o @ M @ A ) )
     => ( ( member_real @ X @ ( sigma_space_real @ M ) )
       => ( member_o @ ( F @ X ) @ ( sigma_space_o @ A ) ) ) ) ).

% measurable_space
thf(fact_458_measurable__space,axiom,
    ! [F: real > extend8495563244428889912nnreal,M: sigma_measure_real,A: sigma_7234349610311085201nnreal,X: real] :
      ( ( member2919562650594848410nnreal @ F @ ( sigma_9017504469962657078nnreal @ M @ A ) )
     => ( ( member_real @ X @ ( sigma_space_real @ M ) )
       => ( member7908768830364227535nnreal @ ( F @ X ) @ ( sigma_3147302497200244656nnreal @ A ) ) ) ) ).

% measurable_space
thf(fact_459_measurable__space,axiom,
    ! [F: nat > a,M: sigma_measure_nat,A: sigma_measure_a,X: nat] :
      ( ( member_nat_a @ F @ ( sigma_4105081583803843548_nat_a @ M @ A ) )
     => ( ( member_nat @ X @ ( sigma_space_nat @ M ) )
       => ( member_a @ ( F @ X ) @ ( sigma_space_a @ A ) ) ) ) ).

% measurable_space
thf(fact_460_measurable__space,axiom,
    ! [F: nat > real,M: sigma_measure_nat,A: sigma_measure_real,X: nat] :
      ( ( member_nat_real @ F @ ( sigma_1747752005702207822t_real @ M @ A ) )
     => ( ( member_nat @ X @ ( sigma_space_nat @ M ) )
       => ( member_real @ ( F @ X ) @ ( sigma_space_real @ A ) ) ) ) ).

% measurable_space
thf(fact_461_measurable__space,axiom,
    ! [F: nat > nat,M: sigma_measure_nat,A: sigma_measure_nat,X: nat] :
      ( ( member_nat_nat @ F @ ( sigma_4350458207664084850at_nat @ M @ A ) )
     => ( ( member_nat @ X @ ( sigma_space_nat @ M ) )
       => ( member_nat @ ( F @ X ) @ ( sigma_space_nat @ A ) ) ) ) ).

% measurable_space
thf(fact_462_measurable__space,axiom,
    ! [F: nat > $o,M: sigma_measure_nat,A: sigma_measure_o,X: nat] :
      ( ( member_nat_o @ F @ ( sigma_5101835498682829686_nat_o @ M @ A ) )
     => ( ( member_nat @ X @ ( sigma_space_nat @ M ) )
       => ( member_o @ ( F @ X ) @ ( sigma_space_o @ A ) ) ) ) ).

% measurable_space
thf(fact_463_measurable__space,axiom,
    ! [F: nat > extend8495563244428889912nnreal,M: sigma_measure_nat,A: sigma_7234349610311085201nnreal,X: nat] :
      ( ( member8283130129095025342nnreal @ F @ ( sigma_6306161311797543642nnreal @ M @ A ) )
     => ( ( member_nat @ X @ ( sigma_space_nat @ M ) )
       => ( member7908768830364227535nnreal @ ( F @ X ) @ ( sigma_3147302497200244656nnreal @ A ) ) ) ) ).

% measurable_space
thf(fact_464_measurable__cong__simp,axiom,
    ! [M: sigma_measure_real,N: sigma_measure_real,M2: sigma_measure_b,N2: sigma_measure_b,F: real > b,G: real > b] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: real] :
              ( ( member_real @ W @ ( sigma_space_real @ M ) )
             => ( ( F @ W )
                = ( G @ W ) ) )
         => ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ M2 ) )
            = ( member_real_b @ G @ ( sigma_523072396149930113real_b @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_465_measurable__cong__simp,axiom,
    ! [M: sigma_measure_real,N: sigma_measure_real,M2: sigma_measure_a,N2: sigma_measure_a,F: real > a,G: real > a] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: real] :
              ( ( member_real @ W @ ( sigma_space_real @ M ) )
             => ( ( F @ W )
                = ( G @ W ) ) )
         => ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ M2 ) )
            = ( member_real_a @ G @ ( sigma_523072396149930112real_a @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_466_measurable__cong__simp,axiom,
    ! [M: sigma_measure_real,N: sigma_measure_real,M2: sigma_measure_nat,N2: sigma_measure_nat,F: real > nat,G: real > nat] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: real] :
              ( ( member_real @ W @ ( sigma_space_real @ M ) )
             => ( ( F @ W )
                = ( G @ W ) ) )
         => ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M @ M2 ) )
            = ( member_real_nat @ G @ ( sigma_6315060578831106510al_nat @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_467_measurable__cong__simp,axiom,
    ! [M: sigma_measure_a,N: sigma_measure_a,M2: sigma_3077487657436305159omplex,N2: sigma_3077487657436305159omplex,F: a > complex,G: a > complex] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: a] :
              ( ( member_a @ W @ ( sigma_space_a @ M ) )
             => ( ( F @ W )
                = ( G @ W ) ) )
         => ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ M @ M2 ) )
            = ( member_a_complex @ G @ ( sigma_852363994732143452omplex @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_468_measurable__cong__simp,axiom,
    ! [M: sigma_measure_a,N: sigma_measure_a,M2: sigma_measure_real,N2: sigma_measure_real,F: a > real,G: a > real] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: a] :
              ( ( member_a @ W @ ( sigma_space_a @ M ) )
             => ( ( F @ W )
                = ( G @ W ) ) )
         => ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M @ M2 ) )
            = ( member_a_real @ G @ ( sigma_9116425665531756122a_real @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_469_measurable__cong__simp,axiom,
    ! [M: sigma_measure_a,N: sigma_measure_a,M2: sigma_measure_o,N2: sigma_measure_o,F: a > $o,G: a > $o] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: a] :
              ( ( member_a @ W @ ( sigma_space_a @ M ) )
             => ( ( F @ W )
                = ( G @ W ) ) )
         => ( ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ M2 ) )
            = ( member_a_o @ G @ ( sigma_measurable_a_o @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_470_measurable__cong__simp,axiom,
    ! [M: sigma_measure_a,N: sigma_measure_a,M2: sigma_measure_nat,N2: sigma_measure_nat,F: a > nat,G: a > nat] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: a] :
              ( ( member_a @ W @ ( sigma_space_a @ M ) )
             => ( ( F @ W )
                = ( G @ W ) ) )
         => ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M @ M2 ) )
            = ( member_a_nat @ G @ ( sigma_73150082625557118_a_nat @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_471_measurable__cong__simp,axiom,
    ! [M: sigma_measure_a,N: sigma_measure_a,M2: sigma_measure_a,N2: sigma_measure_a,F: a > a,G: a > a] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: a] :
              ( ( member_a @ W @ ( sigma_space_a @ M ) )
             => ( ( F @ W )
                = ( G @ W ) ) )
         => ( ( member_a_a @ F @ ( sigma_measurable_a_a @ M @ M2 ) )
            = ( member_a_a @ G @ ( sigma_measurable_a_a @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_472_space__restrict__space,axiom,
    ! [M: sigma_measure_real,Omega: set_real] :
      ( ( sigma_space_real @ ( sigma_5414646170262037096e_real @ M @ Omega ) )
      = ( inf_inf_set_real @ Omega @ ( sigma_space_real @ M ) ) ) ).

% space_restrict_space
thf(fact_473_space__restrict__space,axiom,
    ! [M: sigma_measure_nat,Omega: set_nat] :
      ( ( sigma_space_nat @ ( sigma_744083341818469772ce_nat @ M @ Omega ) )
      = ( inf_inf_set_nat @ Omega @ ( sigma_space_nat @ M ) ) ) ).

% space_restrict_space
thf(fact_474_space__restrict__space,axiom,
    ! [M: sigma_measure_o,Omega: set_o] :
      ( ( sigma_space_o @ ( sigma_8520893325391096540pace_o @ M @ Omega ) )
      = ( inf_inf_set_o @ Omega @ ( sigma_space_o @ M ) ) ) ).

% space_restrict_space
thf(fact_475_space__restrict__space,axiom,
    ! [M: sigma_7234349610311085201nnreal,Omega: set_Ex3793607809372303086nnreal] :
      ( ( sigma_3147302497200244656nnreal @ ( sigma_4884701650823297268nnreal @ M @ Omega ) )
      = ( inf_in3368558534146122112nnreal @ Omega @ ( sigma_3147302497200244656nnreal @ M ) ) ) ).

% space_restrict_space
thf(fact_476_space__restrict__space,axiom,
    ! [M: sigma_measure_a,Omega: set_a] :
      ( ( sigma_space_a @ ( sigma_8692839461743104066pace_a @ M @ Omega ) )
      = ( inf_inf_set_a @ Omega @ ( sigma_space_a @ M ) ) ) ).

% space_restrict_space
thf(fact_477__092_060open_062P_A_092_060in_062_Aspace_Areal__borel_A_092_060rightarrow_062_Arange_AP_A_092_060Longrightarrow_062_AP_A_092_060in_062_Areal__borel_A_092_060rightarrow_062_092_060_094sub_062M_Arestrict__space_A_Icount__space_AI_J_A_Irange_AP_J_092_060close_062,axiom,
    ( ( member_real_a @ p
      @ ( pi_real_a @ ( sigma_space_real @ borel_5078946678739801102l_real )
        @ ^ [Uu: real] : ( image_real_a @ p @ top_top_set_real ) ) )
   => ( member_real_a @ p @ ( sigma_523072396149930112real_a @ borel_5078946678739801102l_real @ ( sigma_8692839461743104066pace_a @ ( sigma_count_space_a @ i ) @ ( image_real_a @ p @ top_top_set_real ) ) ) ) ) ).

% \<open>P \<in> space real_borel \<rightarrow> range P \<Longrightarrow> P \<in> real_borel \<rightarrow>\<^sub>M restrict_space (count_space I) (range P)\<close>
thf(fact_478_measurable__top,axiom,
    ! [M: sigma_measure_a] : ( member_a_o @ top_top_a_o @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% measurable_top
thf(fact_479_is__borel__def,axiom,
    ( borel_8160143138670184560omplex
    = ( ^ [F2: a > complex,M3: sigma_measure_a] : ( member_a_complex @ F2 @ ( sigma_852363994732143452omplex @ M3 @ borel_1392132677378845456omplex ) ) ) ) ).

% is_borel_def
thf(fact_480_is__borel__def,axiom,
    ( borel_4993665998515044718a_real
    = ( ^ [F2: a > real,M3: sigma_measure_a] : ( member_a_real @ F2 @ ( sigma_9116425665531756122a_real @ M3 @ borel_5078946678739801102l_real ) ) ) ) ).

% is_borel_def
thf(fact_481_is__borel__def,axiom,
    ( borel_4557508243417129402al_nat
    = ( ^ [F2: real > nat,M3: sigma_measure_real] : ( member_real_nat @ F2 @ ( sigma_6315060578831106510al_nat @ M3 @ borel_8449730974584783410el_nat ) ) ) ) ).

% is_borel_def
thf(fact_482_is__borel__def,axiom,
    ( borel_is_borel_a_nat
    = ( ^ [F2: a > nat,M3: sigma_measure_a] : ( member_a_nat @ F2 @ ( sigma_73150082625557118_a_nat @ M3 @ borel_8449730974584783410el_nat ) ) ) ) ).

% is_borel_def
thf(fact_483_is__borel__def,axiom,
    ( borel_is_borel_a_o
    = ( ^ [F2: a > $o,M3: sigma_measure_a] : ( member_a_o @ F2 @ ( sigma_measurable_a_o @ M3 @ borel_5500255247093592246orel_o ) ) ) ) ).

% is_borel_def
thf(fact_484_restrict__count__space,axiom,
    ! [B2: set_real,A: set_real] :
      ( ( sigma_5414646170262037096e_real @ ( sigma_8508918144308765139e_real @ B2 ) @ A )
      = ( sigma_8508918144308765139e_real @ ( inf_inf_set_real @ A @ B2 ) ) ) ).

% restrict_count_space
thf(fact_485_restrict__count__space,axiom,
    ! [B2: set_o,A: set_o] :
      ( ( sigma_8520893325391096540pace_o @ ( sigma_count_space_o @ B2 ) @ A )
      = ( sigma_count_space_o @ ( inf_inf_set_o @ A @ B2 ) ) ) ).

% restrict_count_space
thf(fact_486_restrict__count__space,axiom,
    ! [B2: set_nat,A: set_nat] :
      ( ( sigma_744083341818469772ce_nat @ ( sigma_7685844798829912695ce_nat @ B2 ) @ A )
      = ( sigma_7685844798829912695ce_nat @ ( inf_inf_set_nat @ A @ B2 ) ) ) ).

% restrict_count_space
thf(fact_487_restrict__count__space,axiom,
    ! [B2: set_Ex3793607809372303086nnreal,A: set_Ex3793607809372303086nnreal] :
      ( ( sigma_4884701650823297268nnreal @ ( sigma_7204664791115113951nnreal @ B2 ) @ A )
      = ( sigma_7204664791115113951nnreal @ ( inf_in3368558534146122112nnreal @ A @ B2 ) ) ) ).

% restrict_count_space
thf(fact_488_restrict__count__space,axiom,
    ! [B2: set_complex,A: set_complex] :
      ( ( sigma_216592511309337194omplex @ ( sigma_3977070789342921045omplex @ B2 ) @ A )
      = ( sigma_3977070789342921045omplex @ ( inf_inf_set_complex @ A @ B2 ) ) ) ).

% restrict_count_space
thf(fact_489_restrict__count__space,axiom,
    ! [B2: set_b,A: set_b] :
      ( ( sigma_8692839461743104067pace_b @ ( sigma_count_space_b @ B2 ) @ A )
      = ( sigma_count_space_b @ ( inf_inf_set_b @ A @ B2 ) ) ) ).

% restrict_count_space
thf(fact_490_restrict__count__space,axiom,
    ! [B2: set_a,A: set_a] :
      ( ( sigma_8692839461743104066pace_a @ ( sigma_count_space_a @ B2 ) @ A )
      = ( sigma_count_space_a @ ( inf_inf_set_a @ A @ B2 ) ) ) ).

% restrict_count_space
thf(fact_491_top__empty__eq,axiom,
    ( top_to5118619752887738471real_o
    = ( ^ [X4: extend8495563244428889912nnreal] : ( member7908768830364227535nnreal @ X4 @ top_to7994903218803871134nnreal ) ) ) ).

% top_empty_eq
thf(fact_492_top__empty__eq,axiom,
    ( top_top_complex_o
    = ( ^ [X4: complex] : ( member_complex @ X4 @ top_top_set_complex ) ) ) ).

% top_empty_eq
thf(fact_493_top__empty__eq,axiom,
    ( top_top_real_o
    = ( ^ [X4: real] : ( member_real @ X4 @ top_top_set_real ) ) ) ).

% top_empty_eq
thf(fact_494_top__empty__eq,axiom,
    ( top_top_o_o
    = ( ^ [X4: $o] : ( member_o @ X4 @ top_top_set_o ) ) ) ).

% top_empty_eq
thf(fact_495_top__empty__eq,axiom,
    ( top_top_nat_o
    = ( ^ [X4: nat] : ( member_nat @ X4 @ top_top_set_nat ) ) ) ).

% top_empty_eq
thf(fact_496_top__empty__eq,axiom,
    ( top_top_a_o
    = ( ^ [X4: a] : ( member_a @ X4 @ top_top_set_a ) ) ) ).

% top_empty_eq
thf(fact_497_top__empty__eq,axiom,
    ( top_top_b_o
    = ( ^ [X4: b] : ( member_b @ X4 @ top_top_set_b ) ) ) ).

% top_empty_eq
thf(fact_498_top__empty__eq,axiom,
    ( top_top_a_complex_o
    = ( ^ [X4: a > complex] : ( member_a_complex @ X4 @ top_to8623610131301960013omplex ) ) ) ).

% top_empty_eq
thf(fact_499_top__empty__eq,axiom,
    ( top_top_a_real_o
    = ( ^ [X4: a > real] : ( member_a_real @ X4 @ top_top_set_a_real ) ) ) ).

% top_empty_eq
thf(fact_500_top__empty__eq,axiom,
    ( top_top_a_o_o
    = ( ^ [X4: a > $o] : ( member_a_o @ X4 @ top_top_set_a_o ) ) ) ).

% top_empty_eq
thf(fact_501_real_Ospace__UNIV,axiom,
    ( ( sigma_space_real @ borel_5078946678739801102l_real )
    = top_top_set_real ) ).

% real.space_UNIV
thf(fact_502_boolean__algebra_Oconj__one__right,axiom,
    ! [X: set_Ex3793607809372303086nnreal] :
      ( ( inf_in3368558534146122112nnreal @ X @ top_to7994903218803871134nnreal )
      = X ) ).

% boolean_algebra.conj_one_right
thf(fact_503_boolean__algebra_Oconj__one__right,axiom,
    ! [X: set_complex] :
      ( ( inf_inf_set_complex @ X @ top_top_set_complex )
      = X ) ).

% boolean_algebra.conj_one_right
thf(fact_504_boolean__algebra_Oconj__one__right,axiom,
    ! [X: set_real] :
      ( ( inf_inf_set_real @ X @ top_top_set_real )
      = X ) ).

% boolean_algebra.conj_one_right
thf(fact_505_boolean__algebra_Oconj__one__right,axiom,
    ! [X: set_o] :
      ( ( inf_inf_set_o @ X @ top_top_set_o )
      = X ) ).

% boolean_algebra.conj_one_right
thf(fact_506_boolean__algebra_Oconj__one__right,axiom,
    ! [X: set_nat] :
      ( ( inf_inf_set_nat @ X @ top_top_set_nat )
      = X ) ).

% boolean_algebra.conj_one_right
thf(fact_507_boolean__algebra_Oconj__one__right,axiom,
    ! [X: set_a] :
      ( ( inf_inf_set_a @ X @ top_top_set_a )
      = X ) ).

% boolean_algebra.conj_one_right
thf(fact_508_boolean__algebra_Oconj__one__right,axiom,
    ! [X: set_b] :
      ( ( inf_inf_set_b @ X @ top_top_set_b )
      = X ) ).

% boolean_algebra.conj_one_right
thf(fact_509_boolean__algebra_Oconj__one__right,axiom,
    ! [X: set_real_a] :
      ( ( inf_inf_set_real_a @ X @ top_top_set_real_a )
      = X ) ).

% boolean_algebra.conj_one_right
thf(fact_510_boolean__algebra_Oconj__one__right,axiom,
    ! [X: set_real_b] :
      ( ( inf_inf_set_real_b @ X @ top_top_set_real_b )
      = X ) ).

% boolean_algebra.conj_one_right
thf(fact_511_boolean__algebra_Oconj__one__right,axiom,
    ! [X: set_real_nat] :
      ( ( inf_inf_set_real_nat @ X @ top_top_set_real_nat )
      = X ) ).

% boolean_algebra.conj_one_right
thf(fact_512_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > nat,X5: quasi_borel_nat,R: real] :
      ( ( member_real_nat @ Alpha @ ( qbs_Mx_nat @ X5 ) )
     => ( member_nat @ ( Alpha @ R ) @ ( qbs_space_nat @ X5 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_513_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > a,X5: quasi_borel_a,R: real] :
      ( ( member_real_a @ Alpha @ ( qbs_Mx_a @ X5 ) )
     => ( member_a @ ( Alpha @ R ) @ ( qbs_space_a @ X5 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_514_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > b,X5: quasi_borel_b,R: real] :
      ( ( member_real_b @ Alpha @ ( qbs_Mx_b @ X5 ) )
     => ( member_b @ ( Alpha @ R ) @ ( qbs_space_b @ X5 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_515_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > real > nat,X5: quasi_borel_real_nat,R: real] :
      ( ( member_real_real_nat @ Alpha @ ( qbs_Mx_real_nat @ X5 ) )
     => ( member_real_nat @ ( Alpha @ R ) @ ( qbs_space_real_nat @ X5 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_516_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > real > b,X5: quasi_borel_real_b,R: real] :
      ( ( member_real_real_b @ Alpha @ ( qbs_Mx_real_b @ X5 ) )
     => ( member_real_b @ ( Alpha @ R ) @ ( qbs_space_real_b @ X5 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_517_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > real > a,X5: quasi_borel_real_a,R: real] :
      ( ( member_real_real_a @ Alpha @ ( qbs_Mx_real_a @ X5 ) )
     => ( member_real_a @ ( Alpha @ R ) @ ( qbs_space_real_a @ X5 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_518_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > a > complex,X5: quasi_4365677710772687427omplex,R: real] :
      ( ( member8749487273670996305omplex @ Alpha @ ( qbs_Mx_a_complex @ X5 ) )
     => ( member_a_complex @ ( Alpha @ R ) @ ( qbs_space_a_complex @ X5 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_519_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > a > real,X5: quasi_borel_a_real,R: real] :
      ( ( member_real_a_real @ Alpha @ ( qbs_Mx_a_real @ X5 ) )
     => ( member_a_real @ ( Alpha @ R ) @ ( qbs_space_a_real @ X5 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_520_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > a > $o,X5: quasi_borel_a_o,R: real] :
      ( ( member_real_a_o2 @ Alpha @ ( qbs_Mx_a_o @ X5 ) )
     => ( member_a_o @ ( Alpha @ R ) @ ( qbs_space_a_o @ X5 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_521_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > a > nat,X5: quasi_borel_a_nat,R: real] :
      ( ( member_real_a_nat @ Alpha @ ( qbs_Mx_a_nat @ X5 ) )
     => ( member_a_nat @ ( Alpha @ R ) @ ( qbs_space_a_nat @ X5 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_522_uncountable__UNIV__real,axiom,
    ~ ( counta7319604579010473777e_real @ top_top_set_real ) ).

% uncountable_UNIV_real
thf(fact_523_image__ident,axiom,
    ! [Y3: set_real] :
      ( ( image_real_real
        @ ^ [X4: real] : X4
        @ Y3 )
      = Y3 ) ).

% image_ident
thf(fact_524_image__ident,axiom,
    ! [Y3: set_a] :
      ( ( image_a_a
        @ ^ [X4: a] : X4
        @ Y3 )
      = Y3 ) ).

% image_ident
thf(fact_525_measurable__count__space__eq1,axiom,
    ! [F: a > extend8495563244428889912nnreal,A: set_a,M: sigma_7234349610311085201nnreal] :
      ( ( member298456594901751504nnreal @ F @ ( sigma_214952329563889126nnreal @ ( sigma_count_space_a @ A ) @ M ) )
      = ( member298456594901751504nnreal @ F
        @ ( pi_a_E4973063519588424107nnreal @ A
          @ ^ [Uu: a] : ( sigma_3147302497200244656nnreal @ M ) ) ) ) ).

% measurable_count_space_eq1
thf(fact_526_measurable__count__space__eq1,axiom,
    ! [F: a > complex,A: set_a,M: sigma_3077487657436305159omplex] :
      ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ ( sigma_count_space_a @ A ) @ M ) )
      = ( member_a_complex @ F
        @ ( pi_a_complex @ A
          @ ^ [Uu: a] : ( sigma_space_complex @ M ) ) ) ) ).

% measurable_count_space_eq1
thf(fact_527_measurable__count__space__eq1,axiom,
    ! [F: a > real,A: set_a,M: sigma_measure_real] :
      ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ ( sigma_count_space_a @ A ) @ M ) )
      = ( member_a_real @ F
        @ ( pi_a_real @ A
          @ ^ [Uu: a] : ( sigma_space_real @ M ) ) ) ) ).

% measurable_count_space_eq1
thf(fact_528_measurable__count__space__eq1,axiom,
    ! [F: a > $o,A: set_a,M: sigma_measure_o] :
      ( ( member_a_o @ F @ ( sigma_measurable_a_o @ ( sigma_count_space_a @ A ) @ M ) )
      = ( member_a_o @ F
        @ ( pi_a_o @ A
          @ ^ [Uu: a] : ( sigma_space_o @ M ) ) ) ) ).

% measurable_count_space_eq1
thf(fact_529_measurable__count__space__eq1,axiom,
    ! [F: a > nat,A: set_a,M: sigma_measure_nat] :
      ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ ( sigma_count_space_a @ A ) @ M ) )
      = ( member_a_nat @ F
        @ ( pi_a_nat @ A
          @ ^ [Uu: a] : ( sigma_space_nat @ M ) ) ) ) ).

% measurable_count_space_eq1
thf(fact_530_measurable__count__space__eq1,axiom,
    ! [F: a > a,A: set_a,M: sigma_measure_a] :
      ( ( member_a_a @ F @ ( sigma_measurable_a_a @ ( sigma_count_space_a @ A ) @ M ) )
      = ( member_a_a @ F
        @ ( pi_a_a @ A
          @ ^ [Uu: a] : ( sigma_space_a @ M ) ) ) ) ).

% measurable_count_space_eq1
thf(fact_531_measurable__count__space__eq1,axiom,
    ! [F: real > b,A: set_real,M: sigma_measure_b] :
      ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ ( sigma_8508918144308765139e_real @ A ) @ M ) )
      = ( member_real_b @ F
        @ ( pi_real_b @ A
          @ ^ [Uu: real] : ( sigma_space_b @ M ) ) ) ) ).

% measurable_count_space_eq1
thf(fact_532_measurable__count__space__eq1,axiom,
    ! [F: real > real,A: set_real,M: sigma_measure_real] :
      ( ( member_real_real @ F @ ( sigma_5267869275261027754l_real @ ( sigma_8508918144308765139e_real @ A ) @ M ) )
      = ( member_real_real @ F
        @ ( pi_real_real @ A
          @ ^ [Uu: real] : ( sigma_space_real @ M ) ) ) ) ).

% measurable_count_space_eq1
thf(fact_533_measurable__count__space__eq1,axiom,
    ! [F: real > $o,A: set_real,M: sigma_measure_o] :
      ( ( member_real_o @ F @ ( sigma_3939073009482781210real_o @ ( sigma_8508918144308765139e_real @ A ) @ M ) )
      = ( member_real_o @ F
        @ ( pi_real_o @ A
          @ ^ [Uu: real] : ( sigma_space_o @ M ) ) ) ) ).

% measurable_count_space_eq1
thf(fact_534_measurable__count__space__eq1,axiom,
    ! [F: real > extend8495563244428889912nnreal,A: set_real,M: sigma_7234349610311085201nnreal] :
      ( ( member2919562650594848410nnreal @ F @ ( sigma_9017504469962657078nnreal @ ( sigma_8508918144308765139e_real @ A ) @ M ) )
      = ( member2919562650594848410nnreal @ F
        @ ( pi_rea7198910874028739761nnreal @ A
          @ ^ [Uu: real] : ( sigma_3147302497200244656nnreal @ M ) ) ) ) ).

% measurable_count_space_eq1
thf(fact_535_pred__intros__logic_I12_J,axiom,
    ! [F: a > nat,A: a > set_nat,M: sigma_measure_a,B2: a > set_nat] :
      ( ( member_a_o
        @ ^ [X4: a] : ( member_nat @ ( F @ X4 ) @ ( A @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o
          @ ^ [X4: a] : ( member_nat @ ( F @ X4 ) @ ( B2 @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] : ( member_nat @ ( F @ X4 ) @ ( inf_inf_set_nat @ ( A @ X4 ) @ ( B2 @ X4 ) ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(12)
thf(fact_536_pred__intros__logic_I12_J,axiom,
    ! [F: a > real > nat,A: a > set_real_nat,M: sigma_measure_a,B2: a > set_real_nat] :
      ( ( member_a_o
        @ ^ [X4: a] : ( member_real_nat @ ( F @ X4 ) @ ( A @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o
          @ ^ [X4: a] : ( member_real_nat @ ( F @ X4 ) @ ( B2 @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] : ( member_real_nat @ ( F @ X4 ) @ ( inf_inf_set_real_nat @ ( A @ X4 ) @ ( B2 @ X4 ) ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(12)
thf(fact_537_pred__intros__logic_I12_J,axiom,
    ! [F: a > real > b,A: a > set_real_b,M: sigma_measure_a,B2: a > set_real_b] :
      ( ( member_a_o
        @ ^ [X4: a] : ( member_real_b @ ( F @ X4 ) @ ( A @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o
          @ ^ [X4: a] : ( member_real_b @ ( F @ X4 ) @ ( B2 @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] : ( member_real_b @ ( F @ X4 ) @ ( inf_inf_set_real_b @ ( A @ X4 ) @ ( B2 @ X4 ) ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(12)
thf(fact_538_pred__intros__logic_I12_J,axiom,
    ! [F: a > real > a,A: a > set_real_a,M: sigma_measure_a,B2: a > set_real_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( member_real_a @ ( F @ X4 ) @ ( A @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o
          @ ^ [X4: a] : ( member_real_a @ ( F @ X4 ) @ ( B2 @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] : ( member_real_a @ ( F @ X4 ) @ ( inf_inf_set_real_a @ ( A @ X4 ) @ ( B2 @ X4 ) ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(12)
thf(fact_539_pred__intros__logic_I12_J,axiom,
    ! [F: a > a > complex,A: a > set_a_complex,M: sigma_measure_a,B2: a > set_a_complex] :
      ( ( member_a_o
        @ ^ [X4: a] : ( member_a_complex @ ( F @ X4 ) @ ( A @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o
          @ ^ [X4: a] : ( member_a_complex @ ( F @ X4 ) @ ( B2 @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] : ( member_a_complex @ ( F @ X4 ) @ ( inf_in3709910040937683179omplex @ ( A @ X4 ) @ ( B2 @ X4 ) ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(12)
thf(fact_540_pred__intros__logic_I12_J,axiom,
    ! [F: a > a > real,A: a > set_a_real,M: sigma_measure_a,B2: a > set_a_real] :
      ( ( member_a_o
        @ ^ [X4: a] : ( member_a_real @ ( F @ X4 ) @ ( A @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o
          @ ^ [X4: a] : ( member_a_real @ ( F @ X4 ) @ ( B2 @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] : ( member_a_real @ ( F @ X4 ) @ ( inf_inf_set_a_real @ ( A @ X4 ) @ ( B2 @ X4 ) ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(12)
thf(fact_541_pred__intros__logic_I12_J,axiom,
    ! [F: a > a > $o,A: a > set_a_o,M: sigma_measure_a,B2: a > set_a_o] :
      ( ( member_a_o
        @ ^ [X4: a] : ( member_a_o @ ( F @ X4 ) @ ( A @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o
          @ ^ [X4: a] : ( member_a_o @ ( F @ X4 ) @ ( B2 @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] : ( member_a_o @ ( F @ X4 ) @ ( inf_inf_set_a_o @ ( A @ X4 ) @ ( B2 @ X4 ) ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(12)
thf(fact_542_pred__intros__logic_I12_J,axiom,
    ! [F: a > a > nat,A: a > set_a_nat,M: sigma_measure_a,B2: a > set_a_nat] :
      ( ( member_a_o
        @ ^ [X4: a] : ( member_a_nat @ ( F @ X4 ) @ ( A @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o
          @ ^ [X4: a] : ( member_a_nat @ ( F @ X4 ) @ ( B2 @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] : ( member_a_nat @ ( F @ X4 ) @ ( inf_inf_set_a_nat @ ( A @ X4 ) @ ( B2 @ X4 ) ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(12)
thf(fact_543_pred__intros__logic_I12_J,axiom,
    ! [F: a > a > a,A: a > set_a_a,M: sigma_measure_a,B2: a > set_a_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( member_a_a @ ( F @ X4 ) @ ( A @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o
          @ ^ [X4: a] : ( member_a_a @ ( F @ X4 ) @ ( B2 @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] : ( member_a_a @ ( F @ X4 ) @ ( inf_inf_set_a_a @ ( A @ X4 ) @ ( B2 @ X4 ) ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(12)
thf(fact_544_pred__intros__logic_I12_J,axiom,
    ! [F: a > a,A: a > set_a,M: sigma_measure_a,B2: a > set_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( member_a @ ( F @ X4 ) @ ( A @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o
          @ ^ [X4: a] : ( member_a @ ( F @ X4 ) @ ( B2 @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] : ( member_a @ ( F @ X4 ) @ ( inf_inf_set_a @ ( A @ X4 ) @ ( B2 @ X4 ) ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(12)
thf(fact_545_pred__intros__logic_I7_J,axiom,
    ! [F: a > extend8495563244428889912nnreal,M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : ( member7908768830364227535nnreal @ ( F @ X4 ) @ top_to7994903218803871134nnreal )
      @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(7)
thf(fact_546_pred__intros__logic_I7_J,axiom,
    ! [F: a > complex,M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : ( member_complex @ ( F @ X4 ) @ top_top_set_complex )
      @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(7)
thf(fact_547_pred__intros__logic_I7_J,axiom,
    ! [F: a > real,M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : ( member_real @ ( F @ X4 ) @ top_top_set_real )
      @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(7)
thf(fact_548_pred__intros__logic_I7_J,axiom,
    ! [F: a > $o,M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : ( member_o @ ( F @ X4 ) @ top_top_set_o )
      @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(7)
thf(fact_549_pred__intros__logic_I7_J,axiom,
    ! [F: a > nat,M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : ( member_nat @ ( F @ X4 ) @ top_top_set_nat )
      @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(7)
thf(fact_550_pred__intros__logic_I7_J,axiom,
    ! [F: a > a,M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : ( member_a @ ( F @ X4 ) @ top_top_set_a )
      @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(7)
thf(fact_551_pred__intros__logic_I7_J,axiom,
    ! [F: a > b,M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : ( member_b @ ( F @ X4 ) @ top_top_set_b )
      @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(7)
thf(fact_552_pred__intros__logic_I7_J,axiom,
    ! [F: a > a > complex,M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : ( member_a_complex @ ( F @ X4 ) @ top_to8623610131301960013omplex )
      @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(7)
thf(fact_553_pred__intros__logic_I7_J,axiom,
    ! [F: a > a > real,M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : ( member_a_real @ ( F @ X4 ) @ top_top_set_a_real )
      @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(7)
thf(fact_554_pred__intros__logic_I7_J,axiom,
    ! [F: a > a > $o,M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : ( member_a_o @ ( F @ X4 ) @ top_top_set_a_o )
      @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(7)
thf(fact_555_pred__intros__logic_I1_J,axiom,
    ! [M: sigma_measure_real] :
      ( member_real_o
      @ ^ [X4: real] : ( member_real @ X4 @ ( sigma_space_real @ M ) )
      @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(1)
thf(fact_556_pred__intros__logic_I1_J,axiom,
    ! [M: sigma_measure_nat] :
      ( member_nat_o
      @ ^ [X4: nat] : ( member_nat @ X4 @ ( sigma_space_nat @ M ) )
      @ ( sigma_5101835498682829686_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(1)
thf(fact_557_pred__intros__logic_I1_J,axiom,
    ! [M: sigma_measure_o] :
      ( member_o_o
      @ ^ [X4: $o] : ( member_o @ X4 @ ( sigma_space_o @ M ) )
      @ ( sigma_measurable_o_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(1)
thf(fact_558_pred__intros__logic_I1_J,axiom,
    ! [M: sigma_7234349610311085201nnreal] :
      ( member8095236870201115968real_o
      @ ^ [X4: extend8495563244428889912nnreal] : ( member7908768830364227535nnreal @ X4 @ ( sigma_3147302497200244656nnreal @ M ) )
      @ ( sigma_6279906219187228174real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(1)
thf(fact_559_pred__intros__logic_I1_J,axiom,
    ! [M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : ( member_a @ X4 @ ( sigma_space_a @ M ) )
      @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(1)
thf(fact_560_pred__intros__logic_I1_J,axiom,
    ! [M: sigma_6586288717683155060al_nat] :
      ( member_real_nat_o
      @ ^ [X4: real > nat] : ( member_real_nat @ X4 @ ( sigma_space_real_nat @ M ) )
      @ ( sigma_4110928884538380267_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(1)
thf(fact_561_pred__intros__logic_I1_J,axiom,
    ! [M: sigma_measure_real_b] :
      ( member_real_b_o
      @ ^ [X4: real > b] : ( member_real_b @ X4 @ ( sigma_space_real_b @ M ) )
      @ ( sigma_7338419842690513246al_b_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(1)
thf(fact_562_pred__intros__logic_I1_J,axiom,
    ! [M: sigma_measure_real_a] :
      ( member_real_a_o
      @ ^ [X4: real > a] : ( member_real_a @ X4 @ ( sigma_space_real_a @ M ) )
      @ ( sigma_902503387808413471al_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(1)
thf(fact_563_pred__intros__logic_I1_J,axiom,
    ! [M: sigma_2418697800065292186omplex] :
      ( member_a_complex_o
      @ ^ [X4: a > complex] : ( member_a_complex @ X4 @ ( sigma_2448487161356845349omplex @ M ) )
      @ ( sigma_2293258167702796171plex_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(1)
thf(fact_564_pred__intros__logic_I1_J,axiom,
    ! [M: sigma_measure_a_real] :
      ( member_a_real_o
      @ ^ [X4: a > real] : ( member_a_real @ X4 @ ( sigma_space_a_real @ M ) )
      @ ( sigma_9085598459323199629real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% pred_intros_logic(1)
thf(fact_565_inf__set__def,axiom,
    ( inf_inf_set_real_nat
    = ( ^ [A2: set_real_nat,B3: set_real_nat] :
          ( collect_real_nat
          @ ( inf_inf_real_nat_o
            @ ^ [X4: real > nat] : ( member_real_nat @ X4 @ A2 )
            @ ^ [X4: real > nat] : ( member_real_nat @ X4 @ B3 ) ) ) ) ) ).

% inf_set_def
thf(fact_566_inf__set__def,axiom,
    ( inf_inf_set_real_b
    = ( ^ [A2: set_real_b,B3: set_real_b] :
          ( collect_real_b
          @ ( inf_inf_real_b_o
            @ ^ [X4: real > b] : ( member_real_b @ X4 @ A2 )
            @ ^ [X4: real > b] : ( member_real_b @ X4 @ B3 ) ) ) ) ) ).

% inf_set_def
thf(fact_567_inf__set__def,axiom,
    ( inf_inf_set_real_a
    = ( ^ [A2: set_real_a,B3: set_real_a] :
          ( collect_real_a
          @ ( inf_inf_real_a_o
            @ ^ [X4: real > a] : ( member_real_a @ X4 @ A2 )
            @ ^ [X4: real > a] : ( member_real_a @ X4 @ B3 ) ) ) ) ) ).

% inf_set_def
thf(fact_568_inf__set__def,axiom,
    ( inf_in3709910040937683179omplex
    = ( ^ [A2: set_a_complex,B3: set_a_complex] :
          ( collect_a_complex
          @ ( inf_inf_a_complex_o
            @ ^ [X4: a > complex] : ( member_a_complex @ X4 @ A2 )
            @ ^ [X4: a > complex] : ( member_a_complex @ X4 @ B3 ) ) ) ) ) ).

% inf_set_def
thf(fact_569_inf__set__def,axiom,
    ( inf_inf_set_a_real
    = ( ^ [A2: set_a_real,B3: set_a_real] :
          ( collect_a_real
          @ ( inf_inf_a_real_o
            @ ^ [X4: a > real] : ( member_a_real @ X4 @ A2 )
            @ ^ [X4: a > real] : ( member_a_real @ X4 @ B3 ) ) ) ) ) ).

% inf_set_def
thf(fact_570_inf__set__def,axiom,
    ( inf_inf_set_a_o
    = ( ^ [A2: set_a_o,B3: set_a_o] :
          ( collect_a_o
          @ ( inf_inf_a_o_o
            @ ^ [X4: a > $o] : ( member_a_o @ X4 @ A2 )
            @ ^ [X4: a > $o] : ( member_a_o @ X4 @ B3 ) ) ) ) ) ).

% inf_set_def
thf(fact_571_inf__set__def,axiom,
    ( inf_inf_set_a_nat
    = ( ^ [A2: set_a_nat,B3: set_a_nat] :
          ( collect_a_nat
          @ ( inf_inf_a_nat_o
            @ ^ [X4: a > nat] : ( member_a_nat @ X4 @ A2 )
            @ ^ [X4: a > nat] : ( member_a_nat @ X4 @ B3 ) ) ) ) ) ).

% inf_set_def
thf(fact_572_inf__set__def,axiom,
    ( inf_inf_set_a_a
    = ( ^ [A2: set_a_a,B3: set_a_a] :
          ( collect_a_a
          @ ( inf_inf_a_a_o
            @ ^ [X4: a > a] : ( member_a_a @ X4 @ A2 )
            @ ^ [X4: a > a] : ( member_a_a @ X4 @ B3 ) ) ) ) ) ).

% inf_set_def
thf(fact_573_inf__set__def,axiom,
    ( inf_inf_set_nat
    = ( ^ [A2: set_nat,B3: set_nat] :
          ( collect_nat
          @ ( inf_inf_nat_o
            @ ^ [X4: nat] : ( member_nat @ X4 @ A2 )
            @ ^ [X4: nat] : ( member_nat @ X4 @ B3 ) ) ) ) ) ).

% inf_set_def
thf(fact_574_inf__set__def,axiom,
    ( inf_inf_set_a
    = ( ^ [A2: set_a,B3: set_a] :
          ( collect_a
          @ ( inf_inf_a_o
            @ ^ [X4: a] : ( member_a @ X4 @ A2 )
            @ ^ [X4: a] : ( member_a @ X4 @ B3 ) ) ) ) ) ).

% inf_set_def
thf(fact_575_inf__Int__eq,axiom,
    ! [R2: set_nat,S: set_nat] :
      ( ( inf_inf_nat_o
        @ ^ [X4: nat] : ( member_nat @ X4 @ R2 )
        @ ^ [X4: nat] : ( member_nat @ X4 @ S ) )
      = ( ^ [X4: nat] : ( member_nat @ X4 @ ( inf_inf_set_nat @ R2 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_576_inf__Int__eq,axiom,
    ! [R2: set_real_nat,S: set_real_nat] :
      ( ( inf_inf_real_nat_o
        @ ^ [X4: real > nat] : ( member_real_nat @ X4 @ R2 )
        @ ^ [X4: real > nat] : ( member_real_nat @ X4 @ S ) )
      = ( ^ [X4: real > nat] : ( member_real_nat @ X4 @ ( inf_inf_set_real_nat @ R2 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_577_inf__Int__eq,axiom,
    ! [R2: set_real_b,S: set_real_b] :
      ( ( inf_inf_real_b_o
        @ ^ [X4: real > b] : ( member_real_b @ X4 @ R2 )
        @ ^ [X4: real > b] : ( member_real_b @ X4 @ S ) )
      = ( ^ [X4: real > b] : ( member_real_b @ X4 @ ( inf_inf_set_real_b @ R2 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_578_inf__Int__eq,axiom,
    ! [R2: set_real_a,S: set_real_a] :
      ( ( inf_inf_real_a_o
        @ ^ [X4: real > a] : ( member_real_a @ X4 @ R2 )
        @ ^ [X4: real > a] : ( member_real_a @ X4 @ S ) )
      = ( ^ [X4: real > a] : ( member_real_a @ X4 @ ( inf_inf_set_real_a @ R2 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_579_inf__Int__eq,axiom,
    ! [R2: set_a_complex,S: set_a_complex] :
      ( ( inf_inf_a_complex_o
        @ ^ [X4: a > complex] : ( member_a_complex @ X4 @ R2 )
        @ ^ [X4: a > complex] : ( member_a_complex @ X4 @ S ) )
      = ( ^ [X4: a > complex] : ( member_a_complex @ X4 @ ( inf_in3709910040937683179omplex @ R2 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_580_inf__Int__eq,axiom,
    ! [R2: set_a_real,S: set_a_real] :
      ( ( inf_inf_a_real_o
        @ ^ [X4: a > real] : ( member_a_real @ X4 @ R2 )
        @ ^ [X4: a > real] : ( member_a_real @ X4 @ S ) )
      = ( ^ [X4: a > real] : ( member_a_real @ X4 @ ( inf_inf_set_a_real @ R2 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_581_inf__Int__eq,axiom,
    ! [R2: set_a_o,S: set_a_o] :
      ( ( inf_inf_a_o_o
        @ ^ [X4: a > $o] : ( member_a_o @ X4 @ R2 )
        @ ^ [X4: a > $o] : ( member_a_o @ X4 @ S ) )
      = ( ^ [X4: a > $o] : ( member_a_o @ X4 @ ( inf_inf_set_a_o @ R2 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_582_inf__Int__eq,axiom,
    ! [R2: set_a_nat,S: set_a_nat] :
      ( ( inf_inf_a_nat_o
        @ ^ [X4: a > nat] : ( member_a_nat @ X4 @ R2 )
        @ ^ [X4: a > nat] : ( member_a_nat @ X4 @ S ) )
      = ( ^ [X4: a > nat] : ( member_a_nat @ X4 @ ( inf_inf_set_a_nat @ R2 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_583_inf__Int__eq,axiom,
    ! [R2: set_a_a,S: set_a_a] :
      ( ( inf_inf_a_a_o
        @ ^ [X4: a > a] : ( member_a_a @ X4 @ R2 )
        @ ^ [X4: a > a] : ( member_a_a @ X4 @ S ) )
      = ( ^ [X4: a > a] : ( member_a_a @ X4 @ ( inf_inf_set_a_a @ R2 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_584_inf__Int__eq,axiom,
    ! [R2: set_a,S: set_a] :
      ( ( inf_inf_a_o
        @ ^ [X4: a] : ( member_a @ X4 @ R2 )
        @ ^ [X4: a] : ( member_a @ X4 @ S ) )
      = ( ^ [X4: a] : ( member_a @ X4 @ ( inf_inf_set_a @ R2 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_585_countable__Collect,axiom,
    ! [A: set_complex,Phi: complex > $o] :
      ( ( counta5113917769705169331omplex @ A )
     => ( counta5113917769705169331omplex
        @ ( collect_complex
          @ ^ [A4: complex] :
              ( ( member_complex @ A4 @ A )
              & ( Phi @ A4 ) ) ) ) ) ).

% countable_Collect
thf(fact_586_countable__Collect,axiom,
    ! [A: set_real,Phi: real > $o] :
      ( ( counta7319604579010473777e_real @ A )
     => ( counta7319604579010473777e_real
        @ ( collect_real
          @ ^ [A4: real] :
              ( ( member_real @ A4 @ A )
              & ( Phi @ A4 ) ) ) ) ) ).

% countable_Collect
thf(fact_587_countable__Collect,axiom,
    ! [A: set_o,Phi: $o > $o] :
      ( ( counta5976203206615340371able_o @ A )
     => ( counta5976203206615340371able_o
        @ ( collect_o
          @ ^ [A4: $o] :
              ( ( member_o @ A4 @ A )
              & ( Phi @ A4 ) ) ) ) ) ).

% countable_Collect
thf(fact_588_countable__Collect,axiom,
    ! [A: set_nat,Phi: nat > $o] :
      ( ( counta1168086296615599829le_nat @ A )
     => ( counta1168086296615599829le_nat
        @ ( collect_nat
          @ ^ [A4: nat] :
              ( ( member_nat @ A4 @ A )
              & ( Phi @ A4 ) ) ) ) ) ).

% countable_Collect
thf(fact_589_countable__Collect,axiom,
    ! [A: set_a,Phi: a > $o] :
      ( ( counta4098120917673242425able_a @ A )
     => ( counta4098120917673242425able_a
        @ ( collect_a
          @ ^ [A4: a] :
              ( ( member_a @ A4 @ A )
              & ( Phi @ A4 ) ) ) ) ) ).

% countable_Collect
thf(fact_590_countable__Collect,axiom,
    ! [A: set_real_nat,Phi: ( real > nat ) > $o] :
      ( ( counta7410736174393390496al_nat @ A )
     => ( counta7410736174393390496al_nat
        @ ( collect_real_nat
          @ ^ [A4: real > nat] :
              ( ( member_real_nat @ A4 @ A )
              & ( Phi @ A4 ) ) ) ) ) ).

% countable_Collect
thf(fact_591_countable__Collect,axiom,
    ! [A: set_real_b,Phi: ( real > b ) > $o] :
      ( ( counta6639396087987402821real_b @ A )
     => ( counta6639396087987402821real_b
        @ ( collect_real_b
          @ ^ [A4: real > b] :
              ( ( member_real_b @ A4 @ A )
              & ( Phi @ A4 ) ) ) ) ) ).

% countable_Collect
thf(fact_592_countable__Collect,axiom,
    ! [A: set_real_a,Phi: ( real > a ) > $o] :
      ( ( counta6639396083684174020real_a @ A )
     => ( counta6639396083684174020real_a
        @ ( collect_real_a
          @ ^ [A4: real > a] :
              ( ( member_real_a @ A4 @ A )
              & ( Phi @ A4 ) ) ) ) ) ).

% countable_Collect
thf(fact_593_countable__Collect,axiom,
    ! [A: set_a_complex,Phi: ( a > complex ) > $o] :
      ( ( counta599731762510375256omplex @ A )
     => ( counta599731762510375256omplex
        @ ( collect_a_complex
          @ ^ [A4: a > complex] :
              ( ( member_a_complex @ A4 @ A )
              & ( Phi @ A4 ) ) ) ) ) ).

% countable_Collect
thf(fact_594_countable__Collect,axiom,
    ! [A: set_a_real,Phi: ( a > real ) > $o] :
      ( ( counta6122129581416836822a_real @ A )
     => ( counta6122129581416836822a_real
        @ ( collect_a_real
          @ ^ [A4: a > real] :
              ( ( member_a_real @ A4 @ A )
              & ( Phi @ A4 ) ) ) ) ) ).

% countable_Collect
thf(fact_595_UNIV__def,axiom,
    ( top_to7994903218803871134nnreal
    = ( collec6648975593938027277nnreal
      @ ^ [X4: extend8495563244428889912nnreal] : $true ) ) ).

% UNIV_def
thf(fact_596_UNIV__def,axiom,
    ( top_top_set_complex
    = ( collect_complex
      @ ^ [X4: complex] : $true ) ) ).

% UNIV_def
thf(fact_597_UNIV__def,axiom,
    ( top_top_set_real
    = ( collect_real
      @ ^ [X4: real] : $true ) ) ).

% UNIV_def
thf(fact_598_UNIV__def,axiom,
    ( top_top_set_o
    = ( collect_o
      @ ^ [X4: $o] : $true ) ) ).

% UNIV_def
thf(fact_599_UNIV__def,axiom,
    ( top_top_set_nat
    = ( collect_nat
      @ ^ [X4: nat] : $true ) ) ).

% UNIV_def
thf(fact_600_UNIV__def,axiom,
    ( top_top_set_a
    = ( collect_a
      @ ^ [X4: a] : $true ) ) ).

% UNIV_def
thf(fact_601_UNIV__def,axiom,
    ( top_top_set_b
    = ( collect_b
      @ ^ [X4: b] : $true ) ) ).

% UNIV_def
thf(fact_602_UNIV__def,axiom,
    ( top_top_set_real_a
    = ( collect_real_a
      @ ^ [X4: real > a] : $true ) ) ).

% UNIV_def
thf(fact_603_UNIV__def,axiom,
    ( top_top_set_real_b
    = ( collect_real_b
      @ ^ [X4: real > b] : $true ) ) ).

% UNIV_def
thf(fact_604_UNIV__def,axiom,
    ( top_top_set_real_nat
    = ( collect_real_nat
      @ ^ [X4: real > nat] : $true ) ) ).

% UNIV_def
thf(fact_605_Compr__image__eq,axiom,
    ! [F: real > real,A: set_real,P: real > $o] :
      ( ( collect_real
        @ ^ [X4: real] :
            ( ( member_real @ X4 @ ( image_real_real @ F @ A ) )
            & ( P @ X4 ) ) )
      = ( image_real_real @ F
        @ ( collect_real
          @ ^ [X4: real] :
              ( ( member_real @ X4 @ A )
              & ( P @ ( F @ X4 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_606_Compr__image__eq,axiom,
    ! [F: real > a,A: set_real,P: a > $o] :
      ( ( collect_a
        @ ^ [X4: a] :
            ( ( member_a @ X4 @ ( image_real_a @ F @ A ) )
            & ( P @ X4 ) ) )
      = ( image_real_a @ F
        @ ( collect_real
          @ ^ [X4: real] :
              ( ( member_real @ X4 @ A )
              & ( P @ ( F @ X4 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_607_Compr__image__eq,axiom,
    ! [F: a > a,A: set_a,P: a > $o] :
      ( ( collect_a
        @ ^ [X4: a] :
            ( ( member_a @ X4 @ ( image_a_a @ F @ A ) )
            & ( P @ X4 ) ) )
      = ( image_a_a @ F
        @ ( collect_a
          @ ^ [X4: a] :
              ( ( member_a @ X4 @ A )
              & ( P @ ( F @ X4 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_608_Compr__image__eq,axiom,
    ! [F: nat > real,A: set_nat,P: real > $o] :
      ( ( collect_real
        @ ^ [X4: real] :
            ( ( member_real @ X4 @ ( image_nat_real @ F @ A ) )
            & ( P @ X4 ) ) )
      = ( image_nat_real @ F
        @ ( collect_nat
          @ ^ [X4: nat] :
              ( ( member_nat @ X4 @ A )
              & ( P @ ( F @ X4 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_609_Compr__image__eq,axiom,
    ! [F: nat > complex,A: set_nat,P: complex > $o] :
      ( ( collect_complex
        @ ^ [X4: complex] :
            ( ( member_complex @ X4 @ ( image_nat_complex @ F @ A ) )
            & ( P @ X4 ) ) )
      = ( image_nat_complex @ F
        @ ( collect_nat
          @ ^ [X4: nat] :
              ( ( member_nat @ X4 @ A )
              & ( P @ ( F @ X4 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_610_Compr__image__eq,axiom,
    ! [F: nat > a,A: set_nat,P: a > $o] :
      ( ( collect_a
        @ ^ [X4: a] :
            ( ( member_a @ X4 @ ( image_nat_a @ F @ A ) )
            & ( P @ X4 ) ) )
      = ( image_nat_a @ F
        @ ( collect_nat
          @ ^ [X4: nat] :
              ( ( member_nat @ X4 @ A )
              & ( P @ ( F @ X4 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_611_Compr__image__eq,axiom,
    ! [F: a > nat,A: set_a,P: nat > $o] :
      ( ( collect_nat
        @ ^ [X4: nat] :
            ( ( member_nat @ X4 @ ( image_a_nat @ F @ A ) )
            & ( P @ X4 ) ) )
      = ( image_a_nat @ F
        @ ( collect_a
          @ ^ [X4: a] :
              ( ( member_a @ X4 @ A )
              & ( P @ ( F @ X4 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_612_Compr__image__eq,axiom,
    ! [F: nat > nat,A: set_nat,P: nat > $o] :
      ( ( collect_nat
        @ ^ [X4: nat] :
            ( ( member_nat @ X4 @ ( image_nat_nat @ F @ A ) )
            & ( P @ X4 ) ) )
      = ( image_nat_nat @ F
        @ ( collect_nat
          @ ^ [X4: nat] :
              ( ( member_nat @ X4 @ A )
              & ( P @ ( F @ X4 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_613_Compr__image__eq,axiom,
    ! [F: a > real > nat,A: set_a,P: ( real > nat ) > $o] :
      ( ( collect_real_nat
        @ ^ [X4: real > nat] :
            ( ( member_real_nat @ X4 @ ( image_a_real_nat @ F @ A ) )
            & ( P @ X4 ) ) )
      = ( image_a_real_nat @ F
        @ ( collect_a
          @ ^ [X4: a] :
              ( ( member_a @ X4 @ A )
              & ( P @ ( F @ X4 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_614_Compr__image__eq,axiom,
    ! [F: a > real > b,A: set_a,P: ( real > b ) > $o] :
      ( ( collect_real_b
        @ ^ [X4: real > b] :
            ( ( member_real_b @ X4 @ ( image_a_real_b @ F @ A ) )
            & ( P @ X4 ) ) )
      = ( image_a_real_b @ F
        @ ( collect_a
          @ ^ [X4: a] :
              ( ( member_a @ X4 @ A )
              & ( P @ ( F @ X4 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_615_image__image,axiom,
    ! [F: a > real,G: real > a,A: set_real] :
      ( ( image_a_real @ F @ ( image_real_a @ G @ A ) )
      = ( image_real_real
        @ ^ [X4: real] : ( F @ ( G @ X4 ) )
        @ A ) ) ).

% image_image
thf(fact_616_image__image,axiom,
    ! [F: real > complex,G: nat > real,A: set_nat] :
      ( ( image_real_complex @ F @ ( image_nat_real @ G @ A ) )
      = ( image_nat_complex
        @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
        @ A ) ) ).

% image_image
thf(fact_617_image__image,axiom,
    ! [F: complex > real,G: nat > complex,A: set_nat] :
      ( ( image_complex_real @ F @ ( image_nat_complex @ G @ A ) )
      = ( image_nat_real
        @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
        @ A ) ) ).

% image_image
thf(fact_618_image__image,axiom,
    ! [F: complex > complex,G: nat > complex,A: set_nat] :
      ( ( image_1468599708987790691omplex @ F @ ( image_nat_complex @ G @ A ) )
      = ( image_nat_complex
        @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
        @ A ) ) ).

% image_image
thf(fact_619_image__image,axiom,
    ! [F: nat > nat,G: a > nat,A: set_a] :
      ( ( image_nat_nat @ F @ ( image_a_nat @ G @ A ) )
      = ( image_a_nat
        @ ^ [X4: a] : ( F @ ( G @ X4 ) )
        @ A ) ) ).

% image_image
thf(fact_620_image__image,axiom,
    ! [F: nat > a,G: a > nat,A: set_a] :
      ( ( image_nat_a @ F @ ( image_a_nat @ G @ A ) )
      = ( image_a_a
        @ ^ [X4: a] : ( F @ ( G @ X4 ) )
        @ A ) ) ).

% image_image
thf(fact_621_image__image,axiom,
    ! [F: real > a,G: a > real,A: set_a] :
      ( ( image_real_a @ F @ ( image_a_real @ G @ A ) )
      = ( image_a_a
        @ ^ [X4: a] : ( F @ ( G @ X4 ) )
        @ A ) ) ).

% image_image
thf(fact_622_image__image,axiom,
    ! [F: real > a,G: nat > real,A: set_nat] :
      ( ( image_real_a @ F @ ( image_nat_real @ G @ A ) )
      = ( image_nat_a
        @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
        @ A ) ) ).

% image_image
thf(fact_623_image__image,axiom,
    ! [F: real > a,G: real > real,A: set_real] :
      ( ( image_real_a @ F @ ( image_real_real @ G @ A ) )
      = ( image_real_a
        @ ^ [X4: real] : ( F @ ( G @ X4 ) )
        @ A ) ) ).

% image_image
thf(fact_624_image__image,axiom,
    ! [F: nat > real,G: nat > nat,A: set_nat] :
      ( ( image_nat_real @ F @ ( image_nat_nat @ G @ A ) )
      = ( image_nat_real
        @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
        @ A ) ) ).

% image_image
thf(fact_625_imageE,axiom,
    ! [B: real,F: real > real,A: set_real] :
      ( ( member_real @ B @ ( image_real_real @ F @ A ) )
     => ~ ! [X2: real] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_real @ X2 @ A ) ) ) ).

% imageE
thf(fact_626_imageE,axiom,
    ! [B: real,F: nat > real,A: set_nat] :
      ( ( member_real @ B @ ( image_nat_real @ F @ A ) )
     => ~ ! [X2: nat] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_nat @ X2 @ A ) ) ) ).

% imageE
thf(fact_627_imageE,axiom,
    ! [B: complex,F: nat > complex,A: set_nat] :
      ( ( member_complex @ B @ ( image_nat_complex @ F @ A ) )
     => ~ ! [X2: nat] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_nat @ X2 @ A ) ) ) ).

% imageE
thf(fact_628_imageE,axiom,
    ! [B: nat,F: nat > nat,A: set_nat] :
      ( ( member_nat @ B @ ( image_nat_nat @ F @ A ) )
     => ~ ! [X2: nat] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_nat @ X2 @ A ) ) ) ).

% imageE
thf(fact_629_imageE,axiom,
    ! [B: nat,F: a > nat,A: set_a] :
      ( ( member_nat @ B @ ( image_a_nat @ F @ A ) )
     => ~ ! [X2: a] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_a @ X2 @ A ) ) ) ).

% imageE
thf(fact_630_imageE,axiom,
    ! [B: a,F: real > a,A: set_real] :
      ( ( member_a @ B @ ( image_real_a @ F @ A ) )
     => ~ ! [X2: real] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_real @ X2 @ A ) ) ) ).

% imageE
thf(fact_631_imageE,axiom,
    ! [B: a,F: nat > a,A: set_nat] :
      ( ( member_a @ B @ ( image_nat_a @ F @ A ) )
     => ~ ! [X2: nat] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_nat @ X2 @ A ) ) ) ).

% imageE
thf(fact_632_imageE,axiom,
    ! [B: a,F: a > a,A: set_a] :
      ( ( member_a @ B @ ( image_a_a @ F @ A ) )
     => ~ ! [X2: a] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_a @ X2 @ A ) ) ) ).

% imageE
thf(fact_633_imageE,axiom,
    ! [B: nat,F: ( real > nat ) > nat,A: set_real_nat] :
      ( ( member_nat @ B @ ( image_real_nat_nat @ F @ A ) )
     => ~ ! [X2: real > nat] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_real_nat @ X2 @ A ) ) ) ).

% imageE
thf(fact_634_imageE,axiom,
    ! [B: nat,F: ( real > b ) > nat,A: set_real_b] :
      ( ( member_nat @ B @ ( image_real_b_nat @ F @ A ) )
     => ~ ! [X2: real > b] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_real_b @ X2 @ A ) ) ) ).

% imageE
thf(fact_635_Collect__conj__eq,axiom,
    ! [P: nat > $o,Q: nat > $o] :
      ( ( collect_nat
        @ ^ [X4: nat] :
            ( ( P @ X4 )
            & ( Q @ X4 ) ) )
      = ( inf_inf_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).

% Collect_conj_eq
thf(fact_636_Collect__conj__eq,axiom,
    ! [P: a > $o,Q: a > $o] :
      ( ( collect_a
        @ ^ [X4: a] :
            ( ( P @ X4 )
            & ( Q @ X4 ) ) )
      = ( inf_inf_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).

% Collect_conj_eq
thf(fact_637_Int__Collect,axiom,
    ! [X: real > nat,A: set_real_nat,P: ( real > nat ) > $o] :
      ( ( member_real_nat @ X @ ( inf_inf_set_real_nat @ A @ ( collect_real_nat @ P ) ) )
      = ( ( member_real_nat @ X @ A )
        & ( P @ X ) ) ) ).

% Int_Collect
thf(fact_638_Int__Collect,axiom,
    ! [X: real > b,A: set_real_b,P: ( real > b ) > $o] :
      ( ( member_real_b @ X @ ( inf_inf_set_real_b @ A @ ( collect_real_b @ P ) ) )
      = ( ( member_real_b @ X @ A )
        & ( P @ X ) ) ) ).

% Int_Collect
thf(fact_639_Int__Collect,axiom,
    ! [X: real > a,A: set_real_a,P: ( real > a ) > $o] :
      ( ( member_real_a @ X @ ( inf_inf_set_real_a @ A @ ( collect_real_a @ P ) ) )
      = ( ( member_real_a @ X @ A )
        & ( P @ X ) ) ) ).

% Int_Collect
thf(fact_640_Int__Collect,axiom,
    ! [X: a > complex,A: set_a_complex,P: ( a > complex ) > $o] :
      ( ( member_a_complex @ X @ ( inf_in3709910040937683179omplex @ A @ ( collect_a_complex @ P ) ) )
      = ( ( member_a_complex @ X @ A )
        & ( P @ X ) ) ) ).

% Int_Collect
thf(fact_641_Int__Collect,axiom,
    ! [X: a > real,A: set_a_real,P: ( a > real ) > $o] :
      ( ( member_a_real @ X @ ( inf_inf_set_a_real @ A @ ( collect_a_real @ P ) ) )
      = ( ( member_a_real @ X @ A )
        & ( P @ X ) ) ) ).

% Int_Collect
thf(fact_642_Int__Collect,axiom,
    ! [X: a > $o,A: set_a_o,P: ( a > $o ) > $o] :
      ( ( member_a_o @ X @ ( inf_inf_set_a_o @ A @ ( collect_a_o @ P ) ) )
      = ( ( member_a_o @ X @ A )
        & ( P @ X ) ) ) ).

% Int_Collect
thf(fact_643_Int__Collect,axiom,
    ! [X: a > nat,A: set_a_nat,P: ( a > nat ) > $o] :
      ( ( member_a_nat @ X @ ( inf_inf_set_a_nat @ A @ ( collect_a_nat @ P ) ) )
      = ( ( member_a_nat @ X @ A )
        & ( P @ X ) ) ) ).

% Int_Collect
thf(fact_644_Int__Collect,axiom,
    ! [X: a > a,A: set_a_a,P: ( a > a ) > $o] :
      ( ( member_a_a @ X @ ( inf_inf_set_a_a @ A @ ( collect_a_a @ P ) ) )
      = ( ( member_a_a @ X @ A )
        & ( P @ X ) ) ) ).

% Int_Collect
thf(fact_645_Int__Collect,axiom,
    ! [X: nat,A: set_nat,P: nat > $o] :
      ( ( member_nat @ X @ ( inf_inf_set_nat @ A @ ( collect_nat @ P ) ) )
      = ( ( member_nat @ X @ A )
        & ( P @ X ) ) ) ).

% Int_Collect
thf(fact_646_Int__Collect,axiom,
    ! [X: a,A: set_a,P: a > $o] :
      ( ( member_a @ X @ ( inf_inf_set_a @ A @ ( collect_a @ P ) ) )
      = ( ( member_a @ X @ A )
        & ( P @ X ) ) ) ).

% Int_Collect
thf(fact_647_Int__def,axiom,
    ( inf_inf_set_real_nat
    = ( ^ [A2: set_real_nat,B3: set_real_nat] :
          ( collect_real_nat
          @ ^ [X4: real > nat] :
              ( ( member_real_nat @ X4 @ A2 )
              & ( member_real_nat @ X4 @ B3 ) ) ) ) ) ).

% Int_def
thf(fact_648_Int__def,axiom,
    ( inf_inf_set_real_b
    = ( ^ [A2: set_real_b,B3: set_real_b] :
          ( collect_real_b
          @ ^ [X4: real > b] :
              ( ( member_real_b @ X4 @ A2 )
              & ( member_real_b @ X4 @ B3 ) ) ) ) ) ).

% Int_def
thf(fact_649_Int__def,axiom,
    ( inf_inf_set_real_a
    = ( ^ [A2: set_real_a,B3: set_real_a] :
          ( collect_real_a
          @ ^ [X4: real > a] :
              ( ( member_real_a @ X4 @ A2 )
              & ( member_real_a @ X4 @ B3 ) ) ) ) ) ).

% Int_def
thf(fact_650_Int__def,axiom,
    ( inf_in3709910040937683179omplex
    = ( ^ [A2: set_a_complex,B3: set_a_complex] :
          ( collect_a_complex
          @ ^ [X4: a > complex] :
              ( ( member_a_complex @ X4 @ A2 )
              & ( member_a_complex @ X4 @ B3 ) ) ) ) ) ).

% Int_def
thf(fact_651_Int__def,axiom,
    ( inf_inf_set_a_real
    = ( ^ [A2: set_a_real,B3: set_a_real] :
          ( collect_a_real
          @ ^ [X4: a > real] :
              ( ( member_a_real @ X4 @ A2 )
              & ( member_a_real @ X4 @ B3 ) ) ) ) ) ).

% Int_def
thf(fact_652_Int__def,axiom,
    ( inf_inf_set_a_o
    = ( ^ [A2: set_a_o,B3: set_a_o] :
          ( collect_a_o
          @ ^ [X4: a > $o] :
              ( ( member_a_o @ X4 @ A2 )
              & ( member_a_o @ X4 @ B3 ) ) ) ) ) ).

% Int_def
thf(fact_653_Int__def,axiom,
    ( inf_inf_set_a_nat
    = ( ^ [A2: set_a_nat,B3: set_a_nat] :
          ( collect_a_nat
          @ ^ [X4: a > nat] :
              ( ( member_a_nat @ X4 @ A2 )
              & ( member_a_nat @ X4 @ B3 ) ) ) ) ) ).

% Int_def
thf(fact_654_Int__def,axiom,
    ( inf_inf_set_a_a
    = ( ^ [A2: set_a_a,B3: set_a_a] :
          ( collect_a_a
          @ ^ [X4: a > a] :
              ( ( member_a_a @ X4 @ A2 )
              & ( member_a_a @ X4 @ B3 ) ) ) ) ) ).

% Int_def
thf(fact_655_Int__def,axiom,
    ( inf_inf_set_nat
    = ( ^ [A2: set_nat,B3: set_nat] :
          ( collect_nat
          @ ^ [X4: nat] :
              ( ( member_nat @ X4 @ A2 )
              & ( member_nat @ X4 @ B3 ) ) ) ) ) ).

% Int_def
thf(fact_656_Int__def,axiom,
    ( inf_inf_set_a
    = ( ^ [A2: set_a,B3: set_a] :
          ( collect_a
          @ ^ [X4: a] :
              ( ( member_a @ X4 @ A2 )
              & ( member_a @ X4 @ B3 ) ) ) ) ) ).

% Int_def
thf(fact_657_measurable__compose__rev,axiom,
    ! [F: b > b,L: sigma_measure_b,N: sigma_measure_b,G: real > b,M: sigma_measure_real] :
      ( ( member_b_b @ F @ ( sigma_measurable_b_b @ L @ N ) )
     => ( ( member_real_b @ G @ ( sigma_523072396149930113real_b @ M @ L ) )
       => ( member_real_b
          @ ^ [X4: real] : ( F @ ( G @ X4 ) )
          @ ( sigma_523072396149930113real_b @ M @ N ) ) ) ) ).

% measurable_compose_rev
thf(fact_658_measurable__compose__rev,axiom,
    ! [F: real > b,L: sigma_measure_real,N: sigma_measure_b,G: real > real,M: sigma_measure_real] :
      ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ L @ N ) )
     => ( ( member_real_real @ G @ ( sigma_5267869275261027754l_real @ M @ L ) )
       => ( member_real_b
          @ ^ [X4: real] : ( F @ ( G @ X4 ) )
          @ ( sigma_523072396149930113real_b @ M @ N ) ) ) ) ).

% measurable_compose_rev
thf(fact_659_measurable__compose__rev,axiom,
    ! [F: b > a,L: sigma_measure_b,N: sigma_measure_a,G: real > b,M: sigma_measure_real] :
      ( ( member_b_a @ F @ ( sigma_measurable_b_a @ L @ N ) )
     => ( ( member_real_b @ G @ ( sigma_523072396149930113real_b @ M @ L ) )
       => ( member_real_a
          @ ^ [X4: real] : ( F @ ( G @ X4 ) )
          @ ( sigma_523072396149930112real_a @ M @ N ) ) ) ) ).

% measurable_compose_rev
thf(fact_660_measurable__compose__rev,axiom,
    ! [F: b > nat,L: sigma_measure_b,N: sigma_measure_nat,G: real > b,M: sigma_measure_real] :
      ( ( member_b_nat @ F @ ( sigma_1308594411581951615_b_nat @ L @ N ) )
     => ( ( member_real_b @ G @ ( sigma_523072396149930113real_b @ M @ L ) )
       => ( member_real_nat
          @ ^ [X4: real] : ( F @ ( G @ X4 ) )
          @ ( sigma_6315060578831106510al_nat @ M @ N ) ) ) ) ).

% measurable_compose_rev
thf(fact_661_measurable__compose__rev,axiom,
    ! [F: a > b,L: sigma_measure_a,N: sigma_measure_b,G: real > a,M: sigma_measure_real] :
      ( ( member_a_b @ F @ ( sigma_measurable_a_b @ L @ N ) )
     => ( ( member_real_a @ G @ ( sigma_523072396149930112real_a @ M @ L ) )
       => ( member_real_b
          @ ^ [X4: real] : ( F @ ( G @ X4 ) )
          @ ( sigma_523072396149930113real_b @ M @ N ) ) ) ) ).

% measurable_compose_rev
thf(fact_662_measurable__compose__rev,axiom,
    ! [F: nat > b,L: sigma_measure_nat,N: sigma_measure_b,G: real > nat,M: sigma_measure_real] :
      ( ( member_nat_b @ F @ ( sigma_4105081583803843549_nat_b @ L @ N ) )
     => ( ( member_real_nat @ G @ ( sigma_6315060578831106510al_nat @ M @ L ) )
       => ( member_real_b
          @ ^ [X4: real] : ( F @ ( G @ X4 ) )
          @ ( sigma_523072396149930113real_b @ M @ N ) ) ) ) ).

% measurable_compose_rev
thf(fact_663_measurable__compose__rev,axiom,
    ! [F: nat > a,L: sigma_measure_nat,N: sigma_measure_a,G: real > nat,M: sigma_measure_real] :
      ( ( member_nat_a @ F @ ( sigma_4105081583803843548_nat_a @ L @ N ) )
     => ( ( member_real_nat @ G @ ( sigma_6315060578831106510al_nat @ M @ L ) )
       => ( member_real_a
          @ ^ [X4: real] : ( F @ ( G @ X4 ) )
          @ ( sigma_523072396149930112real_a @ M @ N ) ) ) ) ).

% measurable_compose_rev
thf(fact_664_measurable__compose__rev,axiom,
    ! [F: nat > nat,L: sigma_measure_nat,N: sigma_measure_nat,G: real > nat,M: sigma_measure_real] :
      ( ( member_nat_nat @ F @ ( sigma_4350458207664084850at_nat @ L @ N ) )
     => ( ( member_real_nat @ G @ ( sigma_6315060578831106510al_nat @ M @ L ) )
       => ( member_real_nat
          @ ^ [X4: real] : ( F @ ( G @ X4 ) )
          @ ( sigma_6315060578831106510al_nat @ M @ N ) ) ) ) ).

% measurable_compose_rev
thf(fact_665_measurable__compose__rev,axiom,
    ! [F: complex > complex,L: sigma_3077487657436305159omplex,N: sigma_3077487657436305159omplex,G: a > complex,M: sigma_measure_a] :
      ( ( member5128974058612258834omplex @ F @ ( sigma_5867711785444923182omplex @ L @ N ) )
     => ( ( member_a_complex @ G @ ( sigma_852363994732143452omplex @ M @ L ) )
       => ( member_a_complex
          @ ^ [X4: a] : ( F @ ( G @ X4 ) )
          @ ( sigma_852363994732143452omplex @ M @ N ) ) ) ) ).

% measurable_compose_rev
thf(fact_666_measurable__compose__rev,axiom,
    ! [F: complex > real,L: sigma_3077487657436305159omplex,N: sigma_measure_real,G: a > complex,M: sigma_measure_a] :
      ( ( member_complex_real @ F @ ( sigma_9165504702370893100x_real @ L @ N ) )
     => ( ( member_a_complex @ G @ ( sigma_852363994732143452omplex @ M @ L ) )
       => ( member_a_real
          @ ^ [X4: a] : ( F @ ( G @ X4 ) )
          @ ( sigma_9116425665531756122a_real @ M @ N ) ) ) ) ).

% measurable_compose_rev
thf(fact_667_measurable__compose,axiom,
    ! [F: real > real,M: sigma_measure_real,N: sigma_measure_real,G: real > b,L: sigma_measure_b] :
      ( ( member_real_real @ F @ ( sigma_5267869275261027754l_real @ M @ N ) )
     => ( ( member_real_b @ G @ ( sigma_523072396149930113real_b @ N @ L ) )
       => ( member_real_b
          @ ^ [X4: real] : ( G @ ( F @ X4 ) )
          @ ( sigma_523072396149930113real_b @ M @ L ) ) ) ) ).

% measurable_compose
thf(fact_668_measurable__compose,axiom,
    ! [F: real > b,M: sigma_measure_real,N: sigma_measure_b,G: b > b,L: sigma_measure_b] :
      ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ N ) )
     => ( ( member_b_b @ G @ ( sigma_measurable_b_b @ N @ L ) )
       => ( member_real_b
          @ ^ [X4: real] : ( G @ ( F @ X4 ) )
          @ ( sigma_523072396149930113real_b @ M @ L ) ) ) ) ).

% measurable_compose
thf(fact_669_measurable__compose,axiom,
    ! [F: real > b,M: sigma_measure_real,N: sigma_measure_b,G: b > a,L: sigma_measure_a] :
      ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ N ) )
     => ( ( member_b_a @ G @ ( sigma_measurable_b_a @ N @ L ) )
       => ( member_real_a
          @ ^ [X4: real] : ( G @ ( F @ X4 ) )
          @ ( sigma_523072396149930112real_a @ M @ L ) ) ) ) ).

% measurable_compose
thf(fact_670_measurable__compose,axiom,
    ! [F: real > b,M: sigma_measure_real,N: sigma_measure_b,G: b > nat,L: sigma_measure_nat] :
      ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ N ) )
     => ( ( member_b_nat @ G @ ( sigma_1308594411581951615_b_nat @ N @ L ) )
       => ( member_real_nat
          @ ^ [X4: real] : ( G @ ( F @ X4 ) )
          @ ( sigma_6315060578831106510al_nat @ M @ L ) ) ) ) ).

% measurable_compose
thf(fact_671_measurable__compose,axiom,
    ! [F: real > real,M: sigma_measure_real,N: sigma_measure_real,G: real > a,L: sigma_measure_a] :
      ( ( member_real_real @ F @ ( sigma_5267869275261027754l_real @ M @ N ) )
     => ( ( member_real_a @ G @ ( sigma_523072396149930112real_a @ N @ L ) )
       => ( member_real_a
          @ ^ [X4: real] : ( G @ ( F @ X4 ) )
          @ ( sigma_523072396149930112real_a @ M @ L ) ) ) ) ).

% measurable_compose
thf(fact_672_measurable__compose,axiom,
    ! [F: real > real,M: sigma_measure_real,N: sigma_measure_real,G: real > nat,L: sigma_measure_nat] :
      ( ( member_real_real @ F @ ( sigma_5267869275261027754l_real @ M @ N ) )
     => ( ( member_real_nat @ G @ ( sigma_6315060578831106510al_nat @ N @ L ) )
       => ( member_real_nat
          @ ^ [X4: real] : ( G @ ( F @ X4 ) )
          @ ( sigma_6315060578831106510al_nat @ M @ L ) ) ) ) ).

% measurable_compose
thf(fact_673_measurable__compose,axiom,
    ! [F: real > a,M: sigma_measure_real,N: sigma_measure_a,G: a > b,L: sigma_measure_b] :
      ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ N ) )
     => ( ( member_a_b @ G @ ( sigma_measurable_a_b @ N @ L ) )
       => ( member_real_b
          @ ^ [X4: real] : ( G @ ( F @ X4 ) )
          @ ( sigma_523072396149930113real_b @ M @ L ) ) ) ) ).

% measurable_compose
thf(fact_674_measurable__compose,axiom,
    ! [F: real > a,M: sigma_measure_real,N: sigma_measure_a,G: a > complex,L: sigma_3077487657436305159omplex] :
      ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ N ) )
     => ( ( member_a_complex @ G @ ( sigma_852363994732143452omplex @ N @ L ) )
       => ( member_real_complex
          @ ^ [X4: real] : ( G @ ( F @ X4 ) )
          @ ( sigma_9111916201866572460omplex @ M @ L ) ) ) ) ).

% measurable_compose
thf(fact_675_measurable__compose,axiom,
    ! [F: real > a,M: sigma_measure_real,N: sigma_measure_a,G: a > real,L: sigma_measure_real] :
      ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ N ) )
     => ( ( member_a_real @ G @ ( sigma_9116425665531756122a_real @ N @ L ) )
       => ( member_real_real
          @ ^ [X4: real] : ( G @ ( F @ X4 ) )
          @ ( sigma_5267869275261027754l_real @ M @ L ) ) ) ) ).

% measurable_compose
thf(fact_676_measurable__compose,axiom,
    ! [F: real > a,M: sigma_measure_real,N: sigma_measure_a,G: a > $o,L: sigma_measure_o] :
      ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ N ) )
     => ( ( member_a_o @ G @ ( sigma_measurable_a_o @ N @ L ) )
       => ( member_real_o
          @ ^ [X4: real] : ( G @ ( F @ X4 ) )
          @ ( sigma_3939073009482781210real_o @ M @ L ) ) ) ) ).

% measurable_compose
thf(fact_677_measurable__id,axiom,
    ! [M: sigma_measure_a] :
      ( member_a_a
      @ ^ [X4: a] : X4
      @ ( sigma_measurable_a_a @ M @ M ) ) ).

% measurable_id
thf(fact_678_qbs__closed2__dest,axiom,
    ! [X: nat,X5: quasi_borel_nat] :
      ( ( member_nat @ X @ ( qbs_space_nat @ X5 ) )
     => ( member_real_nat
        @ ^ [R3: real] : X
        @ ( qbs_Mx_nat @ X5 ) ) ) ).

% qbs_closed2_dest
thf(fact_679_qbs__closed2__dest,axiom,
    ! [X: a,X5: quasi_borel_a] :
      ( ( member_a @ X @ ( qbs_space_a @ X5 ) )
     => ( member_real_a
        @ ^ [R3: real] : X
        @ ( qbs_Mx_a @ X5 ) ) ) ).

% qbs_closed2_dest
thf(fact_680_qbs__closed2__dest,axiom,
    ! [X: b,X5: quasi_borel_b] :
      ( ( member_b @ X @ ( qbs_space_b @ X5 ) )
     => ( member_real_b
        @ ^ [R3: real] : X
        @ ( qbs_Mx_b @ X5 ) ) ) ).

% qbs_closed2_dest
thf(fact_681_qbs__closed2__dest,axiom,
    ! [X: real > nat,X5: quasi_borel_real_nat] :
      ( ( member_real_nat @ X @ ( qbs_space_real_nat @ X5 ) )
     => ( member_real_real_nat
        @ ^ [R3: real] : X
        @ ( qbs_Mx_real_nat @ X5 ) ) ) ).

% qbs_closed2_dest
thf(fact_682_qbs__closed2__dest,axiom,
    ! [X: real > b,X5: quasi_borel_real_b] :
      ( ( member_real_b @ X @ ( qbs_space_real_b @ X5 ) )
     => ( member_real_real_b
        @ ^ [R3: real] : X
        @ ( qbs_Mx_real_b @ X5 ) ) ) ).

% qbs_closed2_dest
thf(fact_683_qbs__closed2__dest,axiom,
    ! [X: real > a,X5: quasi_borel_real_a] :
      ( ( member_real_a @ X @ ( qbs_space_real_a @ X5 ) )
     => ( member_real_real_a
        @ ^ [R3: real] : X
        @ ( qbs_Mx_real_a @ X5 ) ) ) ).

% qbs_closed2_dest
thf(fact_684_qbs__closed2__dest,axiom,
    ! [X: a > complex,X5: quasi_4365677710772687427omplex] :
      ( ( member_a_complex @ X @ ( qbs_space_a_complex @ X5 ) )
     => ( member8749487273670996305omplex
        @ ^ [R3: real] : X
        @ ( qbs_Mx_a_complex @ X5 ) ) ) ).

% qbs_closed2_dest
thf(fact_685_qbs__closed2__dest,axiom,
    ! [X: a > real,X5: quasi_borel_a_real] :
      ( ( member_a_real @ X @ ( qbs_space_a_real @ X5 ) )
     => ( member_real_a_real
        @ ^ [R3: real] : X
        @ ( qbs_Mx_a_real @ X5 ) ) ) ).

% qbs_closed2_dest
thf(fact_686_qbs__closed2__dest,axiom,
    ! [X: a > $o,X5: quasi_borel_a_o] :
      ( ( member_a_o @ X @ ( qbs_space_a_o @ X5 ) )
     => ( member_real_a_o2
        @ ^ [R3: real] : X
        @ ( qbs_Mx_a_o @ X5 ) ) ) ).

% qbs_closed2_dest
thf(fact_687_qbs__closed2__dest,axiom,
    ! [X: a > nat,X5: quasi_borel_a_nat] :
      ( ( member_a_nat @ X @ ( qbs_space_a_nat @ X5 ) )
     => ( member_real_a_nat
        @ ^ [R3: real] : X
        @ ( qbs_Mx_a_nat @ X5 ) ) ) ).

% qbs_closed2_dest
thf(fact_688_qbs__Mx__to__X_I1_J,axiom,
    ! [Alpha: real > nat,X5: quasi_borel_nat] :
      ( ( member_real_nat @ Alpha @ ( qbs_Mx_nat @ X5 ) )
     => ( member_real_nat @ Alpha
        @ ( pi_real_nat @ top_top_set_real
          @ ^ [Uu: real] : ( qbs_space_nat @ X5 ) ) ) ) ).

% qbs_Mx_to_X(1)
thf(fact_689_qbs__Mx__to__X_I1_J,axiom,
    ! [Alpha: real > a,X5: quasi_borel_a] :
      ( ( member_real_a @ Alpha @ ( qbs_Mx_a @ X5 ) )
     => ( member_real_a @ Alpha
        @ ( pi_real_a @ top_top_set_real
          @ ^ [Uu: real] : ( qbs_space_a @ X5 ) ) ) ) ).

% qbs_Mx_to_X(1)
thf(fact_690_qbs__Mx__to__X_I1_J,axiom,
    ! [Alpha: real > b,X5: quasi_borel_b] :
      ( ( member_real_b @ Alpha @ ( qbs_Mx_b @ X5 ) )
     => ( member_real_b @ Alpha
        @ ( pi_real_b @ top_top_set_real
          @ ^ [Uu: real] : ( qbs_space_b @ X5 ) ) ) ) ).

% qbs_Mx_to_X(1)
thf(fact_691_measurable__restrict__space3,axiom,
    ! [F: real > b,M: sigma_measure_real,N: sigma_measure_b,A: set_real,B2: set_b] :
      ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ N ) )
     => ( ( member_real_b @ F
          @ ( pi_real_b @ A
            @ ^ [Uu: real] : B2 ) )
       => ( member_real_b @ F @ ( sigma_523072396149930113real_b @ ( sigma_5414646170262037096e_real @ M @ A ) @ ( sigma_8692839461743104067pace_b @ N @ B2 ) ) ) ) ) ).

% measurable_restrict_space3
thf(fact_692_measurable__restrict__space3,axiom,
    ! [F: real > nat,M: sigma_measure_real,N: sigma_measure_nat,A: set_real,B2: set_nat] :
      ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M @ N ) )
     => ( ( member_real_nat @ F
          @ ( pi_real_nat @ A
            @ ^ [Uu: real] : B2 ) )
       => ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ ( sigma_5414646170262037096e_real @ M @ A ) @ ( sigma_744083341818469772ce_nat @ N @ B2 ) ) ) ) ) ).

% measurable_restrict_space3
thf(fact_693_measurable__restrict__space3,axiom,
    ! [F: real > a,M: sigma_measure_real,N: sigma_measure_a,A: set_real,B2: set_a] :
      ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ N ) )
     => ( ( member_real_a @ F
          @ ( pi_real_a @ A
            @ ^ [Uu: real] : B2 ) )
       => ( member_real_a @ F @ ( sigma_523072396149930112real_a @ ( sigma_5414646170262037096e_real @ M @ A ) @ ( sigma_8692839461743104066pace_a @ N @ B2 ) ) ) ) ) ).

% measurable_restrict_space3
thf(fact_694_measurable__restrict__space3,axiom,
    ! [F: a > complex,M: sigma_measure_a,N: sigma_3077487657436305159omplex,A: set_a,B2: set_complex] :
      ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ M @ N ) )
     => ( ( member_a_complex @ F
          @ ( pi_a_complex @ A
            @ ^ [Uu: a] : B2 ) )
       => ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ ( sigma_8692839461743104066pace_a @ M @ A ) @ ( sigma_216592511309337194omplex @ N @ B2 ) ) ) ) ) ).

% measurable_restrict_space3
thf(fact_695_measurable__restrict__space3,axiom,
    ! [F: a > real,M: sigma_measure_a,N: sigma_measure_real,A: set_a,B2: set_real] :
      ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M @ N ) )
     => ( ( member_a_real @ F
          @ ( pi_a_real @ A
            @ ^ [Uu: a] : B2 ) )
       => ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ ( sigma_8692839461743104066pace_a @ M @ A ) @ ( sigma_5414646170262037096e_real @ N @ B2 ) ) ) ) ) ).

% measurable_restrict_space3
thf(fact_696_measurable__restrict__space3,axiom,
    ! [F: a > $o,M: sigma_measure_a,N: sigma_measure_o,A: set_a,B2: set_o] :
      ( ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ N ) )
     => ( ( member_a_o @ F
          @ ( pi_a_o @ A
            @ ^ [Uu: a] : B2 ) )
       => ( member_a_o @ F @ ( sigma_measurable_a_o @ ( sigma_8692839461743104066pace_a @ M @ A ) @ ( sigma_8520893325391096540pace_o @ N @ B2 ) ) ) ) ) ).

% measurable_restrict_space3
thf(fact_697_measurable__restrict__space3,axiom,
    ! [F: a > nat,M: sigma_measure_a,N: sigma_measure_nat,A: set_a,B2: set_nat] :
      ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M @ N ) )
     => ( ( member_a_nat @ F
          @ ( pi_a_nat @ A
            @ ^ [Uu: a] : B2 ) )
       => ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ ( sigma_8692839461743104066pace_a @ M @ A ) @ ( sigma_744083341818469772ce_nat @ N @ B2 ) ) ) ) ) ).

% measurable_restrict_space3
thf(fact_698_measurable__restrict__space3,axiom,
    ! [F: a > a,M: sigma_measure_a,N: sigma_measure_a,A: set_a,B2: set_a] :
      ( ( member_a_a @ F @ ( sigma_measurable_a_a @ M @ N ) )
     => ( ( member_a_a @ F
          @ ( pi_a_a @ A
            @ ^ [Uu: a] : B2 ) )
       => ( member_a_a @ F @ ( sigma_measurable_a_a @ ( sigma_8692839461743104066pace_a @ M @ A ) @ ( sigma_8692839461743104066pace_a @ N @ B2 ) ) ) ) ) ).

% measurable_restrict_space3
thf(fact_699_range__composition,axiom,
    ! [F: real > a,G: extend8495563244428889912nnreal > real] :
      ( ( image_7862617044475835263real_a
        @ ^ [X4: extend8495563244428889912nnreal] : ( F @ ( G @ X4 ) )
        @ top_to7994903218803871134nnreal )
      = ( image_real_a @ F @ ( image_5648444867695151211l_real @ G @ top_to7994903218803871134nnreal ) ) ) ).

% range_composition
thf(fact_700_range__composition,axiom,
    ! [F: nat > real,G: extend8495563244428889912nnreal > nat] :
      ( ( image_5648444867695151211l_real
        @ ^ [X4: extend8495563244428889912nnreal] : ( F @ ( G @ X4 ) )
        @ top_to7994903218803871134nnreal )
      = ( image_nat_real @ F @ ( image_4010189972324537615al_nat @ G @ top_to7994903218803871134nnreal ) ) ) ).

% range_composition
thf(fact_701_range__composition,axiom,
    ! [F: nat > complex,G: extend8495563244428889912nnreal > nat] :
      ( ( image_3781532184644764653omplex
        @ ^ [X4: extend8495563244428889912nnreal] : ( F @ ( G @ X4 ) )
        @ top_to7994903218803871134nnreal )
      = ( image_nat_complex @ F @ ( image_4010189972324537615al_nat @ G @ top_to7994903218803871134nnreal ) ) ) ).

% range_composition
thf(fact_702_range__composition,axiom,
    ! [F: real > real,G: extend8495563244428889912nnreal > real] :
      ( ( image_5648444867695151211l_real
        @ ^ [X4: extend8495563244428889912nnreal] : ( F @ ( G @ X4 ) )
        @ top_to7994903218803871134nnreal )
      = ( image_real_real @ F @ ( image_5648444867695151211l_real @ G @ top_to7994903218803871134nnreal ) ) ) ).

% range_composition
thf(fact_703_range__composition,axiom,
    ! [F: a > nat,G: extend8495563244428889912nnreal > a] :
      ( ( image_4010189972324537615al_nat
        @ ^ [X4: extend8495563244428889912nnreal] : ( F @ ( G @ X4 ) )
        @ top_to7994903218803871134nnreal )
      = ( image_a_nat @ F @ ( image_7862617044475835263real_a @ G @ top_to7994903218803871134nnreal ) ) ) ).

% range_composition
thf(fact_704_range__composition,axiom,
    ! [F: a > a,G: extend8495563244428889912nnreal > a] :
      ( ( image_7862617044475835263real_a
        @ ^ [X4: extend8495563244428889912nnreal] : ( F @ ( G @ X4 ) )
        @ top_to7994903218803871134nnreal )
      = ( image_a_a @ F @ ( image_7862617044475835263real_a @ G @ top_to7994903218803871134nnreal ) ) ) ).

% range_composition
thf(fact_705_range__composition,axiom,
    ! [F: real > a,G: complex > real] :
      ( ( image_complex_a
        @ ^ [X4: complex] : ( F @ ( G @ X4 ) )
        @ top_top_set_complex )
      = ( image_real_a @ F @ ( image_complex_real @ G @ top_top_set_complex ) ) ) ).

% range_composition
thf(fact_706_range__composition,axiom,
    ! [F: nat > real,G: complex > nat] :
      ( ( image_complex_real
        @ ^ [X4: complex] : ( F @ ( G @ X4 ) )
        @ top_top_set_complex )
      = ( image_nat_real @ F @ ( image_complex_nat @ G @ top_top_set_complex ) ) ) ).

% range_composition
thf(fact_707_range__composition,axiom,
    ! [F: nat > complex,G: complex > nat] :
      ( ( image_1468599708987790691omplex
        @ ^ [X4: complex] : ( F @ ( G @ X4 ) )
        @ top_top_set_complex )
      = ( image_nat_complex @ F @ ( image_complex_nat @ G @ top_top_set_complex ) ) ) ).

% range_composition
thf(fact_708_range__composition,axiom,
    ! [F: real > real,G: complex > real] :
      ( ( image_complex_real
        @ ^ [X4: complex] : ( F @ ( G @ X4 ) )
        @ top_top_set_complex )
      = ( image_real_real @ F @ ( image_complex_real @ G @ top_top_set_complex ) ) ) ).

% range_composition
thf(fact_709_rangeE,axiom,
    ! [B: nat,F: extend8495563244428889912nnreal > nat] :
      ( ( member_nat @ B @ ( image_4010189972324537615al_nat @ F @ top_to7994903218803871134nnreal ) )
     => ~ ! [X2: extend8495563244428889912nnreal] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_710_rangeE,axiom,
    ! [B: a,F: extend8495563244428889912nnreal > a] :
      ( ( member_a @ B @ ( image_7862617044475835263real_a @ F @ top_to7994903218803871134nnreal ) )
     => ~ ! [X2: extend8495563244428889912nnreal] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_711_rangeE,axiom,
    ! [B: nat,F: complex > nat] :
      ( ( member_nat @ B @ ( image_complex_nat @ F @ top_top_set_complex ) )
     => ~ ! [X2: complex] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_712_rangeE,axiom,
    ! [B: a,F: complex > a] :
      ( ( member_a @ B @ ( image_complex_a @ F @ top_top_set_complex ) )
     => ~ ! [X2: complex] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_713_rangeE,axiom,
    ! [B: real,F: real > real] :
      ( ( member_real @ B @ ( image_real_real @ F @ top_top_set_real ) )
     => ~ ! [X2: real] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_714_rangeE,axiom,
    ! [B: nat,F: real > nat] :
      ( ( member_nat @ B @ ( image_real_nat @ F @ top_top_set_real ) )
     => ~ ! [X2: real] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_715_rangeE,axiom,
    ! [B: a,F: real > a] :
      ( ( member_a @ B @ ( image_real_a @ F @ top_top_set_real ) )
     => ~ ! [X2: real] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_716_rangeE,axiom,
    ! [B: nat,F: $o > nat] :
      ( ( member_nat @ B @ ( image_o_nat @ F @ top_top_set_o ) )
     => ~ ! [X2: $o] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_717_rangeE,axiom,
    ! [B: a,F: $o > a] :
      ( ( member_a @ B @ ( image_o_a @ F @ top_top_set_o ) )
     => ~ ! [X2: $o] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_718_rangeE,axiom,
    ! [B: real,F: nat > real] :
      ( ( member_real @ B @ ( image_nat_real @ F @ top_top_set_nat ) )
     => ~ ! [X2: nat] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_719_borel__measurable__const,axiom,
    ! [C: complex,M: sigma_measure_a] :
      ( member_a_complex
      @ ^ [X4: a] : C
      @ ( sigma_852363994732143452omplex @ M @ borel_1392132677378845456omplex ) ) ).

% borel_measurable_const
thf(fact_720_borel__measurable__const,axiom,
    ! [C: real,M: sigma_measure_a] :
      ( member_a_real
      @ ^ [X4: a] : C
      @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) ).

% borel_measurable_const
thf(fact_721_borel__measurable__const,axiom,
    ! [C: nat,M: sigma_measure_real] :
      ( member_real_nat
      @ ^ [X4: real] : C
      @ ( sigma_6315060578831106510al_nat @ M @ borel_8449730974584783410el_nat ) ) ).

% borel_measurable_const
thf(fact_722_borel__measurable__const,axiom,
    ! [C: nat,M: sigma_measure_a] :
      ( member_a_nat
      @ ^ [X4: a] : C
      @ ( sigma_73150082625557118_a_nat @ M @ borel_8449730974584783410el_nat ) ) ).

% borel_measurable_const
thf(fact_723_borel__measurable__const,axiom,
    ! [C: $o,M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : C
      @ ( sigma_measurable_a_o @ M @ borel_5500255247093592246orel_o ) ) ).

% borel_measurable_const
thf(fact_724_measurable__const,axiom,
    ! [C: b,M2: sigma_measure_b,M: sigma_measure_real] :
      ( ( member_b @ C @ ( sigma_space_b @ M2 ) )
     => ( member_real_b
        @ ^ [X4: real] : C
        @ ( sigma_523072396149930113real_b @ M @ M2 ) ) ) ).

% measurable_const
thf(fact_725_measurable__const,axiom,
    ! [C: a,M2: sigma_measure_a,M: sigma_measure_real] :
      ( ( member_a @ C @ ( sigma_space_a @ M2 ) )
     => ( member_real_a
        @ ^ [X4: real] : C
        @ ( sigma_523072396149930112real_a @ M @ M2 ) ) ) ).

% measurable_const
thf(fact_726_measurable__const,axiom,
    ! [C: nat,M2: sigma_measure_nat,M: sigma_measure_real] :
      ( ( member_nat @ C @ ( sigma_space_nat @ M2 ) )
     => ( member_real_nat
        @ ^ [X4: real] : C
        @ ( sigma_6315060578831106510al_nat @ M @ M2 ) ) ) ).

% measurable_const
thf(fact_727_measurable__const,axiom,
    ! [C: complex,M2: sigma_3077487657436305159omplex,M: sigma_measure_a] :
      ( ( member_complex @ C @ ( sigma_space_complex @ M2 ) )
     => ( member_a_complex
        @ ^ [X4: a] : C
        @ ( sigma_852363994732143452omplex @ M @ M2 ) ) ) ).

% measurable_const
thf(fact_728_measurable__const,axiom,
    ! [C: real,M2: sigma_measure_real,M: sigma_measure_a] :
      ( ( member_real @ C @ ( sigma_space_real @ M2 ) )
     => ( member_a_real
        @ ^ [X4: a] : C
        @ ( sigma_9116425665531756122a_real @ M @ M2 ) ) ) ).

% measurable_const
thf(fact_729_measurable__const,axiom,
    ! [C: $o,M2: sigma_measure_o,M: sigma_measure_a] :
      ( ( member_o @ C @ ( sigma_space_o @ M2 ) )
     => ( member_a_o
        @ ^ [X4: a] : C
        @ ( sigma_measurable_a_o @ M @ M2 ) ) ) ).

% measurable_const
thf(fact_730_measurable__const,axiom,
    ! [C: nat,M2: sigma_measure_nat,M: sigma_measure_a] :
      ( ( member_nat @ C @ ( sigma_space_nat @ M2 ) )
     => ( member_a_nat
        @ ^ [X4: a] : C
        @ ( sigma_73150082625557118_a_nat @ M @ M2 ) ) ) ).

% measurable_const
thf(fact_731_measurable__const,axiom,
    ! [C: a,M2: sigma_measure_a,M: sigma_measure_a] :
      ( ( member_a @ C @ ( sigma_space_a @ M2 ) )
     => ( member_a_a
        @ ^ [X4: a] : C
        @ ( sigma_measurable_a_a @ M @ M2 ) ) ) ).

% measurable_const
thf(fact_732_pred__count__space__const2,axiom,
    ! [F: real > a,M: sigma_measure_real,C: a] :
      ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) )
     => ( member_real_o
        @ ^ [X4: real] :
            ( C
            = ( F @ X4 ) )
        @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const2
thf(fact_733_pred__count__space__const2,axiom,
    ! [F: a > a,M: sigma_measure_a,C: a] :
      ( ( member_a_a @ F @ ( sigma_measurable_a_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( C
            = ( F @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const2
thf(fact_734_pred__count__space__const2,axiom,
    ! [F: a > real,M: sigma_measure_a,C: real] :
      ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M @ ( sigma_8508918144308765139e_real @ top_top_set_real ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( C
            = ( F @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const2
thf(fact_735_pred__count__space__const2,axiom,
    ! [F: a > $o,M: sigma_measure_a,C: $o] :
      ( ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( C
            = ( F @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const2
thf(fact_736_pred__count__space__const2,axiom,
    ! [F: real > nat,M: sigma_measure_real,C: nat] :
      ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) )
     => ( member_real_o
        @ ^ [X4: real] :
            ( C
            = ( F @ X4 ) )
        @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const2
thf(fact_737_pred__count__space__const2,axiom,
    ! [F: a > nat,M: sigma_measure_a,C: nat] :
      ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( C
            = ( F @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const2
thf(fact_738_pred__count__space__const2,axiom,
    ! [F: a > extend8495563244428889912nnreal,M: sigma_measure_a,C: extend8495563244428889912nnreal] :
      ( ( member298456594901751504nnreal @ F @ ( sigma_214952329563889126nnreal @ M @ ( sigma_7204664791115113951nnreal @ top_to7994903218803871134nnreal ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( C
            = ( F @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const2
thf(fact_739_pred__count__space__const2,axiom,
    ! [F: a > complex,M: sigma_measure_a,C: complex] :
      ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ M @ ( sigma_3977070789342921045omplex @ top_top_set_complex ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( C
            = ( F @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const2
thf(fact_740_pred__count__space__const2,axiom,
    ! [F: real > b,M: sigma_measure_real,C: b] :
      ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ ( sigma_count_space_b @ top_top_set_b ) ) )
     => ( member_real_o
        @ ^ [X4: real] :
            ( C
            = ( F @ X4 ) )
        @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const2
thf(fact_741_pred__count__space__const2,axiom,
    ! [F: a > b,M: sigma_measure_a,C: b] :
      ( ( member_a_b @ F @ ( sigma_measurable_a_b @ M @ ( sigma_count_space_b @ top_top_set_b ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( C
            = ( F @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const2
thf(fact_742_pred__count__space__const1,axiom,
    ! [F: real > a,M: sigma_measure_real,C: a] :
      ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) )
     => ( member_real_o
        @ ^ [X4: real] :
            ( ( F @ X4 )
            = C )
        @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const1
thf(fact_743_pred__count__space__const1,axiom,
    ! [F: a > a,M: sigma_measure_a,C: a] :
      ( ( member_a_a @ F @ ( sigma_measurable_a_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( ( F @ X4 )
            = C )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const1
thf(fact_744_pred__count__space__const1,axiom,
    ! [F: a > real,M: sigma_measure_a,C: real] :
      ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M @ ( sigma_8508918144308765139e_real @ top_top_set_real ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( ( F @ X4 )
            = C )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const1
thf(fact_745_pred__count__space__const1,axiom,
    ! [F: a > $o,M: sigma_measure_a,C: $o] :
      ( ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( ( F @ X4 )
            = C )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const1
thf(fact_746_pred__count__space__const1,axiom,
    ! [F: real > nat,M: sigma_measure_real,C: nat] :
      ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) )
     => ( member_real_o
        @ ^ [X4: real] :
            ( ( F @ X4 )
            = C )
        @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const1
thf(fact_747_pred__count__space__const1,axiom,
    ! [F: a > nat,M: sigma_measure_a,C: nat] :
      ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( ( F @ X4 )
            = C )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const1
thf(fact_748_pred__count__space__const1,axiom,
    ! [F: a > extend8495563244428889912nnreal,M: sigma_measure_a,C: extend8495563244428889912nnreal] :
      ( ( member298456594901751504nnreal @ F @ ( sigma_214952329563889126nnreal @ M @ ( sigma_7204664791115113951nnreal @ top_to7994903218803871134nnreal ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( ( F @ X4 )
            = C )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const1
thf(fact_749_pred__count__space__const1,axiom,
    ! [F: a > complex,M: sigma_measure_a,C: complex] :
      ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ M @ ( sigma_3977070789342921045omplex @ top_top_set_complex ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( ( F @ X4 )
            = C )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const1
thf(fact_750_pred__count__space__const1,axiom,
    ! [F: real > b,M: sigma_measure_real,C: b] :
      ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ ( sigma_count_space_b @ top_top_set_b ) ) )
     => ( member_real_o
        @ ^ [X4: real] :
            ( ( F @ X4 )
            = C )
        @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const1
thf(fact_751_pred__count__space__const1,axiom,
    ! [F: a > b,M: sigma_measure_a,C: b] :
      ( ( member_a_b @ F @ ( sigma_measurable_a_b @ M @ ( sigma_count_space_b @ top_top_set_b ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( ( F @ X4 )
            = C )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_count_space_const1
thf(fact_752_qbs__closed3__dest_H,axiom,
    ! [P: real > nat,Fi: nat > real > nat,X5: quasi_borel_nat] :
      ( ( member_real_nat @ P @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ borel_8449730974584783410el_nat ) )
     => ( ! [I2: nat] : ( member_real_nat @ ( Fi @ I2 ) @ ( qbs_Mx_nat @ X5 ) )
       => ( member_real_nat
          @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
          @ ( qbs_Mx_nat @ X5 ) ) ) ) ).

% qbs_closed3_dest'
thf(fact_753_qbs__closed3__dest_H,axiom,
    ! [P: real > nat,Fi: nat > real > a,X5: quasi_borel_a] :
      ( ( member_real_nat @ P @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ borel_8449730974584783410el_nat ) )
     => ( ! [I2: nat] : ( member_real_a @ ( Fi @ I2 ) @ ( qbs_Mx_a @ X5 ) )
       => ( member_real_a
          @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
          @ ( qbs_Mx_a @ X5 ) ) ) ) ).

% qbs_closed3_dest'
thf(fact_754_qbs__closed3__dest_H,axiom,
    ! [P: real > nat,Fi: nat > real > b,X5: quasi_borel_b] :
      ( ( member_real_nat @ P @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ borel_8449730974584783410el_nat ) )
     => ( ! [I2: nat] : ( member_real_b @ ( Fi @ I2 ) @ ( qbs_Mx_b @ X5 ) )
       => ( member_real_b
          @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
          @ ( qbs_Mx_b @ X5 ) ) ) ) ).

% qbs_closed3_dest'
thf(fact_755_measurable__restrict__space2,axiom,
    ! [F: real > b,M: sigma_measure_real,Omega: set_b,N: sigma_measure_b] :
      ( ( member_real_b @ F
        @ ( pi_real_b @ ( sigma_space_real @ M )
          @ ^ [Uu: real] : Omega ) )
     => ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ N ) )
       => ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ ( sigma_8692839461743104067pace_b @ N @ Omega ) ) ) ) ) ).

% measurable_restrict_space2
thf(fact_756_measurable__restrict__space2,axiom,
    ! [F: real > nat,M: sigma_measure_real,Omega: set_nat,N: sigma_measure_nat] :
      ( ( member_real_nat @ F
        @ ( pi_real_nat @ ( sigma_space_real @ M )
          @ ^ [Uu: real] : Omega ) )
     => ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M @ N ) )
       => ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M @ ( sigma_744083341818469772ce_nat @ N @ Omega ) ) ) ) ) ).

% measurable_restrict_space2
thf(fact_757_measurable__restrict__space2,axiom,
    ! [F: a > complex,M: sigma_measure_a,Omega: set_complex,N: sigma_3077487657436305159omplex] :
      ( ( member_a_complex @ F
        @ ( pi_a_complex @ ( sigma_space_a @ M )
          @ ^ [Uu: a] : Omega ) )
     => ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ M @ N ) )
       => ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ M @ ( sigma_216592511309337194omplex @ N @ Omega ) ) ) ) ) ).

% measurable_restrict_space2
thf(fact_758_measurable__restrict__space2,axiom,
    ! [F: a > real,M: sigma_measure_a,Omega: set_real,N: sigma_measure_real] :
      ( ( member_a_real @ F
        @ ( pi_a_real @ ( sigma_space_a @ M )
          @ ^ [Uu: a] : Omega ) )
     => ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M @ N ) )
       => ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M @ ( sigma_5414646170262037096e_real @ N @ Omega ) ) ) ) ) ).

% measurable_restrict_space2
thf(fact_759_measurable__restrict__space2,axiom,
    ! [F: a > $o,M: sigma_measure_a,Omega: set_o,N: sigma_measure_o] :
      ( ( member_a_o @ F
        @ ( pi_a_o @ ( sigma_space_a @ M )
          @ ^ [Uu: a] : Omega ) )
     => ( ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ N ) )
       => ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ ( sigma_8520893325391096540pace_o @ N @ Omega ) ) ) ) ) ).

% measurable_restrict_space2
thf(fact_760_measurable__restrict__space2,axiom,
    ! [F: a > nat,M: sigma_measure_a,Omega: set_nat,N: sigma_measure_nat] :
      ( ( member_a_nat @ F
        @ ( pi_a_nat @ ( sigma_space_a @ M )
          @ ^ [Uu: a] : Omega ) )
     => ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M @ N ) )
       => ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M @ ( sigma_744083341818469772ce_nat @ N @ Omega ) ) ) ) ) ).

% measurable_restrict_space2
thf(fact_761_measurable__restrict__space2,axiom,
    ! [F: nat > a,M: sigma_measure_nat,Omega: set_a,N: sigma_measure_a] :
      ( ( member_nat_a @ F
        @ ( pi_nat_a @ ( sigma_space_nat @ M )
          @ ^ [Uu: nat] : Omega ) )
     => ( ( member_nat_a @ F @ ( sigma_4105081583803843548_nat_a @ M @ N ) )
       => ( member_nat_a @ F @ ( sigma_4105081583803843548_nat_a @ M @ ( sigma_8692839461743104066pace_a @ N @ Omega ) ) ) ) ) ).

% measurable_restrict_space2
thf(fact_762_measurable__restrict__space2,axiom,
    ! [F: $o > a,M: sigma_measure_o,Omega: set_a,N: sigma_measure_a] :
      ( ( member_o_a @ F
        @ ( pi_o_a @ ( sigma_space_o @ M )
          @ ^ [Uu: $o] : Omega ) )
     => ( ( member_o_a @ F @ ( sigma_measurable_o_a @ M @ N ) )
       => ( member_o_a @ F @ ( sigma_measurable_o_a @ M @ ( sigma_8692839461743104066pace_a @ N @ Omega ) ) ) ) ) ).

% measurable_restrict_space2
thf(fact_763_measurable__restrict__space2,axiom,
    ! [F: extend8495563244428889912nnreal > a,M: sigma_7234349610311085201nnreal,Omega: set_a,N: sigma_measure_a] :
      ( ( member4924430693770431270real_a @ F
        @ ( pi_Ext7789591913556194873real_a @ ( sigma_3147302497200244656nnreal @ M )
          @ ^ [Uu: extend8495563244428889912nnreal] : Omega ) )
     => ( ( member4924430693770431270real_a @ F @ ( sigma_3031480723531659892real_a @ M @ N ) )
       => ( member4924430693770431270real_a @ F @ ( sigma_3031480723531659892real_a @ M @ ( sigma_8692839461743104066pace_a @ N @ Omega ) ) ) ) ) ).

% measurable_restrict_space2
thf(fact_764_measurable__restrict__space2,axiom,
    ! [F: real > a,M: sigma_measure_real,Omega: set_a,N: sigma_measure_a] :
      ( ( member_real_a @ F
        @ ( pi_real_a @ ( sigma_space_real @ M )
          @ ^ [Uu: real] : Omega ) )
     => ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ N ) )
       => ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ ( sigma_8692839461743104066pace_a @ N @ Omega ) ) ) ) ) ).

% measurable_restrict_space2
thf(fact_765_measurable__restrict__space2__iff,axiom,
    ! [F: real > b,M: sigma_measure_real,N: sigma_measure_b,Omega: set_b] :
      ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ ( sigma_8692839461743104067pace_b @ N @ Omega ) ) )
      = ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ N ) )
        & ( member_real_b @ F
          @ ( pi_real_b @ ( sigma_space_real @ M )
            @ ^ [Uu: real] : Omega ) ) ) ) ).

% measurable_restrict_space2_iff
thf(fact_766_measurable__restrict__space2__iff,axiom,
    ! [F: real > nat,M: sigma_measure_real,N: sigma_measure_nat,Omega: set_nat] :
      ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M @ ( sigma_744083341818469772ce_nat @ N @ Omega ) ) )
      = ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M @ N ) )
        & ( member_real_nat @ F
          @ ( pi_real_nat @ ( sigma_space_real @ M )
            @ ^ [Uu: real] : Omega ) ) ) ) ).

% measurable_restrict_space2_iff
thf(fact_767_measurable__restrict__space2__iff,axiom,
    ! [F: a > complex,M: sigma_measure_a,N: sigma_3077487657436305159omplex,Omega: set_complex] :
      ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ M @ ( sigma_216592511309337194omplex @ N @ Omega ) ) )
      = ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ M @ N ) )
        & ( member_a_complex @ F
          @ ( pi_a_complex @ ( sigma_space_a @ M )
            @ ^ [Uu: a] : Omega ) ) ) ) ).

% measurable_restrict_space2_iff
thf(fact_768_measurable__restrict__space2__iff,axiom,
    ! [F: a > real,M: sigma_measure_a,N: sigma_measure_real,Omega: set_real] :
      ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M @ ( sigma_5414646170262037096e_real @ N @ Omega ) ) )
      = ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M @ N ) )
        & ( member_a_real @ F
          @ ( pi_a_real @ ( sigma_space_a @ M )
            @ ^ [Uu: a] : Omega ) ) ) ) ).

% measurable_restrict_space2_iff
thf(fact_769_measurable__restrict__space2__iff,axiom,
    ! [F: a > $o,M: sigma_measure_a,N: sigma_measure_o,Omega: set_o] :
      ( ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ ( sigma_8520893325391096540pace_o @ N @ Omega ) ) )
      = ( ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ N ) )
        & ( member_a_o @ F
          @ ( pi_a_o @ ( sigma_space_a @ M )
            @ ^ [Uu: a] : Omega ) ) ) ) ).

% measurable_restrict_space2_iff
thf(fact_770_measurable__restrict__space2__iff,axiom,
    ! [F: a > nat,M: sigma_measure_a,N: sigma_measure_nat,Omega: set_nat] :
      ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M @ ( sigma_744083341818469772ce_nat @ N @ Omega ) ) )
      = ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M @ N ) )
        & ( member_a_nat @ F
          @ ( pi_a_nat @ ( sigma_space_a @ M )
            @ ^ [Uu: a] : Omega ) ) ) ) ).

% measurable_restrict_space2_iff
thf(fact_771_measurable__restrict__space2__iff,axiom,
    ! [F: nat > a,M: sigma_measure_nat,N: sigma_measure_a,Omega: set_a] :
      ( ( member_nat_a @ F @ ( sigma_4105081583803843548_nat_a @ M @ ( sigma_8692839461743104066pace_a @ N @ Omega ) ) )
      = ( ( member_nat_a @ F @ ( sigma_4105081583803843548_nat_a @ M @ N ) )
        & ( member_nat_a @ F
          @ ( pi_nat_a @ ( sigma_space_nat @ M )
            @ ^ [Uu: nat] : Omega ) ) ) ) ).

% measurable_restrict_space2_iff
thf(fact_772_measurable__restrict__space2__iff,axiom,
    ! [F: $o > a,M: sigma_measure_o,N: sigma_measure_a,Omega: set_a] :
      ( ( member_o_a @ F @ ( sigma_measurable_o_a @ M @ ( sigma_8692839461743104066pace_a @ N @ Omega ) ) )
      = ( ( member_o_a @ F @ ( sigma_measurable_o_a @ M @ N ) )
        & ( member_o_a @ F
          @ ( pi_o_a @ ( sigma_space_o @ M )
            @ ^ [Uu: $o] : Omega ) ) ) ) ).

% measurable_restrict_space2_iff
thf(fact_773_measurable__restrict__space2__iff,axiom,
    ! [F: extend8495563244428889912nnreal > a,M: sigma_7234349610311085201nnreal,N: sigma_measure_a,Omega: set_a] :
      ( ( member4924430693770431270real_a @ F @ ( sigma_3031480723531659892real_a @ M @ ( sigma_8692839461743104066pace_a @ N @ Omega ) ) )
      = ( ( member4924430693770431270real_a @ F @ ( sigma_3031480723531659892real_a @ M @ N ) )
        & ( member4924430693770431270real_a @ F
          @ ( pi_Ext7789591913556194873real_a @ ( sigma_3147302497200244656nnreal @ M )
            @ ^ [Uu: extend8495563244428889912nnreal] : Omega ) ) ) ) ).

% measurable_restrict_space2_iff
thf(fact_774_measurable__restrict__space2__iff,axiom,
    ! [F: real > a,M: sigma_measure_real,N: sigma_measure_a,Omega: set_a] :
      ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ ( sigma_8692839461743104066pace_a @ N @ Omega ) ) )
      = ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ N ) )
        & ( member_real_a @ F
          @ ( pi_real_a @ ( sigma_space_real @ M )
            @ ^ [Uu: real] : Omega ) ) ) ) ).

% measurable_restrict_space2_iff
thf(fact_775_borel__measurable__inf,axiom,
    ! [F: a > real,M: sigma_measure_a,G: a > real] :
      ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) )
     => ( ( member_a_real @ G @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) )
       => ( member_a_real
          @ ^ [X4: a] : ( inf_inf_real @ ( G @ X4 ) @ ( F @ X4 ) )
          @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) ) ) ).

% borel_measurable_inf
thf(fact_776_borel__measurable__inf,axiom,
    ! [F: real > nat,M: sigma_measure_real,G: real > nat] :
      ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M @ borel_8449730974584783410el_nat ) )
     => ( ( member_real_nat @ G @ ( sigma_6315060578831106510al_nat @ M @ borel_8449730974584783410el_nat ) )
       => ( member_real_nat
          @ ^ [X4: real] : ( inf_inf_nat @ ( G @ X4 ) @ ( F @ X4 ) )
          @ ( sigma_6315060578831106510al_nat @ M @ borel_8449730974584783410el_nat ) ) ) ) ).

% borel_measurable_inf
thf(fact_777_borel__measurable__inf,axiom,
    ! [F: a > nat,M: sigma_measure_a,G: a > nat] :
      ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M @ borel_8449730974584783410el_nat ) )
     => ( ( member_a_nat @ G @ ( sigma_73150082625557118_a_nat @ M @ borel_8449730974584783410el_nat ) )
       => ( member_a_nat
          @ ^ [X4: a] : ( inf_inf_nat @ ( G @ X4 ) @ ( F @ X4 ) )
          @ ( sigma_73150082625557118_a_nat @ M @ borel_8449730974584783410el_nat ) ) ) ) ).

% borel_measurable_inf
thf(fact_778_measurable__count__space__const,axiom,
    ! [C: a,M: sigma_measure_real] :
      ( member_real_a
      @ ^ [X4: real] : C
      @ ( sigma_523072396149930112real_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) ) ).

% measurable_count_space_const
thf(fact_779_measurable__count__space__const,axiom,
    ! [C: a,M: sigma_measure_a] :
      ( member_a_a
      @ ^ [X4: a] : C
      @ ( sigma_measurable_a_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) ) ).

% measurable_count_space_const
thf(fact_780_measurable__count__space__const,axiom,
    ! [C: real,M: sigma_measure_a] :
      ( member_a_real
      @ ^ [X4: a] : C
      @ ( sigma_9116425665531756122a_real @ M @ ( sigma_8508918144308765139e_real @ top_top_set_real ) ) ) ).

% measurable_count_space_const
thf(fact_781_measurable__count__space__const,axiom,
    ! [C: $o,M: sigma_measure_a] :
      ( member_a_o
      @ ^ [X4: a] : C
      @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ).

% measurable_count_space_const
thf(fact_782_measurable__count__space__const,axiom,
    ! [C: nat,M: sigma_measure_real] :
      ( member_real_nat
      @ ^ [X4: real] : C
      @ ( sigma_6315060578831106510al_nat @ M @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) ) ).

% measurable_count_space_const
thf(fact_783_measurable__count__space__const,axiom,
    ! [C: nat,M: sigma_measure_a] :
      ( member_a_nat
      @ ^ [X4: a] : C
      @ ( sigma_73150082625557118_a_nat @ M @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) ) ).

% measurable_count_space_const
thf(fact_784_measurable__count__space__const,axiom,
    ! [C: complex,M: sigma_measure_a] :
      ( member_a_complex
      @ ^ [X4: a] : C
      @ ( sigma_852363994732143452omplex @ M @ ( sigma_3977070789342921045omplex @ top_top_set_complex ) ) ) ).

% measurable_count_space_const
thf(fact_785_measurable__count__space__const,axiom,
    ! [C: b,M: sigma_measure_real] :
      ( member_real_b
      @ ^ [X4: real] : C
      @ ( sigma_523072396149930113real_b @ M @ ( sigma_count_space_b @ top_top_set_b ) ) ) ).

% measurable_count_space_const
thf(fact_786_measurable__compose__countable,axiom,
    ! [F: $o > real > b,M: sigma_measure_real,N: sigma_measure_b,G: real > $o] :
      ( ! [I2: $o] : ( member_real_b @ ( F @ I2 ) @ ( sigma_523072396149930113real_b @ M @ N ) )
     => ( ( member_real_o @ G @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_real_b
          @ ^ [X4: real] : ( F @ ( G @ X4 ) @ X4 )
          @ ( sigma_523072396149930113real_b @ M @ N ) ) ) ) ).

% measurable_compose_countable
thf(fact_787_measurable__compose__countable,axiom,
    ! [F: $o > real > a,M: sigma_measure_real,N: sigma_measure_a,G: real > $o] :
      ( ! [I2: $o] : ( member_real_a @ ( F @ I2 ) @ ( sigma_523072396149930112real_a @ M @ N ) )
     => ( ( member_real_o @ G @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_real_a
          @ ^ [X4: real] : ( F @ ( G @ X4 ) @ X4 )
          @ ( sigma_523072396149930112real_a @ M @ N ) ) ) ) ).

% measurable_compose_countable
thf(fact_788_measurable__compose__countable,axiom,
    ! [F: $o > real > nat,M: sigma_measure_real,N: sigma_measure_nat,G: real > $o] :
      ( ! [I2: $o] : ( member_real_nat @ ( F @ I2 ) @ ( sigma_6315060578831106510al_nat @ M @ N ) )
     => ( ( member_real_o @ G @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_real_nat
          @ ^ [X4: real] : ( F @ ( G @ X4 ) @ X4 )
          @ ( sigma_6315060578831106510al_nat @ M @ N ) ) ) ) ).

% measurable_compose_countable
thf(fact_789_measurable__compose__countable,axiom,
    ! [F: $o > a > complex,M: sigma_measure_a,N: sigma_3077487657436305159omplex,G: a > $o] :
      ( ! [I2: $o] : ( member_a_complex @ ( F @ I2 ) @ ( sigma_852363994732143452omplex @ M @ N ) )
     => ( ( member_a_o @ G @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_complex
          @ ^ [X4: a] : ( F @ ( G @ X4 ) @ X4 )
          @ ( sigma_852363994732143452omplex @ M @ N ) ) ) ) ).

% measurable_compose_countable
thf(fact_790_measurable__compose__countable,axiom,
    ! [F: $o > a > real,M: sigma_measure_a,N: sigma_measure_real,G: a > $o] :
      ( ! [I2: $o] : ( member_a_real @ ( F @ I2 ) @ ( sigma_9116425665531756122a_real @ M @ N ) )
     => ( ( member_a_o @ G @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_real
          @ ^ [X4: a] : ( F @ ( G @ X4 ) @ X4 )
          @ ( sigma_9116425665531756122a_real @ M @ N ) ) ) ) ).

% measurable_compose_countable
thf(fact_791_measurable__compose__countable,axiom,
    ! [F: $o > a > $o,M: sigma_measure_a,N: sigma_measure_o,G: a > $o] :
      ( ! [I2: $o] : ( member_a_o @ ( F @ I2 ) @ ( sigma_measurable_a_o @ M @ N ) )
     => ( ( member_a_o @ G @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] : ( F @ ( G @ X4 ) @ X4 )
          @ ( sigma_measurable_a_o @ M @ N ) ) ) ) ).

% measurable_compose_countable
thf(fact_792_measurable__compose__countable,axiom,
    ! [F: $o > a > nat,M: sigma_measure_a,N: sigma_measure_nat,G: a > $o] :
      ( ! [I2: $o] : ( member_a_nat @ ( F @ I2 ) @ ( sigma_73150082625557118_a_nat @ M @ N ) )
     => ( ( member_a_o @ G @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_nat
          @ ^ [X4: a] : ( F @ ( G @ X4 ) @ X4 )
          @ ( sigma_73150082625557118_a_nat @ M @ N ) ) ) ) ).

% measurable_compose_countable
thf(fact_793_measurable__compose__countable,axiom,
    ! [F: $o > a > a,M: sigma_measure_a,N: sigma_measure_a,G: a > $o] :
      ( ! [I2: $o] : ( member_a_a @ ( F @ I2 ) @ ( sigma_measurable_a_a @ M @ N ) )
     => ( ( member_a_o @ G @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_a
          @ ^ [X4: a] : ( F @ ( G @ X4 ) @ X4 )
          @ ( sigma_measurable_a_a @ M @ N ) ) ) ) ).

% measurable_compose_countable
thf(fact_794_measurable__compose__countable,axiom,
    ! [F: nat > real > b,M: sigma_measure_real,N: sigma_measure_b,G: real > nat] :
      ( ! [I2: nat] : ( member_real_b @ ( F @ I2 ) @ ( sigma_523072396149930113real_b @ M @ N ) )
     => ( ( member_real_nat @ G @ ( sigma_6315060578831106510al_nat @ M @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) )
       => ( member_real_b
          @ ^ [X4: real] : ( F @ ( G @ X4 ) @ X4 )
          @ ( sigma_523072396149930113real_b @ M @ N ) ) ) ) ).

% measurable_compose_countable
thf(fact_795_measurable__compose__countable,axiom,
    ! [F: nat > real > a,M: sigma_measure_real,N: sigma_measure_a,G: real > nat] :
      ( ! [I2: nat] : ( member_real_a @ ( F @ I2 ) @ ( sigma_523072396149930112real_a @ M @ N ) )
     => ( ( member_real_nat @ G @ ( sigma_6315060578831106510al_nat @ M @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) )
       => ( member_real_a
          @ ^ [X4: real] : ( F @ ( G @ X4 ) @ X4 )
          @ ( sigma_523072396149930112real_a @ M @ N ) ) ) ) ).

% measurable_compose_countable
thf(fact_796_measurable__compose__countable_H,axiom,
    ! [I3: set_a,F: a > real > b,M: sigma_measure_real,N: sigma_measure_b,G: real > a] :
      ( ! [I2: a] :
          ( ( member_a @ I2 @ I3 )
         => ( member_real_b @ ( F @ I2 ) @ ( sigma_523072396149930113real_b @ M @ N ) ) )
     => ( ( member_real_a @ G @ ( sigma_523072396149930112real_a @ M @ ( sigma_count_space_a @ I3 ) ) )
       => ( ( counta4098120917673242425able_a @ I3 )
         => ( member_real_b
            @ ^ [X4: real] : ( F @ ( G @ X4 ) @ X4 )
            @ ( sigma_523072396149930113real_b @ M @ N ) ) ) ) ) ).

% measurable_compose_countable'
thf(fact_797_measurable__compose__countable_H,axiom,
    ! [I3: set_a,F: a > real > a,M: sigma_measure_real,N: sigma_measure_a,G: real > a] :
      ( ! [I2: a] :
          ( ( member_a @ I2 @ I3 )
         => ( member_real_a @ ( F @ I2 ) @ ( sigma_523072396149930112real_a @ M @ N ) ) )
     => ( ( member_real_a @ G @ ( sigma_523072396149930112real_a @ M @ ( sigma_count_space_a @ I3 ) ) )
       => ( ( counta4098120917673242425able_a @ I3 )
         => ( member_real_a
            @ ^ [X4: real] : ( F @ ( G @ X4 ) @ X4 )
            @ ( sigma_523072396149930112real_a @ M @ N ) ) ) ) ) ).

% measurable_compose_countable'
thf(fact_798_measurable__compose__countable_H,axiom,
    ! [I3: set_a,F: a > real > nat,M: sigma_measure_real,N: sigma_measure_nat,G: real > a] :
      ( ! [I2: a] :
          ( ( member_a @ I2 @ I3 )
         => ( member_real_nat @ ( F @ I2 ) @ ( sigma_6315060578831106510al_nat @ M @ N ) ) )
     => ( ( member_real_a @ G @ ( sigma_523072396149930112real_a @ M @ ( sigma_count_space_a @ I3 ) ) )
       => ( ( counta4098120917673242425able_a @ I3 )
         => ( member_real_nat
            @ ^ [X4: real] : ( F @ ( G @ X4 ) @ X4 )
            @ ( sigma_6315060578831106510al_nat @ M @ N ) ) ) ) ) ).

% measurable_compose_countable'
thf(fact_799_measurable__compose__countable_H,axiom,
    ! [I3: set_a,F: a > a > complex,M: sigma_measure_a,N: sigma_3077487657436305159omplex,G: a > a] :
      ( ! [I2: a] :
          ( ( member_a @ I2 @ I3 )
         => ( member_a_complex @ ( F @ I2 ) @ ( sigma_852363994732143452omplex @ M @ N ) ) )
     => ( ( member_a_a @ G @ ( sigma_measurable_a_a @ M @ ( sigma_count_space_a @ I3 ) ) )
       => ( ( counta4098120917673242425able_a @ I3 )
         => ( member_a_complex
            @ ^ [X4: a] : ( F @ ( G @ X4 ) @ X4 )
            @ ( sigma_852363994732143452omplex @ M @ N ) ) ) ) ) ).

% measurable_compose_countable'
thf(fact_800_measurable__compose__countable_H,axiom,
    ! [I3: set_a,F: a > a > real,M: sigma_measure_a,N: sigma_measure_real,G: a > a] :
      ( ! [I2: a] :
          ( ( member_a @ I2 @ I3 )
         => ( member_a_real @ ( F @ I2 ) @ ( sigma_9116425665531756122a_real @ M @ N ) ) )
     => ( ( member_a_a @ G @ ( sigma_measurable_a_a @ M @ ( sigma_count_space_a @ I3 ) ) )
       => ( ( counta4098120917673242425able_a @ I3 )
         => ( member_a_real
            @ ^ [X4: a] : ( F @ ( G @ X4 ) @ X4 )
            @ ( sigma_9116425665531756122a_real @ M @ N ) ) ) ) ) ).

% measurable_compose_countable'
thf(fact_801_measurable__compose__countable_H,axiom,
    ! [I3: set_a,F: a > a > $o,M: sigma_measure_a,N: sigma_measure_o,G: a > a] :
      ( ! [I2: a] :
          ( ( member_a @ I2 @ I3 )
         => ( member_a_o @ ( F @ I2 ) @ ( sigma_measurable_a_o @ M @ N ) ) )
     => ( ( member_a_a @ G @ ( sigma_measurable_a_a @ M @ ( sigma_count_space_a @ I3 ) ) )
       => ( ( counta4098120917673242425able_a @ I3 )
         => ( member_a_o
            @ ^ [X4: a] : ( F @ ( G @ X4 ) @ X4 )
            @ ( sigma_measurable_a_o @ M @ N ) ) ) ) ) ).

% measurable_compose_countable'
thf(fact_802_measurable__compose__countable_H,axiom,
    ! [I3: set_a,F: a > a > nat,M: sigma_measure_a,N: sigma_measure_nat,G: a > a] :
      ( ! [I2: a] :
          ( ( member_a @ I2 @ I3 )
         => ( member_a_nat @ ( F @ I2 ) @ ( sigma_73150082625557118_a_nat @ M @ N ) ) )
     => ( ( member_a_a @ G @ ( sigma_measurable_a_a @ M @ ( sigma_count_space_a @ I3 ) ) )
       => ( ( counta4098120917673242425able_a @ I3 )
         => ( member_a_nat
            @ ^ [X4: a] : ( F @ ( G @ X4 ) @ X4 )
            @ ( sigma_73150082625557118_a_nat @ M @ N ) ) ) ) ) ).

% measurable_compose_countable'
thf(fact_803_measurable__compose__countable_H,axiom,
    ! [I3: set_a,F: a > a > a,M: sigma_measure_a,N: sigma_measure_a,G: a > a] :
      ( ! [I2: a] :
          ( ( member_a @ I2 @ I3 )
         => ( member_a_a @ ( F @ I2 ) @ ( sigma_measurable_a_a @ M @ N ) ) )
     => ( ( member_a_a @ G @ ( sigma_measurable_a_a @ M @ ( sigma_count_space_a @ I3 ) ) )
       => ( ( counta4098120917673242425able_a @ I3 )
         => ( member_a_a
            @ ^ [X4: a] : ( F @ ( G @ X4 ) @ X4 )
            @ ( sigma_measurable_a_a @ M @ N ) ) ) ) ) ).

% measurable_compose_countable'
thf(fact_804_measurable__compose__countable_H,axiom,
    ! [I3: set_real,F: real > real > b,M: sigma_measure_real,N: sigma_measure_b,G: real > real] :
      ( ! [I2: real] :
          ( ( member_real @ I2 @ I3 )
         => ( member_real_b @ ( F @ I2 ) @ ( sigma_523072396149930113real_b @ M @ N ) ) )
     => ( ( member_real_real @ G @ ( sigma_5267869275261027754l_real @ M @ ( sigma_8508918144308765139e_real @ I3 ) ) )
       => ( ( counta7319604579010473777e_real @ I3 )
         => ( member_real_b
            @ ^ [X4: real] : ( F @ ( G @ X4 ) @ X4 )
            @ ( sigma_523072396149930113real_b @ M @ N ) ) ) ) ) ).

% measurable_compose_countable'
thf(fact_805_measurable__compose__countable_H,axiom,
    ! [I3: set_real,F: real > real > a,M: sigma_measure_real,N: sigma_measure_a,G: real > real] :
      ( ! [I2: real] :
          ( ( member_real @ I2 @ I3 )
         => ( member_real_a @ ( F @ I2 ) @ ( sigma_523072396149930112real_a @ M @ N ) ) )
     => ( ( member_real_real @ G @ ( sigma_5267869275261027754l_real @ M @ ( sigma_8508918144308765139e_real @ I3 ) ) )
       => ( ( counta7319604579010473777e_real @ I3 )
         => ( member_real_a
            @ ^ [X4: real] : ( F @ ( G @ X4 ) @ X4 )
            @ ( sigma_523072396149930112real_a @ M @ N ) ) ) ) ) ).

% measurable_compose_countable'
thf(fact_806_measurable__compose__countable__restrict,axiom,
    ! [P: a > $o,F: real > a,M: sigma_measure_real,Q: a > real > $o] :
      ( ( counta4098120917673242425able_a @ ( collect_a @ P ) )
     => ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) )
       => ( ! [I2: a] :
              ( ( P @ I2 )
             => ( member_real_o @ ( Q @ I2 ) @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
         => ( member_real_o
            @ ^ [X4: real] :
                ( ( P @ ( F @ X4 ) )
                & ( Q @ ( F @ X4 ) @ X4 ) )
            @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ) ).

% measurable_compose_countable_restrict
thf(fact_807_measurable__compose__countable__restrict,axiom,
    ! [P: a > $o,F: a > a,M: sigma_measure_a,Q: a > a > $o] :
      ( ( counta4098120917673242425able_a @ ( collect_a @ P ) )
     => ( ( member_a_a @ F @ ( sigma_measurable_a_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) )
       => ( ! [I2: a] :
              ( ( P @ I2 )
             => ( member_a_o @ ( Q @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
         => ( member_a_o
            @ ^ [X4: a] :
                ( ( P @ ( F @ X4 ) )
                & ( Q @ ( F @ X4 ) @ X4 ) )
            @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ) ).

% measurable_compose_countable_restrict
thf(fact_808_measurable__compose__countable__restrict,axiom,
    ! [P: real > $o,F: a > real,M: sigma_measure_a,Q: real > a > $o] :
      ( ( counta7319604579010473777e_real @ ( collect_real @ P ) )
     => ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M @ ( sigma_8508918144308765139e_real @ top_top_set_real ) ) )
       => ( ! [I2: real] :
              ( ( P @ I2 )
             => ( member_a_o @ ( Q @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
         => ( member_a_o
            @ ^ [X4: a] :
                ( ( P @ ( F @ X4 ) )
                & ( Q @ ( F @ X4 ) @ X4 ) )
            @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ) ).

% measurable_compose_countable_restrict
thf(fact_809_measurable__compose__countable__restrict,axiom,
    ! [P: $o > $o,F: a > $o,M: sigma_measure_a,Q: $o > a > $o] :
      ( ( counta5976203206615340371able_o @ ( collect_o @ P ) )
     => ( ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( ! [I2: $o] :
              ( ( P @ I2 )
             => ( member_a_o @ ( Q @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
         => ( member_a_o
            @ ^ [X4: a] :
                ( ( P @ ( F @ X4 ) )
                & ( Q @ ( F @ X4 ) @ X4 ) )
            @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ) ).

% measurable_compose_countable_restrict
thf(fact_810_measurable__compose__countable__restrict,axiom,
    ! [P: nat > $o,F: real > nat,M: sigma_measure_real,Q: nat > real > $o] :
      ( ( counta1168086296615599829le_nat @ ( collect_nat @ P ) )
     => ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) )
       => ( ! [I2: nat] :
              ( ( P @ I2 )
             => ( member_real_o @ ( Q @ I2 ) @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
         => ( member_real_o
            @ ^ [X4: real] :
                ( ( P @ ( F @ X4 ) )
                & ( Q @ ( F @ X4 ) @ X4 ) )
            @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ) ).

% measurable_compose_countable_restrict
thf(fact_811_measurable__compose__countable__restrict,axiom,
    ! [P: nat > $o,F: a > nat,M: sigma_measure_a,Q: nat > a > $o] :
      ( ( counta1168086296615599829le_nat @ ( collect_nat @ P ) )
     => ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) )
       => ( ! [I2: nat] :
              ( ( P @ I2 )
             => ( member_a_o @ ( Q @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
         => ( member_a_o
            @ ^ [X4: a] :
                ( ( P @ ( F @ X4 ) )
                & ( Q @ ( F @ X4 ) @ X4 ) )
            @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ) ).

% measurable_compose_countable_restrict
thf(fact_812_measurable__compose__countable__restrict,axiom,
    ! [P: extend8495563244428889912nnreal > $o,F: a > extend8495563244428889912nnreal,M: sigma_measure_a,Q: extend8495563244428889912nnreal > a > $o] :
      ( ( counta8439243037236335165nnreal @ ( collec6648975593938027277nnreal @ P ) )
     => ( ( member298456594901751504nnreal @ F @ ( sigma_214952329563889126nnreal @ M @ ( sigma_7204664791115113951nnreal @ top_to7994903218803871134nnreal ) ) )
       => ( ! [I2: extend8495563244428889912nnreal] :
              ( ( P @ I2 )
             => ( member_a_o @ ( Q @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
         => ( member_a_o
            @ ^ [X4: a] :
                ( ( P @ ( F @ X4 ) )
                & ( Q @ ( F @ X4 ) @ X4 ) )
            @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ) ).

% measurable_compose_countable_restrict
thf(fact_813_measurable__compose__countable__restrict,axiom,
    ! [P: complex > $o,F: a > complex,M: sigma_measure_a,Q: complex > a > $o] :
      ( ( counta5113917769705169331omplex @ ( collect_complex @ P ) )
     => ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ M @ ( sigma_3977070789342921045omplex @ top_top_set_complex ) ) )
       => ( ! [I2: complex] :
              ( ( P @ I2 )
             => ( member_a_o @ ( Q @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
         => ( member_a_o
            @ ^ [X4: a] :
                ( ( P @ ( F @ X4 ) )
                & ( Q @ ( F @ X4 ) @ X4 ) )
            @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ) ).

% measurable_compose_countable_restrict
thf(fact_814_measurable__compose__countable__restrict,axiom,
    ! [P: b > $o,F: real > b,M: sigma_measure_real,Q: b > real > $o] :
      ( ( counta4098120917673242426able_b @ ( collect_b @ P ) )
     => ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M @ ( sigma_count_space_b @ top_top_set_b ) ) )
       => ( ! [I2: b] :
              ( ( P @ I2 )
             => ( member_real_o @ ( Q @ I2 ) @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
         => ( member_real_o
            @ ^ [X4: real] :
                ( ( P @ ( F @ X4 ) )
                & ( Q @ ( F @ X4 ) @ X4 ) )
            @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ) ).

% measurable_compose_countable_restrict
thf(fact_815_measurable__compose__countable__restrict,axiom,
    ! [P: b > $o,F: a > b,M: sigma_measure_a,Q: b > a > $o] :
      ( ( counta4098120917673242426able_b @ ( collect_b @ P ) )
     => ( ( member_a_b @ F @ ( sigma_measurable_a_b @ M @ ( sigma_count_space_b @ top_top_set_b ) ) )
       => ( ! [I2: b] :
              ( ( P @ I2 )
             => ( member_a_o @ ( Q @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
         => ( member_a_o
            @ ^ [X4: a] :
                ( ( P @ ( F @ X4 ) )
                & ( Q @ ( F @ X4 ) @ X4 ) )
            @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ) ).

% measurable_compose_countable_restrict
thf(fact_816_qbs__closed3__dest2,axiom,
    ! [I3: set_a,P: real > a,Fi: a > real > nat,X5: quasi_borel_nat] :
      ( ( counta4098120917673242425able_a @ I3 )
     => ( ( member_real_a @ P @ ( sigma_523072396149930112real_a @ borel_5078946678739801102l_real @ ( sigma_count_space_a @ I3 ) ) )
       => ( ! [I2: a] :
              ( ( member_a @ I2 @ I3 )
             => ( member_real_nat @ ( Fi @ I2 ) @ ( qbs_Mx_nat @ X5 ) ) )
         => ( member_real_nat
            @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
            @ ( qbs_Mx_nat @ X5 ) ) ) ) ) ).

% qbs_closed3_dest2
thf(fact_817_qbs__closed3__dest2,axiom,
    ! [I3: set_a,P: real > a,Fi: a > real > a,X5: quasi_borel_a] :
      ( ( counta4098120917673242425able_a @ I3 )
     => ( ( member_real_a @ P @ ( sigma_523072396149930112real_a @ borel_5078946678739801102l_real @ ( sigma_count_space_a @ I3 ) ) )
       => ( ! [I2: a] :
              ( ( member_a @ I2 @ I3 )
             => ( member_real_a @ ( Fi @ I2 ) @ ( qbs_Mx_a @ X5 ) ) )
         => ( member_real_a
            @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
            @ ( qbs_Mx_a @ X5 ) ) ) ) ) ).

% qbs_closed3_dest2
thf(fact_818_qbs__closed3__dest2,axiom,
    ! [I3: set_a,P: real > a,Fi: a > real > b,X5: quasi_borel_b] :
      ( ( counta4098120917673242425able_a @ I3 )
     => ( ( member_real_a @ P @ ( sigma_523072396149930112real_a @ borel_5078946678739801102l_real @ ( sigma_count_space_a @ I3 ) ) )
       => ( ! [I2: a] :
              ( ( member_a @ I2 @ I3 )
             => ( member_real_b @ ( Fi @ I2 ) @ ( qbs_Mx_b @ X5 ) ) )
         => ( member_real_b
            @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
            @ ( qbs_Mx_b @ X5 ) ) ) ) ) ).

% qbs_closed3_dest2
thf(fact_819_qbs__closed3__dest2,axiom,
    ! [I3: set_real,P: real > real,Fi: real > real > nat,X5: quasi_borel_nat] :
      ( ( counta7319604579010473777e_real @ I3 )
     => ( ( member_real_real @ P @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ ( sigma_8508918144308765139e_real @ I3 ) ) )
       => ( ! [I2: real] :
              ( ( member_real @ I2 @ I3 )
             => ( member_real_nat @ ( Fi @ I2 ) @ ( qbs_Mx_nat @ X5 ) ) )
         => ( member_real_nat
            @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
            @ ( qbs_Mx_nat @ X5 ) ) ) ) ) ).

% qbs_closed3_dest2
thf(fact_820_qbs__closed3__dest2,axiom,
    ! [I3: set_real,P: real > real,Fi: real > real > a,X5: quasi_borel_a] :
      ( ( counta7319604579010473777e_real @ I3 )
     => ( ( member_real_real @ P @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ ( sigma_8508918144308765139e_real @ I3 ) ) )
       => ( ! [I2: real] :
              ( ( member_real @ I2 @ I3 )
             => ( member_real_a @ ( Fi @ I2 ) @ ( qbs_Mx_a @ X5 ) ) )
         => ( member_real_a
            @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
            @ ( qbs_Mx_a @ X5 ) ) ) ) ) ).

% qbs_closed3_dest2
thf(fact_821_qbs__closed3__dest2,axiom,
    ! [I3: set_real,P: real > real,Fi: real > real > b,X5: quasi_borel_b] :
      ( ( counta7319604579010473777e_real @ I3 )
     => ( ( member_real_real @ P @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ ( sigma_8508918144308765139e_real @ I3 ) ) )
       => ( ! [I2: real] :
              ( ( member_real @ I2 @ I3 )
             => ( member_real_b @ ( Fi @ I2 ) @ ( qbs_Mx_b @ X5 ) ) )
         => ( member_real_b
            @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
            @ ( qbs_Mx_b @ X5 ) ) ) ) ) ).

% qbs_closed3_dest2
thf(fact_822_qbs__closed3__dest2,axiom,
    ! [I3: set_o,P: real > $o,Fi: $o > real > nat,X5: quasi_borel_nat] :
      ( ( counta5976203206615340371able_o @ I3 )
     => ( ( member_real_o @ P @ ( sigma_3939073009482781210real_o @ borel_5078946678739801102l_real @ ( sigma_count_space_o @ I3 ) ) )
       => ( ! [I2: $o] :
              ( ( member_o @ I2 @ I3 )
             => ( member_real_nat @ ( Fi @ I2 ) @ ( qbs_Mx_nat @ X5 ) ) )
         => ( member_real_nat
            @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
            @ ( qbs_Mx_nat @ X5 ) ) ) ) ) ).

% qbs_closed3_dest2
thf(fact_823_qbs__closed3__dest2,axiom,
    ! [I3: set_o,P: real > $o,Fi: $o > real > a,X5: quasi_borel_a] :
      ( ( counta5976203206615340371able_o @ I3 )
     => ( ( member_real_o @ P @ ( sigma_3939073009482781210real_o @ borel_5078946678739801102l_real @ ( sigma_count_space_o @ I3 ) ) )
       => ( ! [I2: $o] :
              ( ( member_o @ I2 @ I3 )
             => ( member_real_a @ ( Fi @ I2 ) @ ( qbs_Mx_a @ X5 ) ) )
         => ( member_real_a
            @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
            @ ( qbs_Mx_a @ X5 ) ) ) ) ) ).

% qbs_closed3_dest2
thf(fact_824_qbs__closed3__dest2,axiom,
    ! [I3: set_o,P: real > $o,Fi: $o > real > b,X5: quasi_borel_b] :
      ( ( counta5976203206615340371able_o @ I3 )
     => ( ( member_real_o @ P @ ( sigma_3939073009482781210real_o @ borel_5078946678739801102l_real @ ( sigma_count_space_o @ I3 ) ) )
       => ( ! [I2: $o] :
              ( ( member_o @ I2 @ I3 )
             => ( member_real_b @ ( Fi @ I2 ) @ ( qbs_Mx_b @ X5 ) ) )
         => ( member_real_b
            @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
            @ ( qbs_Mx_b @ X5 ) ) ) ) ) ).

% qbs_closed3_dest2
thf(fact_825_qbs__closed3__dest2,axiom,
    ! [I3: set_nat,P: real > nat,Fi: nat > real > nat,X5: quasi_borel_nat] :
      ( ( counta1168086296615599829le_nat @ I3 )
     => ( ( member_real_nat @ P @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ ( sigma_7685844798829912695ce_nat @ I3 ) ) )
       => ( ! [I2: nat] :
              ( ( member_nat @ I2 @ I3 )
             => ( member_real_nat @ ( Fi @ I2 ) @ ( qbs_Mx_nat @ X5 ) ) )
         => ( member_real_nat
            @ ^ [R3: real] : ( Fi @ ( P @ R3 ) @ R3 )
            @ ( qbs_Mx_nat @ X5 ) ) ) ) ) ).

% qbs_closed3_dest2
thf(fact_826_boolean__algebra__cancel_Oinf1,axiom,
    ! [A: set_a,K: set_a,A3: set_a,B: set_a] :
      ( ( A
        = ( inf_inf_set_a @ K @ A3 ) )
     => ( ( inf_inf_set_a @ A @ B )
        = ( inf_inf_set_a @ K @ ( inf_inf_set_a @ A3 @ B ) ) ) ) ).

% boolean_algebra_cancel.inf1
thf(fact_827_boolean__algebra__cancel_Oinf2,axiom,
    ! [B2: set_a,K: set_a,B: set_a,A3: set_a] :
      ( ( B2
        = ( inf_inf_set_a @ K @ B ) )
     => ( ( inf_inf_set_a @ A3 @ B2 )
        = ( inf_inf_set_a @ K @ ( inf_inf_set_a @ A3 @ B ) ) ) ) ).

% boolean_algebra_cancel.inf2
thf(fact_828_real__non__denum,axiom,
    ~ ? [F3: nat > real] :
        ( ( image_nat_real @ F3 @ top_top_set_nat )
        = top_top_set_real ) ).

% real_non_denum
thf(fact_829_Pi__UNIV,axiom,
    ! [A: set_real] :
      ( ( pi_real_nat @ A
        @ ^ [Uu: real] : top_top_set_nat )
      = top_top_set_real_nat ) ).

% Pi_UNIV
thf(fact_830_Pi__UNIV,axiom,
    ! [A: set_real] :
      ( ( pi_real_a @ A
        @ ^ [Uu: real] : top_top_set_a )
      = top_top_set_real_a ) ).

% Pi_UNIV
thf(fact_831_Pi__UNIV,axiom,
    ! [A: set_real] :
      ( ( pi_real_b @ A
        @ ^ [Uu: real] : top_top_set_b )
      = top_top_set_real_b ) ).

% Pi_UNIV
thf(fact_832_Pi__I,axiom,
    ! [A: set_real,F: real > b,B2: real > set_b] :
      ( ! [X2: real] :
          ( ( member_real @ X2 @ A )
         => ( member_b @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_real_b @ F @ ( pi_real_b @ A @ B2 ) ) ) ).

% Pi_I
thf(fact_833_Pi__I,axiom,
    ! [A: set_real,F: real > nat,B2: real > set_nat] :
      ( ! [X2: real] :
          ( ( member_real @ X2 @ A )
         => ( member_nat @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_real_nat @ F @ ( pi_real_nat @ A @ B2 ) ) ) ).

% Pi_I
thf(fact_834_Pi__I,axiom,
    ! [A: set_real,F: real > a,B2: real > set_a] :
      ( ! [X2: real] :
          ( ( member_real @ X2 @ A )
         => ( member_a @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_real_a @ F @ ( pi_real_a @ A @ B2 ) ) ) ).

% Pi_I
thf(fact_835_Pi__I,axiom,
    ! [A: set_nat,F: nat > nat,B2: nat > set_nat] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_nat @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_nat_nat @ F @ ( pi_nat_nat @ A @ B2 ) ) ) ).

% Pi_I
thf(fact_836_Pi__I,axiom,
    ! [A: set_nat,F: nat > a,B2: nat > set_a] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_a @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_nat_a @ F @ ( pi_nat_a @ A @ B2 ) ) ) ).

% Pi_I
thf(fact_837_Pi__I,axiom,
    ! [A: set_a,F: a > complex,B2: a > set_complex] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_complex @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_a_complex @ F @ ( pi_a_complex @ A @ B2 ) ) ) ).

% Pi_I
thf(fact_838_Pi__I,axiom,
    ! [A: set_a,F: a > real,B2: a > set_real] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_real @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_a_real @ F @ ( pi_a_real @ A @ B2 ) ) ) ).

% Pi_I
thf(fact_839_Pi__I,axiom,
    ! [A: set_a,F: a > $o,B2: a > set_o] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_o @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_a_o @ F @ ( pi_a_o @ A @ B2 ) ) ) ).

% Pi_I
thf(fact_840_Pi__I,axiom,
    ! [A: set_a,F: a > nat,B2: a > set_nat] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_nat @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_a_nat @ F @ ( pi_a_nat @ A @ B2 ) ) ) ).

% Pi_I
thf(fact_841_Pi__I,axiom,
    ! [A: set_a,F: a > a,B2: a > set_a] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_a @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_a_a @ F @ ( pi_a_a @ A @ B2 ) ) ) ).

% Pi_I
thf(fact_842_Pi__Int,axiom,
    ! [I3: set_real,E: real > set_a,F4: real > set_a] :
      ( ( inf_inf_set_real_a @ ( pi_real_a @ I3 @ E ) @ ( pi_real_a @ I3 @ F4 ) )
      = ( pi_real_a @ I3
        @ ^ [I4: real] : ( inf_inf_set_a @ ( E @ I4 ) @ ( F4 @ I4 ) ) ) ) ).

% Pi_Int
thf(fact_843_measurable__THE,axiom,
    ! [P: a > nat > $o,M: sigma_measure_nat,I3: set_a] :
      ( ! [I2: a] : ( member_nat_o @ ( P @ I2 ) @ ( sigma_5101835498682829686_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( counta4098120917673242425able_a @ I3 )
       => ( ! [I2: a,X2: nat] :
              ( ( member_nat @ X2 @ ( sigma_space_nat @ M ) )
             => ( ( P @ I2 @ X2 )
               => ( member_a @ I2 @ I3 ) ) )
         => ( ! [X2: nat,I2: a,J: a] :
                ( ( member_nat @ X2 @ ( sigma_space_nat @ M ) )
               => ( ( P @ I2 @ X2 )
                 => ( ( P @ J @ X2 )
                   => ( I2 = J ) ) ) )
           => ( member_nat_a
              @ ^ [X4: nat] :
                  ( the_a
                  @ ^ [I4: a] : ( P @ I4 @ X4 ) )
              @ ( sigma_4105081583803843548_nat_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) ) ) ) ) ) ).

% measurable_THE
thf(fact_844_measurable__THE,axiom,
    ! [P: a > $o > $o,M: sigma_measure_o,I3: set_a] :
      ( ! [I2: a] : ( member_o_o @ ( P @ I2 ) @ ( sigma_measurable_o_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( counta4098120917673242425able_a @ I3 )
       => ( ! [I2: a,X2: $o] :
              ( ( member_o @ X2 @ ( sigma_space_o @ M ) )
             => ( ( P @ I2 @ X2 )
               => ( member_a @ I2 @ I3 ) ) )
         => ( ! [X2: $o,I2: a,J: a] :
                ( ( member_o @ X2 @ ( sigma_space_o @ M ) )
               => ( ( P @ I2 @ X2 )
                 => ( ( P @ J @ X2 )
                   => ( I2 = J ) ) ) )
           => ( member_o_a
              @ ^ [X4: $o] :
                  ( the_a
                  @ ^ [I4: a] : ( P @ I4 @ X4 ) )
              @ ( sigma_measurable_o_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) ) ) ) ) ) ).

% measurable_THE
thf(fact_845_measurable__THE,axiom,
    ! [P: a > extend8495563244428889912nnreal > $o,M: sigma_7234349610311085201nnreal,I3: set_a] :
      ( ! [I2: a] : ( member8095236870201115968real_o @ ( P @ I2 ) @ ( sigma_6279906219187228174real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( counta4098120917673242425able_a @ I3 )
       => ( ! [I2: a,X2: extend8495563244428889912nnreal] :
              ( ( member7908768830364227535nnreal @ X2 @ ( sigma_3147302497200244656nnreal @ M ) )
             => ( ( P @ I2 @ X2 )
               => ( member_a @ I2 @ I3 ) ) )
         => ( ! [X2: extend8495563244428889912nnreal,I2: a,J: a] :
                ( ( member7908768830364227535nnreal @ X2 @ ( sigma_3147302497200244656nnreal @ M ) )
               => ( ( P @ I2 @ X2 )
                 => ( ( P @ J @ X2 )
                   => ( I2 = J ) ) ) )
           => ( member4924430693770431270real_a
              @ ^ [X4: extend8495563244428889912nnreal] :
                  ( the_a
                  @ ^ [I4: a] : ( P @ I4 @ X4 ) )
              @ ( sigma_3031480723531659892real_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) ) ) ) ) ) ).

% measurable_THE
thf(fact_846_measurable__THE,axiom,
    ! [P: a > real > $o,M: sigma_measure_real,I3: set_a] :
      ( ! [I2: a] : ( member_real_o @ ( P @ I2 ) @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( counta4098120917673242425able_a @ I3 )
       => ( ! [I2: a,X2: real] :
              ( ( member_real @ X2 @ ( sigma_space_real @ M ) )
             => ( ( P @ I2 @ X2 )
               => ( member_a @ I2 @ I3 ) ) )
         => ( ! [X2: real,I2: a,J: a] :
                ( ( member_real @ X2 @ ( sigma_space_real @ M ) )
               => ( ( P @ I2 @ X2 )
                 => ( ( P @ J @ X2 )
                   => ( I2 = J ) ) ) )
           => ( member_real_a
              @ ^ [X4: real] :
                  ( the_a
                  @ ^ [I4: a] : ( P @ I4 @ X4 ) )
              @ ( sigma_523072396149930112real_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) ) ) ) ) ) ).

% measurable_THE
thf(fact_847_measurable__THE,axiom,
    ! [P: a > a > $o,M: sigma_measure_a,I3: set_a] :
      ( ! [I2: a] : ( member_a_o @ ( P @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( counta4098120917673242425able_a @ I3 )
       => ( ! [I2: a,X2: a] :
              ( ( member_a @ X2 @ ( sigma_space_a @ M ) )
             => ( ( P @ I2 @ X2 )
               => ( member_a @ I2 @ I3 ) ) )
         => ( ! [X2: a,I2: a,J: a] :
                ( ( member_a @ X2 @ ( sigma_space_a @ M ) )
               => ( ( P @ I2 @ X2 )
                 => ( ( P @ J @ X2 )
                   => ( I2 = J ) ) ) )
           => ( member_a_a
              @ ^ [X4: a] :
                  ( the_a
                  @ ^ [I4: a] : ( P @ I4 @ X4 ) )
              @ ( sigma_measurable_a_a @ M @ ( sigma_count_space_a @ top_top_set_a ) ) ) ) ) ) ) ).

% measurable_THE
thf(fact_848_measurable__THE,axiom,
    ! [P: real > real > $o,M: sigma_measure_real,I3: set_real] :
      ( ! [I2: real] : ( member_real_o @ ( P @ I2 ) @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( counta7319604579010473777e_real @ I3 )
       => ( ! [I2: real,X2: real] :
              ( ( member_real @ X2 @ ( sigma_space_real @ M ) )
             => ( ( P @ I2 @ X2 )
               => ( member_real @ I2 @ I3 ) ) )
         => ( ! [X2: real,I2: real,J: real] :
                ( ( member_real @ X2 @ ( sigma_space_real @ M ) )
               => ( ( P @ I2 @ X2 )
                 => ( ( P @ J @ X2 )
                   => ( I2 = J ) ) ) )
           => ( member_real_real
              @ ^ [X4: real] :
                  ( the_real
                  @ ^ [I4: real] : ( P @ I4 @ X4 ) )
              @ ( sigma_5267869275261027754l_real @ M @ ( sigma_8508918144308765139e_real @ top_top_set_real ) ) ) ) ) ) ) ).

% measurable_THE
thf(fact_849_measurable__THE,axiom,
    ! [P: real > nat > $o,M: sigma_measure_nat,I3: set_real] :
      ( ! [I2: real] : ( member_nat_o @ ( P @ I2 ) @ ( sigma_5101835498682829686_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( counta7319604579010473777e_real @ I3 )
       => ( ! [I2: real,X2: nat] :
              ( ( member_nat @ X2 @ ( sigma_space_nat @ M ) )
             => ( ( P @ I2 @ X2 )
               => ( member_real @ I2 @ I3 ) ) )
         => ( ! [X2: nat,I2: real,J: real] :
                ( ( member_nat @ X2 @ ( sigma_space_nat @ M ) )
               => ( ( P @ I2 @ X2 )
                 => ( ( P @ J @ X2 )
                   => ( I2 = J ) ) ) )
           => ( member_nat_real
              @ ^ [X4: nat] :
                  ( the_real
                  @ ^ [I4: real] : ( P @ I4 @ X4 ) )
              @ ( sigma_1747752005702207822t_real @ M @ ( sigma_8508918144308765139e_real @ top_top_set_real ) ) ) ) ) ) ) ).

% measurable_THE
thf(fact_850_measurable__THE,axiom,
    ! [P: real > $o > $o,M: sigma_measure_o,I3: set_real] :
      ( ! [I2: real] : ( member_o_o @ ( P @ I2 ) @ ( sigma_measurable_o_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( counta7319604579010473777e_real @ I3 )
       => ( ! [I2: real,X2: $o] :
              ( ( member_o @ X2 @ ( sigma_space_o @ M ) )
             => ( ( P @ I2 @ X2 )
               => ( member_real @ I2 @ I3 ) ) )
         => ( ! [X2: $o,I2: real,J: real] :
                ( ( member_o @ X2 @ ( sigma_space_o @ M ) )
               => ( ( P @ I2 @ X2 )
                 => ( ( P @ J @ X2 )
                   => ( I2 = J ) ) ) )
           => ( member_o_real
              @ ^ [X4: $o] :
                  ( the_real
                  @ ^ [I4: real] : ( P @ I4 @ X4 ) )
              @ ( sigma_2430008634441611636o_real @ M @ ( sigma_8508918144308765139e_real @ top_top_set_real ) ) ) ) ) ) ) ).

% measurable_THE
thf(fact_851_measurable__THE,axiom,
    ! [P: real > extend8495563244428889912nnreal > $o,M: sigma_7234349610311085201nnreal,I3: set_real] :
      ( ! [I2: real] : ( member8095236870201115968real_o @ ( P @ I2 ) @ ( sigma_6279906219187228174real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( counta7319604579010473777e_real @ I3 )
       => ( ! [I2: real,X2: extend8495563244428889912nnreal] :
              ( ( member7908768830364227535nnreal @ X2 @ ( sigma_3147302497200244656nnreal @ M ) )
             => ( ( P @ I2 @ X2 )
               => ( member_real @ I2 @ I3 ) ) )
         => ( ! [X2: extend8495563244428889912nnreal,I2: real,J: real] :
                ( ( member7908768830364227535nnreal @ X2 @ ( sigma_3147302497200244656nnreal @ M ) )
               => ( ( P @ I2 @ X2 )
                 => ( ( P @ J @ X2 )
                   => ( I2 = J ) ) ) )
           => ( member2874014351250825754l_real
              @ ^ [X4: extend8495563244428889912nnreal] :
                  ( the_real
                  @ ^ [I4: real] : ( P @ I4 @ X4 ) )
              @ ( sigma_7049758200512112822l_real @ M @ ( sigma_8508918144308765139e_real @ top_top_set_real ) ) ) ) ) ) ) ).

% measurable_THE
thf(fact_852_measurable__THE,axiom,
    ! [P: real > a > $o,M: sigma_measure_a,I3: set_real] :
      ( ! [I2: real] : ( member_a_o @ ( P @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( counta7319604579010473777e_real @ I3 )
       => ( ! [I2: real,X2: a] :
              ( ( member_a @ X2 @ ( sigma_space_a @ M ) )
             => ( ( P @ I2 @ X2 )
               => ( member_real @ I2 @ I3 ) ) )
         => ( ! [X2: a,I2: real,J: real] :
                ( ( member_a @ X2 @ ( sigma_space_a @ M ) )
               => ( ( P @ I2 @ X2 )
                 => ( ( P @ J @ X2 )
                   => ( I2 = J ) ) ) )
           => ( member_a_real
              @ ^ [X4: a] :
                  ( the_real
                  @ ^ [I4: real] : ( P @ I4 @ X4 ) )
              @ ( sigma_9116425665531756122a_real @ M @ ( sigma_8508918144308765139e_real @ top_top_set_real ) ) ) ) ) ) ) ).

% measurable_THE
thf(fact_853_measurable__SUP,axiom,
    ! [I3: set_complex,F4: complex > a > $o,M: sigma_measure_a] :
      ( ( counta5113917769705169331omplex @ I3 )
     => ( ! [I2: complex] :
            ( ( member_complex @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Sup_Sup_o
              @ ( image_complex_o
                @ ^ [I4: complex] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_SUP
thf(fact_854_measurable__SUP,axiom,
    ! [I3: set_real,F4: real > a > $o,M: sigma_measure_a] :
      ( ( counta7319604579010473777e_real @ I3 )
     => ( ! [I2: real] :
            ( ( member_real @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Sup_Sup_o
              @ ( image_real_o
                @ ^ [I4: real] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_SUP
thf(fact_855_measurable__SUP,axiom,
    ! [I3: set_o,F4: $o > a > $o,M: sigma_measure_a] :
      ( ( counta5976203206615340371able_o @ I3 )
     => ( ! [I2: $o] :
            ( ( member_o @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Sup_Sup_o
              @ ( image_o_o
                @ ^ [I4: $o] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_SUP
thf(fact_856_measurable__SUP,axiom,
    ! [I3: set_nat,F4: nat > a > $o,M: sigma_measure_a] :
      ( ( counta1168086296615599829le_nat @ I3 )
     => ( ! [I2: nat] :
            ( ( member_nat @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Sup_Sup_o
              @ ( image_nat_o
                @ ^ [I4: nat] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_SUP
thf(fact_857_measurable__SUP,axiom,
    ! [I3: set_a,F4: a > a > $o,M: sigma_measure_a] :
      ( ( counta4098120917673242425able_a @ I3 )
     => ( ! [I2: a] :
            ( ( member_a @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Sup_Sup_o
              @ ( image_a_o
                @ ^ [I4: a] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_SUP
thf(fact_858_measurable__SUP,axiom,
    ! [I3: set_real_nat,F4: ( real > nat ) > a > $o,M: sigma_measure_a] :
      ( ( counta7410736174393390496al_nat @ I3 )
     => ( ! [I2: real > nat] :
            ( ( member_real_nat @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Sup_Sup_o
              @ ( image_real_nat_o
                @ ^ [I4: real > nat] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_SUP
thf(fact_859_measurable__SUP,axiom,
    ! [I3: set_real_b,F4: ( real > b ) > a > $o,M: sigma_measure_a] :
      ( ( counta6639396087987402821real_b @ I3 )
     => ( ! [I2: real > b] :
            ( ( member_real_b @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Sup_Sup_o
              @ ( image_real_b_o
                @ ^ [I4: real > b] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_SUP
thf(fact_860_measurable__SUP,axiom,
    ! [I3: set_real_a,F4: ( real > a ) > a > $o,M: sigma_measure_a] :
      ( ( counta6639396083684174020real_a @ I3 )
     => ( ! [I2: real > a] :
            ( ( member_real_a @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Sup_Sup_o
              @ ( image_real_a_o
                @ ^ [I4: real > a] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_SUP
thf(fact_861_measurable__SUP,axiom,
    ! [I3: set_a_complex,F4: ( a > complex ) > a > $o,M: sigma_measure_a] :
      ( ( counta599731762510375256omplex @ I3 )
     => ( ! [I2: a > complex] :
            ( ( member_a_complex @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Sup_Sup_o
              @ ( image_a_complex_o
                @ ^ [I4: a > complex] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_SUP
thf(fact_862_measurable__SUP,axiom,
    ! [I3: set_a_real,F4: ( a > real ) > a > $o,M: sigma_measure_a] :
      ( ( counta6122129581416836822a_real @ I3 )
     => ( ! [I2: a > real] :
            ( ( member_a_real @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Sup_Sup_o
              @ ( image_a_real_o
                @ ^ [I4: a > real] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_SUP
thf(fact_863_measurable__INF,axiom,
    ! [I3: set_complex,F4: complex > a > $o,M: sigma_measure_a] :
      ( ( counta5113917769705169331omplex @ I3 )
     => ( ! [I2: complex] :
            ( ( member_complex @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Inf_Inf_o
              @ ( image_complex_o
                @ ^ [I4: complex] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_INF
thf(fact_864_measurable__INF,axiom,
    ! [I3: set_real,F4: real > a > $o,M: sigma_measure_a] :
      ( ( counta7319604579010473777e_real @ I3 )
     => ( ! [I2: real] :
            ( ( member_real @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Inf_Inf_o
              @ ( image_real_o
                @ ^ [I4: real] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_INF
thf(fact_865_measurable__INF,axiom,
    ! [I3: set_o,F4: $o > a > $o,M: sigma_measure_a] :
      ( ( counta5976203206615340371able_o @ I3 )
     => ( ! [I2: $o] :
            ( ( member_o @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Inf_Inf_o
              @ ( image_o_o
                @ ^ [I4: $o] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_INF
thf(fact_866_measurable__INF,axiom,
    ! [I3: set_nat,F4: nat > a > $o,M: sigma_measure_a] :
      ( ( counta1168086296615599829le_nat @ I3 )
     => ( ! [I2: nat] :
            ( ( member_nat @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Inf_Inf_o
              @ ( image_nat_o
                @ ^ [I4: nat] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_INF
thf(fact_867_measurable__INF,axiom,
    ! [I3: set_a,F4: a > a > $o,M: sigma_measure_a] :
      ( ( counta4098120917673242425able_a @ I3 )
     => ( ! [I2: a] :
            ( ( member_a @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Inf_Inf_o
              @ ( image_a_o
                @ ^ [I4: a] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_INF
thf(fact_868_measurable__INF,axiom,
    ! [I3: set_real_nat,F4: ( real > nat ) > a > $o,M: sigma_measure_a] :
      ( ( counta7410736174393390496al_nat @ I3 )
     => ( ! [I2: real > nat] :
            ( ( member_real_nat @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Inf_Inf_o
              @ ( image_real_nat_o
                @ ^ [I4: real > nat] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_INF
thf(fact_869_measurable__INF,axiom,
    ! [I3: set_real_b,F4: ( real > b ) > a > $o,M: sigma_measure_a] :
      ( ( counta6639396087987402821real_b @ I3 )
     => ( ! [I2: real > b] :
            ( ( member_real_b @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Inf_Inf_o
              @ ( image_real_b_o
                @ ^ [I4: real > b] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_INF
thf(fact_870_measurable__INF,axiom,
    ! [I3: set_real_a,F4: ( real > a ) > a > $o,M: sigma_measure_a] :
      ( ( counta6639396083684174020real_a @ I3 )
     => ( ! [I2: real > a] :
            ( ( member_real_a @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Inf_Inf_o
              @ ( image_real_a_o
                @ ^ [I4: real > a] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_INF
thf(fact_871_measurable__INF,axiom,
    ! [I3: set_a_complex,F4: ( a > complex ) > a > $o,M: sigma_measure_a] :
      ( ( counta599731762510375256omplex @ I3 )
     => ( ! [I2: a > complex] :
            ( ( member_a_complex @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Inf_Inf_o
              @ ( image_a_complex_o
                @ ^ [I4: a > complex] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_INF
thf(fact_872_measurable__INF,axiom,
    ! [I3: set_a_real,F4: ( a > real ) > a > $o,M: sigma_measure_a] :
      ( ( counta6122129581416836822a_real @ I3 )
     => ( ! [I2: a > real] :
            ( ( member_a_real @ I2 @ I3 )
           => ( member_a_o @ ( F4 @ I2 ) @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( complete_Inf_Inf_o
              @ ( image_a_real_o
                @ ^ [I4: a > real] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% measurable_INF
thf(fact_873_standard__borel__space__UNIV__axioms__def,axiom,
    ( standa602082540683807836nnreal
    = ( ^ [M3: sigma_7234349610311085201nnreal] :
          ( ( sigma_3147302497200244656nnreal @ M3 )
          = top_to7994903218803871134nnreal ) ) ) ).

% standard_borel_space_UNIV_axioms_def
thf(fact_874_standard__borel__space__UNIV__axioms__def,axiom,
    ( standa483509463685453266omplex
    = ( ^ [M3: sigma_3077487657436305159omplex] :
          ( ( sigma_space_complex @ M3 )
          = top_top_set_complex ) ) ) ).

% standard_borel_space_UNIV_axioms_def
thf(fact_875_standard__borel__space__UNIV__axioms__def,axiom,
    ( standa1498722272452280784s_real
    = ( ^ [M3: sigma_measure_real] :
          ( ( sigma_space_real @ M3 )
          = top_top_set_real ) ) ) ).

% standard_borel_space_UNIV_axioms_def
thf(fact_876_standard__borel__space__UNIV__axioms__def,axiom,
    ( standa4575222554423029108ioms_o
    = ( ^ [M3: sigma_measure_o] :
          ( ( sigma_space_o @ M3 )
          = top_top_set_o ) ) ) ).

% standard_borel_space_UNIV_axioms_def
thf(fact_877_standard__borel__space__UNIV__axioms__def,axiom,
    ( standa4898135366436483316ms_nat
    = ( ^ [M3: sigma_measure_nat] :
          ( ( sigma_space_nat @ M3 )
          = top_top_set_nat ) ) ) ).

% standard_borel_space_UNIV_axioms_def
thf(fact_878_standard__borel__space__UNIV__axioms__def,axiom,
    ( standa2153564630574221018ioms_a
    = ( ^ [M3: sigma_measure_a] :
          ( ( sigma_space_a @ M3 )
          = top_top_set_a ) ) ) ).

% standard_borel_space_UNIV_axioms_def
thf(fact_879_standard__borel__space__UNIV__axioms__def,axiom,
    ( standa2153564630574221019ioms_b
    = ( ^ [M3: sigma_measure_b] :
          ( ( sigma_space_b @ M3 )
          = top_top_set_b ) ) ) ).

% standard_borel_space_UNIV_axioms_def
thf(fact_880_standard__borel__space__UNIV__axioms__def,axiom,
    ( standa5303581020940319333real_a
    = ( ^ [M3: sigma_measure_real_a] :
          ( ( sigma_space_real_a @ M3 )
          = top_top_set_real_a ) ) ) ).

% standard_borel_space_UNIV_axioms_def
thf(fact_881_standard__borel__space__UNIV__axioms__def,axiom,
    ( standa5303581025243548134real_b
    = ( ^ [M3: sigma_measure_real_b] :
          ( ( sigma_space_real_b @ M3 )
          = top_top_set_real_b ) ) ) ).

% standard_borel_space_UNIV_axioms_def
thf(fact_882_standard__borel__space__UNIV__axioms__def,axiom,
    ( standa1166615221086727615al_nat
    = ( ^ [M3: sigma_6586288717683155060al_nat] :
          ( ( sigma_space_real_nat @ M3 )
          = top_top_set_real_nat ) ) ) ).

% standard_borel_space_UNIV_axioms_def
thf(fact_883_standard__borel__space__UNIV__axioms_Ointro,axiom,
    ! [M: sigma_7234349610311085201nnreal] :
      ( ( ( sigma_3147302497200244656nnreal @ M )
        = top_to7994903218803871134nnreal )
     => ( standa602082540683807836nnreal @ M ) ) ).

% standard_borel_space_UNIV_axioms.intro
thf(fact_884_standard__borel__space__UNIV__axioms_Ointro,axiom,
    ! [M: sigma_3077487657436305159omplex] :
      ( ( ( sigma_space_complex @ M )
        = top_top_set_complex )
     => ( standa483509463685453266omplex @ M ) ) ).

% standard_borel_space_UNIV_axioms.intro
thf(fact_885_standard__borel__space__UNIV__axioms_Ointro,axiom,
    ! [M: sigma_measure_real] :
      ( ( ( sigma_space_real @ M )
        = top_top_set_real )
     => ( standa1498722272452280784s_real @ M ) ) ).

% standard_borel_space_UNIV_axioms.intro
thf(fact_886_standard__borel__space__UNIV__axioms_Ointro,axiom,
    ! [M: sigma_measure_o] :
      ( ( ( sigma_space_o @ M )
        = top_top_set_o )
     => ( standa4575222554423029108ioms_o @ M ) ) ).

% standard_borel_space_UNIV_axioms.intro
thf(fact_887_standard__borel__space__UNIV__axioms_Ointro,axiom,
    ! [M: sigma_measure_nat] :
      ( ( ( sigma_space_nat @ M )
        = top_top_set_nat )
     => ( standa4898135366436483316ms_nat @ M ) ) ).

% standard_borel_space_UNIV_axioms.intro
thf(fact_888_standard__borel__space__UNIV__axioms_Ointro,axiom,
    ! [M: sigma_measure_a] :
      ( ( ( sigma_space_a @ M )
        = top_top_set_a )
     => ( standa2153564630574221018ioms_a @ M ) ) ).

% standard_borel_space_UNIV_axioms.intro
thf(fact_889_standard__borel__space__UNIV__axioms_Ointro,axiom,
    ! [M: sigma_measure_b] :
      ( ( ( sigma_space_b @ M )
        = top_top_set_b )
     => ( standa2153564630574221019ioms_b @ M ) ) ).

% standard_borel_space_UNIV_axioms.intro
thf(fact_890_standard__borel__space__UNIV__axioms_Ointro,axiom,
    ! [M: sigma_measure_real_a] :
      ( ( ( sigma_space_real_a @ M )
        = top_top_set_real_a )
     => ( standa5303581020940319333real_a @ M ) ) ).

% standard_borel_space_UNIV_axioms.intro
thf(fact_891_standard__borel__space__UNIV__axioms_Ointro,axiom,
    ! [M: sigma_measure_real_b] :
      ( ( ( sigma_space_real_b @ M )
        = top_top_set_real_b )
     => ( standa5303581025243548134real_b @ M ) ) ).

% standard_borel_space_UNIV_axioms.intro
thf(fact_892_standard__borel__space__UNIV__axioms_Ointro,axiom,
    ! [M: sigma_6586288717683155060al_nat] :
      ( ( ( sigma_space_real_nat @ M )
        = top_top_set_real_nat )
     => ( standa1166615221086727615al_nat @ M ) ) ).

% standard_borel_space_UNIV_axioms.intro
thf(fact_893_countable__INT,axiom,
    ! [I: nat,I3: set_nat,A: nat > set_complex] :
      ( ( member_nat @ I @ I3 )
     => ( ( counta5113917769705169331omplex @ ( A @ I ) )
       => ( counta5113917769705169331omplex @ ( comple2956690151646016541omplex @ ( image_6594795319511438139omplex @ A @ I3 ) ) ) ) ) ).

% countable_INT
thf(fact_894_countable__INT,axiom,
    ! [I: a,I3: set_a,A: a > set_complex] :
      ( ( member_a @ I @ I3 )
     => ( ( counta5113917769705169331omplex @ ( A @ I ) )
       => ( counta5113917769705169331omplex @ ( comple2956690151646016541omplex @ ( image_a_set_complex @ A @ I3 ) ) ) ) ) ).

% countable_INT
thf(fact_895_countable__INT,axiom,
    ! [I: nat,I3: set_nat,A: nat > set_real] :
      ( ( member_nat @ I @ I3 )
     => ( ( counta7319604579010473777e_real @ ( A @ I ) )
       => ( counta7319604579010473777e_real @ ( comple8289635161444856091t_real @ ( image_nat_set_real @ A @ I3 ) ) ) ) ) ).

% countable_INT
thf(fact_896_countable__INT,axiom,
    ! [I: a,I3: set_a,A: a > set_real] :
      ( ( member_a @ I @ I3 )
     => ( ( counta7319604579010473777e_real @ ( A @ I ) )
       => ( counta7319604579010473777e_real @ ( comple8289635161444856091t_real @ ( image_a_set_real @ A @ I3 ) ) ) ) ) ).

% countable_INT
thf(fact_897_countable__INT,axiom,
    ! [I: nat,I3: set_nat,A: nat > set_o] :
      ( ( member_nat @ I @ I3 )
     => ( ( counta5976203206615340371able_o @ ( A @ I ) )
       => ( counta5976203206615340371able_o @ ( comple3063163877087187839_set_o @ ( image_nat_set_o @ A @ I3 ) ) ) ) ) ).

% countable_INT
thf(fact_898_countable__INT,axiom,
    ! [I: a,I3: set_a,A: a > set_o] :
      ( ( member_a @ I @ I3 )
     => ( ( counta5976203206615340371able_o @ ( A @ I ) )
       => ( counta5976203206615340371able_o @ ( comple3063163877087187839_set_o @ ( image_a_set_o @ A @ I3 ) ) ) ) ) ).

% countable_INT
thf(fact_899_countable__INT,axiom,
    ! [I: nat,I3: set_nat,A: nat > set_nat] :
      ( ( member_nat @ I @ I3 )
     => ( ( counta1168086296615599829le_nat @ ( A @ I ) )
       => ( counta1168086296615599829le_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A @ I3 ) ) ) ) ) ).

% countable_INT
thf(fact_900_countable__INT,axiom,
    ! [I: a,I3: set_a,A: a > set_nat] :
      ( ( member_a @ I @ I3 )
     => ( ( counta1168086296615599829le_nat @ ( A @ I ) )
       => ( counta1168086296615599829le_nat @ ( comple7806235888213564991et_nat @ ( image_a_set_nat @ A @ I3 ) ) ) ) ) ).

% countable_INT
thf(fact_901_countable__INT,axiom,
    ! [I: nat,I3: set_nat,A: nat > set_a] :
      ( ( member_nat @ I @ I3 )
     => ( ( counta4098120917673242425able_a @ ( A @ I ) )
       => ( counta4098120917673242425able_a @ ( comple6135023378680113637_set_a @ ( image_nat_set_a @ A @ I3 ) ) ) ) ) ).

% countable_INT
thf(fact_902_countable__INT,axiom,
    ! [I: a,I3: set_a,A: a > set_a] :
      ( ( member_a @ I @ I3 )
     => ( ( counta4098120917673242425able_a @ ( A @ I ) )
       => ( counta4098120917673242425able_a @ ( comple6135023378680113637_set_a @ ( image_a_set_a @ A @ I3 ) ) ) ) ) ).

% countable_INT
thf(fact_903_countable__UN,axiom,
    ! [I3: set_complex,A: complex > set_complex] :
      ( ( counta5113917769705169331omplex @ I3 )
     => ( ! [I2: complex] :
            ( ( member_complex @ I2 @ I3 )
           => ( counta5113917769705169331omplex @ ( A @ I2 ) ) )
       => ( counta5113917769705169331omplex @ ( comple8424636186594484919omplex @ ( image_5702600179605932057omplex @ A @ I3 ) ) ) ) ) ).

% countable_UN
thf(fact_904_countable__UN,axiom,
    ! [I3: set_complex,A: complex > set_real] :
      ( ( counta5113917769705169331omplex @ I3 )
     => ( ! [I2: complex] :
            ( ( member_complex @ I2 @ I3 )
           => ( counta7319604579010473777e_real @ ( A @ I2 ) ) )
       => ( counta7319604579010473777e_real @ ( comple3096694443085538997t_real @ ( image_3583993721237978903t_real @ A @ I3 ) ) ) ) ) ).

% countable_UN
thf(fact_905_countable__UN,axiom,
    ! [I3: set_complex,A: complex > set_o] :
      ( ( counta5113917769705169331omplex @ I3 )
     => ( ! [I2: complex] :
            ( ( member_complex @ I2 @ I3 )
           => ( counta5976203206615340371able_o @ ( A @ I2 ) ) )
       => ( counta5976203206615340371able_o @ ( comple90263536869209701_set_o @ ( image_complex_set_o @ A @ I3 ) ) ) ) ) ).

% countable_UN
thf(fact_906_countable__UN,axiom,
    ! [I3: set_complex,A: complex > set_nat] :
      ( ( counta5113917769705169331omplex @ I3 )
     => ( ! [I2: complex] :
            ( ( member_complex @ I2 @ I3 )
           => ( counta1168086296615599829le_nat @ ( A @ I2 ) ) )
       => ( counta1168086296615599829le_nat @ ( comple7399068483239264473et_nat @ ( image_6352962638927555131et_nat @ A @ I3 ) ) ) ) ) ).

% countable_UN
thf(fact_907_countable__UN,axiom,
    ! [I3: set_complex,A: complex > set_a] :
      ( ( counta5113917769705169331omplex @ I3 )
     => ( ! [I2: complex] :
            ( ( member_complex @ I2 @ I3 )
           => ( counta4098120917673242425able_a @ ( A @ I2 ) ) )
       => ( counta4098120917673242425able_a @ ( comple2307003609928055243_set_a @ ( image_complex_set_a @ A @ I3 ) ) ) ) ) ).

% countable_UN
thf(fact_908_countable__UN,axiom,
    ! [I3: set_real,A: real > set_complex] :
      ( ( counta7319604579010473777e_real @ I3 )
     => ( ! [I2: real] :
            ( ( member_real @ I2 @ I3 )
           => ( counta5113917769705169331omplex @ ( A @ I2 ) ) )
       => ( counta5113917769705169331omplex @ ( comple8424636186594484919omplex @ ( image_2129611632225307415omplex @ A @ I3 ) ) ) ) ) ).

% countable_UN
thf(fact_909_countable__UN,axiom,
    ! [I3: set_real,A: real > set_real] :
      ( ( counta7319604579010473777e_real @ I3 )
     => ( ! [I2: real] :
            ( ( member_real @ I2 @ I3 )
           => ( counta7319604579010473777e_real @ ( A @ I2 ) ) )
       => ( counta7319604579010473777e_real @ ( comple3096694443085538997t_real @ ( image_real_set_real @ A @ I3 ) ) ) ) ) ).

% countable_UN
thf(fact_910_countable__UN,axiom,
    ! [I3: set_real,A: real > set_o] :
      ( ( counta7319604579010473777e_real @ I3 )
     => ( ! [I2: real] :
            ( ( member_real @ I2 @ I3 )
           => ( counta5976203206615340371able_o @ ( A @ I2 ) ) )
       => ( counta5976203206615340371able_o @ ( comple90263536869209701_set_o @ ( image_real_set_o @ A @ I3 ) ) ) ) ) ).

% countable_UN
thf(fact_911_countable__UN,axiom,
    ! [I3: set_real,A: real > set_nat] :
      ( ( counta7319604579010473777e_real @ I3 )
     => ( ! [I2: real] :
            ( ( member_real @ I2 @ I3 )
           => ( counta1168086296615599829le_nat @ ( A @ I2 ) ) )
       => ( counta1168086296615599829le_nat @ ( comple7399068483239264473et_nat @ ( image_real_set_nat @ A @ I3 ) ) ) ) ) ).

% countable_UN
thf(fact_912_countable__UN,axiom,
    ! [I3: set_real,A: real > set_a] :
      ( ( counta7319604579010473777e_real @ I3 )
     => ( ! [I2: real] :
            ( ( member_real @ I2 @ I3 )
           => ( counta4098120917673242425able_a @ ( A @ I2 ) ) )
       => ( counta4098120917673242425able_a @ ( comple2307003609928055243_set_a @ ( image_real_set_a @ A @ I3 ) ) ) ) ) ).

% countable_UN
thf(fact_913_pred__intros__logic_I9_J,axiom,
    ! [P2: ( real > nat ) > a > $o,F: a > real > nat,M: sigma_measure_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( P2 @ ( F @ X4 ) @ X4 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( member_real_nat @ ( F @ X4 )
            @ ( collect_real_nat
              @ ^ [Y2: real > nat] : ( P2 @ Y2 @ X4 ) ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_logic(9)
thf(fact_914_pred__intros__logic_I9_J,axiom,
    ! [P2: ( real > b ) > a > $o,F: a > real > b,M: sigma_measure_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( P2 @ ( F @ X4 ) @ X4 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( member_real_b @ ( F @ X4 )
            @ ( collect_real_b
              @ ^ [Y2: real > b] : ( P2 @ Y2 @ X4 ) ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_logic(9)
thf(fact_915_pred__intros__logic_I9_J,axiom,
    ! [P2: ( real > a ) > a > $o,F: a > real > a,M: sigma_measure_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( P2 @ ( F @ X4 ) @ X4 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( member_real_a @ ( F @ X4 )
            @ ( collect_real_a
              @ ^ [Y2: real > a] : ( P2 @ Y2 @ X4 ) ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_logic(9)
thf(fact_916_pred__intros__logic_I9_J,axiom,
    ! [P2: a > a > $o,F: a > a,M: sigma_measure_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( P2 @ ( F @ X4 ) @ X4 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( member_a @ ( F @ X4 )
            @ ( collect_a
              @ ^ [Y2: a] : ( P2 @ Y2 @ X4 ) ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_logic(9)
thf(fact_917_pred__intros__logic_I9_J,axiom,
    ! [P2: ( a > complex ) > a > $o,F: a > a > complex,M: sigma_measure_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( P2 @ ( F @ X4 ) @ X4 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( member_a_complex @ ( F @ X4 )
            @ ( collect_a_complex
              @ ^ [Y2: a > complex] : ( P2 @ Y2 @ X4 ) ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_logic(9)
thf(fact_918_pred__intros__logic_I9_J,axiom,
    ! [P2: ( a > real ) > a > $o,F: a > a > real,M: sigma_measure_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( P2 @ ( F @ X4 ) @ X4 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( member_a_real @ ( F @ X4 )
            @ ( collect_a_real
              @ ^ [Y2: a > real] : ( P2 @ Y2 @ X4 ) ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_logic(9)
thf(fact_919_pred__intros__logic_I9_J,axiom,
    ! [P2: ( a > $o ) > a > $o,F: a > a > $o,M: sigma_measure_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( P2 @ ( F @ X4 ) @ X4 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( member_a_o @ ( F @ X4 )
            @ ( collect_a_o
              @ ^ [Y2: a > $o] : ( P2 @ Y2 @ X4 ) ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_logic(9)
thf(fact_920_pred__intros__logic_I9_J,axiom,
    ! [P2: ( a > nat ) > a > $o,F: a > a > nat,M: sigma_measure_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( P2 @ ( F @ X4 ) @ X4 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( member_a_nat @ ( F @ X4 )
            @ ( collect_a_nat
              @ ^ [Y2: a > nat] : ( P2 @ Y2 @ X4 ) ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_logic(9)
thf(fact_921_pred__intros__logic_I9_J,axiom,
    ! [P2: ( a > a ) > a > $o,F: a > a > a,M: sigma_measure_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( P2 @ ( F @ X4 ) @ X4 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( member_a_a @ ( F @ X4 )
            @ ( collect_a_a
              @ ^ [Y2: a > a] : ( P2 @ Y2 @ X4 ) ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_logic(9)
thf(fact_922_pred__intros__logic_I9_J,axiom,
    ! [P2: nat > a > $o,F: a > nat,M: sigma_measure_a] :
      ( ( member_a_o
        @ ^ [X4: a] : ( P2 @ ( F @ X4 ) @ X4 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( member_nat @ ( F @ X4 )
            @ ( collect_nat
              @ ^ [Y2: nat] : ( P2 @ Y2 @ X4 ) ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_logic(9)
thf(fact_923_pred__intros__logic_I6_J,axiom,
    ! [Q: a > $o,M: sigma_measure_a,P: a > $o] :
      ( ( member_a_o @ Q @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o @ P @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( ( Q @ X4 )
              = ( P @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(6)
thf(fact_924_pred__intros__logic_I5_J,axiom,
    ! [Q: a > $o,M: sigma_measure_a,P: a > $o] :
      ( ( member_a_o @ Q @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o @ P @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( ( Q @ X4 )
              | ( P @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(5)
thf(fact_925_pred__intros__logic_I4_J,axiom,
    ! [Q: a > $o,M: sigma_measure_a,P: a > $o] :
      ( ( member_a_o @ Q @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o @ P @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( ( Q @ X4 )
             => ( P @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(4)
thf(fact_926_pred__intros__logic_I3_J,axiom,
    ! [Q: a > $o,M: sigma_measure_a,P: a > $o] :
      ( ( member_a_o @ Q @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( ( member_a_o @ P @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( ( Q @ X4 )
              & ( P @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_intros_logic(3)
thf(fact_927_pred__intros__logic_I2_J,axiom,
    ! [P: a > $o,M: sigma_measure_a] :
      ( ( member_a_o @ P @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ~ ( P @ X4 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_logic(2)
thf(fact_928_nat_Ospace__UNIV,axiom,
    ( ( sigma_space_nat @ borel_8449730974584783410el_nat )
    = top_top_set_nat ) ).

% nat.space_UNIV
thf(fact_929_bool_Ospace__UNIV,axiom,
    ( ( sigma_space_o @ borel_5500255247093592246orel_o )
    = top_top_set_o ) ).

% bool.space_UNIV
thf(fact_930_pred__in__If,axiom,
    ! [P: $o,A: nat > set_nat,M: sigma_measure_nat,B2: nat > set_nat] :
      ( ( P
       => ( member_nat_o
          @ ^ [X4: nat] : ( member_nat @ X4 @ ( A @ X4 ) )
          @ ( sigma_5101835498682829686_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( ( ~ P
         => ( member_nat_o
            @ ^ [X4: nat] : ( member_nat @ X4 @ ( B2 @ X4 ) )
            @ ( sigma_5101835498682829686_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_nat_o
          @ ^ [X4: nat] :
              ( ( P
               => ( member_nat @ X4 @ ( A @ X4 ) ) )
              & ( ~ P
               => ( member_nat @ X4 @ ( B2 @ X4 ) ) ) )
          @ ( sigma_5101835498682829686_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_in_If
thf(fact_931_pred__in__If,axiom,
    ! [P: $o,A: ( real > nat ) > set_real_nat,M: sigma_6586288717683155060al_nat,B2: ( real > nat ) > set_real_nat] :
      ( ( P
       => ( member_real_nat_o
          @ ^ [X4: real > nat] : ( member_real_nat @ X4 @ ( A @ X4 ) )
          @ ( sigma_4110928884538380267_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( ( ~ P
         => ( member_real_nat_o
            @ ^ [X4: real > nat] : ( member_real_nat @ X4 @ ( B2 @ X4 ) )
            @ ( sigma_4110928884538380267_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_real_nat_o
          @ ^ [X4: real > nat] :
              ( ( P
               => ( member_real_nat @ X4 @ ( A @ X4 ) ) )
              & ( ~ P
               => ( member_real_nat @ X4 @ ( B2 @ X4 ) ) ) )
          @ ( sigma_4110928884538380267_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_in_If
thf(fact_932_pred__in__If,axiom,
    ! [P: $o,A: ( real > b ) > set_real_b,M: sigma_measure_real_b,B2: ( real > b ) > set_real_b] :
      ( ( P
       => ( member_real_b_o
          @ ^ [X4: real > b] : ( member_real_b @ X4 @ ( A @ X4 ) )
          @ ( sigma_7338419842690513246al_b_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( ( ~ P
         => ( member_real_b_o
            @ ^ [X4: real > b] : ( member_real_b @ X4 @ ( B2 @ X4 ) )
            @ ( sigma_7338419842690513246al_b_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_real_b_o
          @ ^ [X4: real > b] :
              ( ( P
               => ( member_real_b @ X4 @ ( A @ X4 ) ) )
              & ( ~ P
               => ( member_real_b @ X4 @ ( B2 @ X4 ) ) ) )
          @ ( sigma_7338419842690513246al_b_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_in_If
thf(fact_933_pred__in__If,axiom,
    ! [P: $o,A: ( real > a ) > set_real_a,M: sigma_measure_real_a,B2: ( real > a ) > set_real_a] :
      ( ( P
       => ( member_real_a_o
          @ ^ [X4: real > a] : ( member_real_a @ X4 @ ( A @ X4 ) )
          @ ( sigma_902503387808413471al_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( ( ~ P
         => ( member_real_a_o
            @ ^ [X4: real > a] : ( member_real_a @ X4 @ ( B2 @ X4 ) )
            @ ( sigma_902503387808413471al_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_real_a_o
          @ ^ [X4: real > a] :
              ( ( P
               => ( member_real_a @ X4 @ ( A @ X4 ) ) )
              & ( ~ P
               => ( member_real_a @ X4 @ ( B2 @ X4 ) ) ) )
          @ ( sigma_902503387808413471al_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_in_If
thf(fact_934_pred__in__If,axiom,
    ! [P: $o,A: ( a > complex ) > set_a_complex,M: sigma_2418697800065292186omplex,B2: ( a > complex ) > set_a_complex] :
      ( ( P
       => ( member_a_complex_o
          @ ^ [X4: a > complex] : ( member_a_complex @ X4 @ ( A @ X4 ) )
          @ ( sigma_2293258167702796171plex_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( ( ~ P
         => ( member_a_complex_o
            @ ^ [X4: a > complex] : ( member_a_complex @ X4 @ ( B2 @ X4 ) )
            @ ( sigma_2293258167702796171plex_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_complex_o
          @ ^ [X4: a > complex] :
              ( ( P
               => ( member_a_complex @ X4 @ ( A @ X4 ) ) )
              & ( ~ P
               => ( member_a_complex @ X4 @ ( B2 @ X4 ) ) ) )
          @ ( sigma_2293258167702796171plex_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_in_If
thf(fact_935_pred__in__If,axiom,
    ! [P: $o,A: ( a > real ) > set_a_real,M: sigma_measure_a_real,B2: ( a > real ) > set_a_real] :
      ( ( P
       => ( member_a_real_o
          @ ^ [X4: a > real] : ( member_a_real @ X4 @ ( A @ X4 ) )
          @ ( sigma_9085598459323199629real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( ( ~ P
         => ( member_a_real_o
            @ ^ [X4: a > real] : ( member_a_real @ X4 @ ( B2 @ X4 ) )
            @ ( sigma_9085598459323199629real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_real_o
          @ ^ [X4: a > real] :
              ( ( P
               => ( member_a_real @ X4 @ ( A @ X4 ) ) )
              & ( ~ P
               => ( member_a_real @ X4 @ ( B2 @ X4 ) ) ) )
          @ ( sigma_9085598459323199629real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_in_If
thf(fact_936_pred__in__If,axiom,
    ! [P: $o,A: ( a > $o ) > set_a_o,M: sigma_measure_a_o,B2: ( a > $o ) > set_a_o] :
      ( ( P
       => ( member_a_o_o
          @ ^ [X4: a > $o] : ( member_a_o @ X4 @ ( A @ X4 ) )
          @ ( sigma_1195952539894209287_a_o_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( ( ~ P
         => ( member_a_o_o
            @ ^ [X4: a > $o] : ( member_a_o @ X4 @ ( B2 @ X4 ) )
            @ ( sigma_1195952539894209287_a_o_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o_o
          @ ^ [X4: a > $o] :
              ( ( P
               => ( member_a_o @ X4 @ ( A @ X4 ) ) )
              & ( ~ P
               => ( member_a_o @ X4 @ ( B2 @ X4 ) ) ) )
          @ ( sigma_1195952539894209287_a_o_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_in_If
thf(fact_937_pred__in__If,axiom,
    ! [P: $o,A: ( a > nat ) > set_a_nat,M: sigma_measure_a_nat,B2: ( a > nat ) > set_a_nat] :
      ( ( P
       => ( member_a_nat_o
          @ ^ [X4: a > nat] : ( member_a_nat @ X4 @ ( A @ X4 ) )
          @ ( sigma_128654050890844905_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( ( ~ P
         => ( member_a_nat_o
            @ ^ [X4: a > nat] : ( member_a_nat @ X4 @ ( B2 @ X4 ) )
            @ ( sigma_128654050890844905_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_nat_o
          @ ^ [X4: a > nat] :
              ( ( P
               => ( member_a_nat @ X4 @ ( A @ X4 ) ) )
              & ( ~ P
               => ( member_a_nat @ X4 @ ( B2 @ X4 ) ) ) )
          @ ( sigma_128654050890844905_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_in_If
thf(fact_938_pred__in__If,axiom,
    ! [P: $o,A: ( a > a ) > set_a_a,M: sigma_measure_a_a,B2: ( a > a ) > set_a_a] :
      ( ( P
       => ( member_a_a_o
          @ ^ [X4: a > a] : ( member_a_a @ X4 @ ( A @ X4 ) )
          @ ( sigma_7605542298065862561_a_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( ( ~ P
         => ( member_a_a_o
            @ ^ [X4: a > a] : ( member_a_a @ X4 @ ( B2 @ X4 ) )
            @ ( sigma_7605542298065862561_a_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_a_o
          @ ^ [X4: a > a] :
              ( ( P
               => ( member_a_a @ X4 @ ( A @ X4 ) ) )
              & ( ~ P
               => ( member_a_a @ X4 @ ( B2 @ X4 ) ) ) )
          @ ( sigma_7605542298065862561_a_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_in_If
thf(fact_939_pred__in__If,axiom,
    ! [P: $o,A: a > set_a,M: sigma_measure_a,B2: a > set_a] :
      ( ( P
       => ( member_a_o
          @ ^ [X4: a] : ( member_a @ X4 @ ( A @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( ( ~ P
         => ( member_a_o
            @ ^ [X4: a] : ( member_a @ X4 @ ( B2 @ X4 ) )
            @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( member_a_o
          @ ^ [X4: a] :
              ( ( P
               => ( member_a @ X4 @ ( A @ X4 ) ) )
              & ( ~ P
               => ( member_a @ X4 @ ( B2 @ X4 ) ) ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ).

% pred_in_If
thf(fact_940_pred__intros__imp_H,axiom,
    ! [K2: $o,P: a > $o,M: sigma_measure_a] :
      ( ( K2
       => ( member_a_o @ P @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( K2
           => ( P @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_imp'
thf(fact_941_pred__intros__conj1_H,axiom,
    ! [K2: $o,P: a > $o,M: sigma_measure_a] :
      ( ( K2
       => ( member_a_o @ P @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( K2
            & ( P @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_conj1'
thf(fact_942_pred__intros__conj2_H,axiom,
    ! [K2: $o,P: a > $o,M: sigma_measure_a] :
      ( ( K2
       => ( member_a_o @ P @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( ( P @ X4 )
            & K2 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_conj2'
thf(fact_943_pred__intros__disj1_H,axiom,
    ! [K2: $o,P: a > $o,M: sigma_measure_a] :
      ( ( ~ K2
       => ( member_a_o @ P @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( K2
            | ( P @ X4 ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_disj1'
thf(fact_944_pred__intros__disj2_H,axiom,
    ! [K2: $o,P: a > $o,M: sigma_measure_a] :
      ( ( ~ K2
       => ( member_a_o @ P @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_o
        @ ^ [X4: a] :
            ( ( P @ X4 )
            | K2 )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_disj2'
thf(fact_945_measurable__if__split,axiom,
    ! [C: $o,F: a > $o,M: sigma_measure_a,G: a > $o] :
      ( ( C
       => ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( ( ~ C
         => ( member_a_o @ G @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
       => ( ( C
           => ( member_a_o @ F @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
          & ( ~ C
           => ( member_a_o @ G @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ) ) ) ).

% measurable_if_split
thf(fact_946_complex__non__denum,axiom,
    ~ ? [F3: nat > complex] :
        ( ( image_nat_complex @ F3 @ top_top_set_nat )
        = top_top_set_complex ) ).

% complex_non_denum
thf(fact_947_measurable__Sup__nat,axiom,
    ! [F4: real > set_nat,M: sigma_measure_real] :
      ( ! [I2: nat] :
          ( member_real_o
          @ ^ [X4: real] : ( member_nat @ I2 @ ( F4 @ X4 ) )
          @ ( sigma_3939073009482781210real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_real_nat
        @ ^ [X4: real] : ( complete_Sup_Sup_nat @ ( F4 @ X4 ) )
        @ ( sigma_6315060578831106510al_nat @ M @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) ) ) ).

% measurable_Sup_nat
thf(fact_948_measurable__Sup__nat,axiom,
    ! [F4: a > set_nat,M: sigma_measure_a] :
      ( ! [I2: nat] :
          ( member_a_o
          @ ^ [X4: a] : ( member_nat @ I2 @ ( F4 @ X4 ) )
          @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) )
     => ( member_a_nat
        @ ^ [X4: a] : ( complete_Sup_Sup_nat @ ( F4 @ X4 ) )
        @ ( sigma_73150082625557118_a_nat @ M @ ( sigma_7685844798829912695ce_nat @ top_top_set_nat ) ) ) ) ).

% measurable_Sup_nat
thf(fact_949_pred__intros__countable__bounded_I1_J,axiom,
    ! [X5: set_nat,N: nat > nat > set_nat,M: sigma_measure_nat] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_nat_o
            @ ^ [X4: nat] : ( member_nat @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_5101835498682829686_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_nat_o
        @ ^ [X4: nat] : ( member_nat @ X4 @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_5101835498682829686_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(1)
thf(fact_950_pred__intros__countable__bounded_I1_J,axiom,
    ! [X5: set_nat,N: ( real > nat ) > nat > set_real_nat,M: sigma_6586288717683155060al_nat] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_real_nat_o
            @ ^ [X4: real > nat] : ( member_real_nat @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_4110928884538380267_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_real_nat_o
        @ ^ [X4: real > nat] : ( member_real_nat @ X4 @ ( comple8071895948329575818al_nat @ ( image_6900357751826779304al_nat @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_4110928884538380267_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(1)
thf(fact_951_pred__intros__countable__bounded_I1_J,axiom,
    ! [X5: set_nat,N: ( real > b ) > nat > set_real_b,M: sigma_measure_real_b] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_real_b_o
            @ ^ [X4: real > b] : ( member_real_b @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_7338419842690513246al_b_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_real_b_o
        @ ^ [X4: real > b] : ( member_real_b @ X4 @ ( comple7721903285369235185real_b @ ( image_nat_set_real_b @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_7338419842690513246al_b_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(1)
thf(fact_952_pred__intros__countable__bounded_I1_J,axiom,
    ! [X5: set_nat,N: ( real > a ) > nat > set_real_a,M: sigma_measure_real_a] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_real_a_o
            @ ^ [X4: real > a] : ( member_real_a @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_902503387808413471al_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_real_a_o
        @ ^ [X4: real > a] : ( member_real_a @ X4 @ ( comple7650869245322889200real_a @ ( image_nat_set_real_a @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_902503387808413471al_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(1)
thf(fact_953_pred__intros__countable__bounded_I1_J,axiom,
    ! [X5: set_nat,N: ( a > complex ) > nat > set_a_complex,M: sigma_2418697800065292186omplex] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_a_complex_o
            @ ^ [X4: a > complex] : ( member_a_complex @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_2293258167702796171plex_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_complex_o
        @ ^ [X4: a > complex] : ( member_a_complex @ X4 @ ( comple987388759867256068omplex @ ( image_3591888402735308390omplex @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_2293258167702796171plex_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(1)
thf(fact_954_pred__intros__countable__bounded_I1_J,axiom,
    ! [X5: set_nat,N: ( a > real ) > nat > set_a_real,M: sigma_measure_a_real] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_a_real_o
            @ ^ [X4: a > real] : ( member_a_real @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_9085598459323199629real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_real_o
        @ ^ [X4: a > real] : ( member_a_real @ X4 @ ( comple5242429829429470466a_real @ ( image_nat_set_a_real @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_9085598459323199629real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(1)
thf(fact_955_pred__intros__countable__bounded_I1_J,axiom,
    ! [X5: set_nat,N: ( a > $o ) > nat > set_a_o,M: sigma_measure_a_o] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_a_o_o
            @ ^ [X4: a > $o] : ( member_a_o @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_1195952539894209287_a_o_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_o_o
        @ ^ [X4: a > $o] : ( member_a_o @ X4 @ ( comple8115264379980766446et_a_o @ ( image_nat_set_a_o @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_1195952539894209287_a_o_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(1)
thf(fact_956_pred__intros__countable__bounded_I1_J,axiom,
    ! [X5: set_nat,N: ( a > nat ) > nat > set_a_nat,M: sigma_measure_a_nat] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_a_nat_o
            @ ^ [X4: a > nat] : ( member_a_nat @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_128654050890844905_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_nat_o
        @ ^ [X4: a > nat] : ( member_a_nat @ X4 @ ( comple4385993935590776358_a_nat @ ( image_nat_set_a_nat @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_128654050890844905_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(1)
thf(fact_957_pred__intros__countable__bounded_I1_J,axiom,
    ! [X5: set_nat,N: ( a > a ) > nat > set_a_a,M: sigma_measure_a_a] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_a_a_o
            @ ^ [X4: a > a] : ( member_a_a @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_7605542298065862561_a_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_a_o
        @ ^ [X4: a > a] : ( member_a_a @ X4 @ ( comple1050673676576882260et_a_a @ ( image_nat_set_a_a @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_7605542298065862561_a_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(1)
thf(fact_958_pred__intros__countable__bounded_I1_J,axiom,
    ! [X5: set_nat,N: a > nat > set_a,M: sigma_measure_a] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_a_o
            @ ^ [X4: a] : ( member_a @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_o
        @ ^ [X4: a] : ( member_a @ X4 @ ( comple6135023378680113637_set_a @ ( image_nat_set_a @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(1)
thf(fact_959_pred__intros__countable__bounded_I2_J,axiom,
    ! [X5: set_nat,N: nat > nat > set_nat,M: sigma_measure_nat] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_nat_o
            @ ^ [X4: nat] : ( member_nat @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_5101835498682829686_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_nat_o
        @ ^ [X4: nat] : ( member_nat @ X4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_5101835498682829686_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(2)
thf(fact_960_pred__intros__countable__bounded_I2_J,axiom,
    ! [X5: set_nat,N: ( real > nat ) > nat > set_real_nat,M: sigma_6586288717683155060al_nat] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_real_nat_o
            @ ^ [X4: real > nat] : ( member_real_nat @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_4110928884538380267_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_real_nat_o
        @ ^ [X4: real > nat] : ( member_real_nat @ X4 @ ( comple266511651042094116al_nat @ ( image_6900357751826779304al_nat @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_4110928884538380267_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(2)
thf(fact_961_pred__intros__countable__bounded_I2_J,axiom,
    ! [X5: set_nat,N: ( real > b ) > nat > set_real_b,M: sigma_measure_real_b] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_real_b_o
            @ ^ [X4: real > b] : ( member_real_b @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_7338419842690513246al_b_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_real_b_o
        @ ^ [X4: real > b] : ( member_real_b @ X4 @ ( comple4296955914004943575real_b @ ( image_nat_set_real_b @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_7338419842690513246al_b_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(2)
thf(fact_962_pred__intros__countable__bounded_I2_J,axiom,
    ! [X5: set_nat,N: ( real > a ) > nat > set_real_a,M: sigma_measure_real_a] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_real_a_o
            @ ^ [X4: real > a] : ( member_real_a @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_902503387808413471al_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_real_a_o
        @ ^ [X4: real > a] : ( member_real_a @ X4 @ ( comple4225921873958597590real_a @ ( image_nat_set_real_a @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_902503387808413471al_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(2)
thf(fact_963_pred__intros__countable__bounded_I2_J,axiom,
    ! [X5: set_nat,N: ( a > complex ) > nat > set_a_complex,M: sigma_2418697800065292186omplex] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_a_complex_o
            @ ^ [X4: a > complex] : ( member_a_complex @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_2293258167702796171plex_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_complex_o
        @ ^ [X4: a > complex] : ( member_a_complex @ X4 @ ( comple8696354750574632938omplex @ ( image_3591888402735308390omplex @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_2293258167702796171plex_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(2)
thf(fact_964_pred__intros__countable__bounded_I2_J,axiom,
    ! [X5: set_nat,N: ( a > real ) > nat > set_a_real,M: sigma_measure_a_real] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_a_real_o
            @ ^ [X4: a > real] : ( member_a_real @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_9085598459323199629real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_real_o
        @ ^ [X4: a > real] : ( member_a_real @ X4 @ ( comple1817482458065178856a_real @ ( image_nat_set_a_real @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_9085598459323199629real_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(2)
thf(fact_965_pred__intros__countable__bounded_I2_J,axiom,
    ! [X5: set_nat,N: ( a > $o ) > nat > set_a_o,M: sigma_measure_a_o] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_a_o_o
            @ ^ [X4: a > $o] : ( member_a_o @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_1195952539894209287_a_o_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_o_o
        @ ^ [X4: a > $o] : ( member_a_o @ X4 @ ( comple3956969172160116872et_a_o @ ( image_nat_set_a_o @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_1195952539894209287_a_o_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(2)
thf(fact_966_pred__intros__countable__bounded_I2_J,axiom,
    ! [X5: set_nat,N: ( a > nat ) > nat > set_a_nat,M: sigma_measure_a_nat] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_a_nat_o
            @ ^ [X4: a > nat] : ( member_a_nat @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_128654050890844905_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_nat_o
        @ ^ [X4: a > nat] : ( member_a_nat @ X4 @ ( comple4286861423968083212_a_nat @ ( image_nat_set_a_nat @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_128654050890844905_nat_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(2)
thf(fact_967_pred__intros__countable__bounded_I2_J,axiom,
    ! [X5: set_nat,N: ( a > a ) > nat > set_a_a,M: sigma_measure_a_a] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_a_a_o
            @ ^ [X4: a > a] : ( member_a_a @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_7605542298065862561_a_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_a_o
        @ ^ [X4: a > a] : ( member_a_a @ X4 @ ( comple6518619711525350638et_a_a @ ( image_nat_set_a_a @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_7605542298065862561_a_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(2)
thf(fact_968_pred__intros__countable__bounded_I2_J,axiom,
    ! [X5: set_nat,N: a > nat > set_a,M: sigma_measure_a] :
      ( ! [I2: nat] :
          ( ( member_nat @ I2 @ X5 )
         => ( member_a_o
            @ ^ [X4: a] : ( member_a @ X4 @ ( N @ X4 @ I2 ) )
            @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) )
     => ( member_a_o
        @ ^ [X4: a] : ( member_a @ X4 @ ( comple2307003609928055243_set_a @ ( image_nat_set_a @ ( N @ X4 ) @ X5 ) ) )
        @ ( sigma_measurable_a_o @ M @ ( sigma_count_space_o @ top_top_set_o ) ) ) ) ).

% pred_intros_countable_bounded(2)
thf(fact_969_space__Sup__eq__UN,axiom,
    ! [M: set_Si6059263944882162789e_real] :
      ( ( sigma_space_real @ ( comple1433435454551854066e_real @ M ) )
      = ( comple3096694443085538997t_real @ ( image_494530498693788066t_real @ sigma_space_real @ M ) ) ) ).

% space_Sup_eq_UN
thf(fact_970_space__Sup__eq__UN,axiom,
    ! [M: set_Si3048223896905877257re_nat] :
      ( ( sigma_space_nat @ ( comple1344625017055687830re_nat @ M ) )
      = ( comple7399068483239264473et_nat @ ( image_8842839924425425258et_nat @ sigma_space_nat @ M ) ) ) ).

% space_Sup_eq_UN
thf(fact_971_space__Sup__eq__UN,axiom,
    ! [M: set_Sigma_measure_o] :
      ( ( sigma_space_o @ ( comple8691778902212741480sure_o @ M ) )
      = ( comple90263536869209701_set_o @ ( image_5027996441425795932_set_o @ sigma_space_o @ M ) ) ) ).

% space_Sup_eq_UN
thf(fact_972_space__Sup__eq__UN,axiom,
    ! [M: set_Si97717610131227249nnreal] :
      ( ( sigma_3147302497200244656nnreal @ ( comple2394123286901040126nnreal @ M ) )
      = ( comple4226387801268262977nnreal @ ( image_5045373228407281722nnreal @ sigma_3147302497200244656nnreal @ M ) ) ) ).

% space_Sup_eq_UN
thf(fact_973_measurable__Sup1,axiom,
    ! [M4: sigma_measure_real,M: set_Si6059263944882162789e_real,F: real > b,N: sigma_measure_b] :
      ( ( member4553183543495551918e_real @ M4 @ M )
     => ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ M4 @ N ) )
       => ( ! [M5: sigma_measure_real,N3: sigma_measure_real] :
              ( ( member4553183543495551918e_real @ M5 @ M )
             => ( ( member4553183543495551918e_real @ N3 @ M )
               => ( ( sigma_space_real @ M5 )
                  = ( sigma_space_real @ N3 ) ) ) )
         => ( member_real_b @ F @ ( sigma_523072396149930113real_b @ ( comple1433435454551854066e_real @ M ) @ N ) ) ) ) ) ).

% measurable_Sup1
thf(fact_974_measurable__Sup1,axiom,
    ! [M4: sigma_measure_real,M: set_Si6059263944882162789e_real,F: real > a,N: sigma_measure_a] :
      ( ( member4553183543495551918e_real @ M4 @ M )
     => ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ M4 @ N ) )
       => ( ! [M5: sigma_measure_real,N3: sigma_measure_real] :
              ( ( member4553183543495551918e_real @ M5 @ M )
             => ( ( member4553183543495551918e_real @ N3 @ M )
               => ( ( sigma_space_real @ M5 )
                  = ( sigma_space_real @ N3 ) ) ) )
         => ( member_real_a @ F @ ( sigma_523072396149930112real_a @ ( comple1433435454551854066e_real @ M ) @ N ) ) ) ) ) ).

% measurable_Sup1
thf(fact_975_measurable__Sup1,axiom,
    ! [M4: sigma_measure_real,M: set_Si6059263944882162789e_real,F: real > nat,N: sigma_measure_nat] :
      ( ( member4553183543495551918e_real @ M4 @ M )
     => ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ M4 @ N ) )
       => ( ! [M5: sigma_measure_real,N3: sigma_measure_real] :
              ( ( member4553183543495551918e_real @ M5 @ M )
             => ( ( member4553183543495551918e_real @ N3 @ M )
               => ( ( sigma_space_real @ M5 )
                  = ( sigma_space_real @ N3 ) ) ) )
         => ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ ( comple1433435454551854066e_real @ M ) @ N ) ) ) ) ) ).

% measurable_Sup1
thf(fact_976_measurable__Sup1,axiom,
    ! [M4: sigma_measure_a,M: set_Sigma_measure_a,F: a > complex,N: sigma_3077487657436305159omplex] :
      ( ( member3534519376729797778sure_a @ M4 @ M )
     => ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ M4 @ N ) )
       => ( ! [M5: sigma_measure_a,N3: sigma_measure_a] :
              ( ( member3534519376729797778sure_a @ M5 @ M )
             => ( ( member3534519376729797778sure_a @ N3 @ M )
               => ( ( sigma_space_a @ M5 )
                  = ( sigma_space_a @ N3 ) ) ) )
         => ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ ( comple2239804592135895886sure_a @ M ) @ N ) ) ) ) ) ).

% measurable_Sup1
thf(fact_977_measurable__Sup1,axiom,
    ! [M4: sigma_measure_a,M: set_Sigma_measure_a,F: a > real,N: sigma_measure_real] :
      ( ( member3534519376729797778sure_a @ M4 @ M )
     => ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ M4 @ N ) )
       => ( ! [M5: sigma_measure_a,N3: sigma_measure_a] :
              ( ( member3534519376729797778sure_a @ M5 @ M )
             => ( ( member3534519376729797778sure_a @ N3 @ M )
               => ( ( sigma_space_a @ M5 )
                  = ( sigma_space_a @ N3 ) ) ) )
         => ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ ( comple2239804592135895886sure_a @ M ) @ N ) ) ) ) ) ).

% measurable_Sup1
thf(fact_978_measurable__Sup1,axiom,
    ! [M4: sigma_measure_a,M: set_Sigma_measure_a,F: a > $o,N: sigma_measure_o] :
      ( ( member3534519376729797778sure_a @ M4 @ M )
     => ( ( member_a_o @ F @ ( sigma_measurable_a_o @ M4 @ N ) )
       => ( ! [M5: sigma_measure_a,N3: sigma_measure_a] :
              ( ( member3534519376729797778sure_a @ M5 @ M )
             => ( ( member3534519376729797778sure_a @ N3 @ M )
               => ( ( sigma_space_a @ M5 )
                  = ( sigma_space_a @ N3 ) ) ) )
         => ( member_a_o @ F @ ( sigma_measurable_a_o @ ( comple2239804592135895886sure_a @ M ) @ N ) ) ) ) ) ).

% measurable_Sup1
thf(fact_979_measurable__Sup1,axiom,
    ! [M4: sigma_measure_a,M: set_Sigma_measure_a,F: a > nat,N: sigma_measure_nat] :
      ( ( member3534519376729797778sure_a @ M4 @ M )
     => ( ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ M4 @ N ) )
       => ( ! [M5: sigma_measure_a,N3: sigma_measure_a] :
              ( ( member3534519376729797778sure_a @ M5 @ M )
             => ( ( member3534519376729797778sure_a @ N3 @ M )
               => ( ( sigma_space_a @ M5 )
                  = ( sigma_space_a @ N3 ) ) ) )
         => ( member_a_nat @ F @ ( sigma_73150082625557118_a_nat @ ( comple2239804592135895886sure_a @ M ) @ N ) ) ) ) ) ).

% measurable_Sup1
thf(fact_980_measurable__Sup1,axiom,
    ! [M4: sigma_measure_a,M: set_Sigma_measure_a,F: a > a,N: sigma_measure_a] :
      ( ( member3534519376729797778sure_a @ M4 @ M )
     => ( ( member_a_a @ F @ ( sigma_measurable_a_a @ M4 @ N ) )
       => ( ! [M5: sigma_measure_a,N3: sigma_measure_a] :
              ( ( member3534519376729797778sure_a @ M5 @ M )
             => ( ( member3534519376729797778sure_a @ N3 @ M )
               => ( ( sigma_space_a @ M5 )
                  = ( sigma_space_a @ N3 ) ) ) )
         => ( member_a_a @ F @ ( sigma_measurable_a_a @ ( comple2239804592135895886sure_a @ M ) @ N ) ) ) ) ) ).

% measurable_Sup1
thf(fact_981_measurable__SUP1,axiom,
    ! [I: nat,I3: set_nat,F: real > b,M: nat > sigma_measure_real,N: sigma_measure_b] :
      ( ( member_nat @ I @ I3 )
     => ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ ( M @ I ) @ N ) )
       => ( ! [M5: nat,N3: nat] :
              ( ( member_nat @ M5 @ I3 )
             => ( ( member_nat @ N3 @ I3 )
               => ( ( sigma_space_real @ ( M @ M5 ) )
                  = ( sigma_space_real @ ( M @ N3 ) ) ) ) )
         => ( member_real_b @ F @ ( sigma_523072396149930113real_b @ ( comple1433435454551854066e_real @ ( image_4672691044420781678e_real @ M @ I3 ) ) @ N ) ) ) ) ) ).

% measurable_SUP1
thf(fact_982_measurable__SUP1,axiom,
    ! [I: a,I3: set_a,F: real > b,M: a > sigma_measure_real,N: sigma_measure_b] :
      ( ( member_a @ I @ I3 )
     => ( ( member_real_b @ F @ ( sigma_523072396149930113real_b @ ( M @ I ) @ N ) )
       => ( ! [M5: a,N3: a] :
              ( ( member_a @ M5 @ I3 )
             => ( ( member_a @ N3 @ I3 )
               => ( ( sigma_space_real @ ( M @ M5 ) )
                  = ( sigma_space_real @ ( M @ N3 ) ) ) ) )
         => ( member_real_b @ F @ ( sigma_523072396149930113real_b @ ( comple1433435454551854066e_real @ ( image_4051082315841709580e_real @ M @ I3 ) ) @ N ) ) ) ) ) ).

% measurable_SUP1
thf(fact_983_measurable__SUP1,axiom,
    ! [I: nat,I3: set_nat,F: real > a,M: nat > sigma_measure_real,N: sigma_measure_a] :
      ( ( member_nat @ I @ I3 )
     => ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ ( M @ I ) @ N ) )
       => ( ! [M5: nat,N3: nat] :
              ( ( member_nat @ M5 @ I3 )
             => ( ( member_nat @ N3 @ I3 )
               => ( ( sigma_space_real @ ( M @ M5 ) )
                  = ( sigma_space_real @ ( M @ N3 ) ) ) ) )
         => ( member_real_a @ F @ ( sigma_523072396149930112real_a @ ( comple1433435454551854066e_real @ ( image_4672691044420781678e_real @ M @ I3 ) ) @ N ) ) ) ) ) ).

% measurable_SUP1
thf(fact_984_measurable__SUP1,axiom,
    ! [I: a,I3: set_a,F: real > a,M: a > sigma_measure_real,N: sigma_measure_a] :
      ( ( member_a @ I @ I3 )
     => ( ( member_real_a @ F @ ( sigma_523072396149930112real_a @ ( M @ I ) @ N ) )
       => ( ! [M5: a,N3: a] :
              ( ( member_a @ M5 @ I3 )
             => ( ( member_a @ N3 @ I3 )
               => ( ( sigma_space_real @ ( M @ M5 ) )
                  = ( sigma_space_real @ ( M @ N3 ) ) ) ) )
         => ( member_real_a @ F @ ( sigma_523072396149930112real_a @ ( comple1433435454551854066e_real @ ( image_4051082315841709580e_real @ M @ I3 ) ) @ N ) ) ) ) ) ).

% measurable_SUP1
thf(fact_985_measurable__SUP1,axiom,
    ! [I: nat,I3: set_nat,F: real > nat,M: nat > sigma_measure_real,N: sigma_measure_nat] :
      ( ( member_nat @ I @ I3 )
     => ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ ( M @ I ) @ N ) )
       => ( ! [M5: nat,N3: nat] :
              ( ( member_nat @ M5 @ I3 )
             => ( ( member_nat @ N3 @ I3 )
               => ( ( sigma_space_real @ ( M @ M5 ) )
                  = ( sigma_space_real @ ( M @ N3 ) ) ) ) )
         => ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ ( comple1433435454551854066e_real @ ( image_4672691044420781678e_real @ M @ I3 ) ) @ N ) ) ) ) ) ).

% measurable_SUP1
thf(fact_986_measurable__SUP1,axiom,
    ! [I: a,I3: set_a,F: real > nat,M: a > sigma_measure_real,N: sigma_measure_nat] :
      ( ( member_a @ I @ I3 )
     => ( ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ ( M @ I ) @ N ) )
       => ( ! [M5: a,N3: a] :
              ( ( member_a @ M5 @ I3 )
             => ( ( member_a @ N3 @ I3 )
               => ( ( sigma_space_real @ ( M @ M5 ) )
                  = ( sigma_space_real @ ( M @ N3 ) ) ) ) )
         => ( member_real_nat @ F @ ( sigma_6315060578831106510al_nat @ ( comple1433435454551854066e_real @ ( image_4051082315841709580e_real @ M @ I3 ) ) @ N ) ) ) ) ) ).

% measurable_SUP1
thf(fact_987_measurable__SUP1,axiom,
    ! [I: nat,I3: set_nat,F: a > complex,M: nat > sigma_measure_a,N: sigma_3077487657436305159omplex] :
      ( ( member_nat @ I @ I3 )
     => ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ ( M @ I ) @ N ) )
       => ( ! [M5: nat,N3: nat] :
              ( ( member_nat @ M5 @ I3 )
             => ( ( member_nat @ N3 @ I3 )
               => ( ( sigma_space_a @ ( M @ M5 ) )
                  = ( sigma_space_a @ ( M @ N3 ) ) ) ) )
         => ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ ( comple2239804592135895886sure_a @ ( image_1114366812419140050sure_a @ M @ I3 ) ) @ N ) ) ) ) ) ).

% measurable_SUP1
thf(fact_988_measurable__SUP1,axiom,
    ! [I: a,I3: set_a,F: a > complex,M: a > sigma_measure_a,N: sigma_3077487657436305159omplex] :
      ( ( member_a @ I @ I3 )
     => ( ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ ( M @ I ) @ N ) )
       => ( ! [M5: a,N3: a] :
              ( ( member_a @ M5 @ I3 )
             => ( ( member_a @ N3 @ I3 )
               => ( ( sigma_space_a @ ( M @ M5 ) )
                  = ( sigma_space_a @ ( M @ N3 ) ) ) ) )
         => ( member_a_complex @ F @ ( sigma_852363994732143452omplex @ ( comple2239804592135895886sure_a @ ( image_5550635671931946676sure_a @ M @ I3 ) ) @ N ) ) ) ) ) ).

% measurable_SUP1
thf(fact_989_measurable__SUP1,axiom,
    ! [I: nat,I3: set_nat,F: a > real,M: nat > sigma_measure_a,N: sigma_measure_real] :
      ( ( member_nat @ I @ I3 )
     => ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ ( M @ I ) @ N ) )
       => ( ! [M5: nat,N3: nat] :
              ( ( member_nat @ M5 @ I3 )
             => ( ( member_nat @ N3 @ I3 )
               => ( ( sigma_space_a @ ( M @ M5 ) )
                  = ( sigma_space_a @ ( M @ N3 ) ) ) ) )
         => ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ ( comple2239804592135895886sure_a @ ( image_1114366812419140050sure_a @ M @ I3 ) ) @ N ) ) ) ) ) ).

% measurable_SUP1
thf(fact_990_measurable__SUP1,axiom,
    ! [I: a,I3: set_a,F: a > real,M: a > sigma_measure_a,N: sigma_measure_real] :
      ( ( member_a @ I @ I3 )
     => ( ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ ( M @ I ) @ N ) )
       => ( ! [M5: a,N3: a] :
              ( ( member_a @ M5 @ I3 )
             => ( ( member_a @ N3 @ I3 )
               => ( ( sigma_space_a @ ( M @ M5 ) )
                  = ( sigma_space_a @ ( M @ N3 ) ) ) ) )
         => ( member_a_real @ F @ ( sigma_9116425665531756122a_real @ ( comple2239804592135895886sure_a @ ( image_5550635671931946676sure_a @ M @ I3 ) ) @ N ) ) ) ) ) ).

% measurable_SUP1
thf(fact_991_borel__measurable__cINF__real,axiom,
    ! [I3: set_complex,F4: complex > a > real,M: sigma_measure_a] :
      ( ( counta5113917769705169331omplex @ I3 )
     => ( ! [I2: complex] :
            ( ( member_complex @ I2 @ I3 )
           => ( member_a_real @ ( F4 @ I2 ) @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) )
       => ( member_a_real
          @ ^ [X4: a] :
              ( comple4887499456419720421f_real
              @ ( image_complex_real
                @ ^ [I4: complex] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) ) ) ).

% borel_measurable_cINF_real
thf(fact_992_borel__measurable__cINF__real,axiom,
    ! [I3: set_real,F4: real > a > real,M: sigma_measure_a] :
      ( ( counta7319604579010473777e_real @ I3 )
     => ( ! [I2: real] :
            ( ( member_real @ I2 @ I3 )
           => ( member_a_real @ ( F4 @ I2 ) @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) )
       => ( member_a_real
          @ ^ [X4: a] :
              ( comple4887499456419720421f_real
              @ ( image_real_real
                @ ^ [I4: real] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) ) ) ).

% borel_measurable_cINF_real
thf(fact_993_borel__measurable__cINF__real,axiom,
    ! [I3: set_o,F4: $o > a > real,M: sigma_measure_a] :
      ( ( counta5976203206615340371able_o @ I3 )
     => ( ! [I2: $o] :
            ( ( member_o @ I2 @ I3 )
           => ( member_a_real @ ( F4 @ I2 ) @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) )
       => ( member_a_real
          @ ^ [X4: a] :
              ( comple4887499456419720421f_real
              @ ( image_o_real
                @ ^ [I4: $o] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) ) ) ).

% borel_measurable_cINF_real
thf(fact_994_borel__measurable__cINF__real,axiom,
    ! [I3: set_nat,F4: nat > a > real,M: sigma_measure_a] :
      ( ( counta1168086296615599829le_nat @ I3 )
     => ( ! [I2: nat] :
            ( ( member_nat @ I2 @ I3 )
           => ( member_a_real @ ( F4 @ I2 ) @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) )
       => ( member_a_real
          @ ^ [X4: a] :
              ( comple4887499456419720421f_real
              @ ( image_nat_real
                @ ^ [I4: nat] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) ) ) ).

% borel_measurable_cINF_real
thf(fact_995_borel__measurable__cINF__real,axiom,
    ! [I3: set_a,F4: a > a > real,M: sigma_measure_a] :
      ( ( counta4098120917673242425able_a @ I3 )
     => ( ! [I2: a] :
            ( ( member_a @ I2 @ I3 )
           => ( member_a_real @ ( F4 @ I2 ) @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) )
       => ( member_a_real
          @ ^ [X4: a] :
              ( comple4887499456419720421f_real
              @ ( image_a_real
                @ ^ [I4: a] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) ) ) ).

% borel_measurable_cINF_real
thf(fact_996_borel__measurable__cINF__real,axiom,
    ! [I3: set_real_nat,F4: ( real > nat ) > a > real,M: sigma_measure_a] :
      ( ( counta7410736174393390496al_nat @ I3 )
     => ( ! [I2: real > nat] :
            ( ( member_real_nat @ I2 @ I3 )
           => ( member_a_real @ ( F4 @ I2 ) @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) )
       => ( member_a_real
          @ ^ [X4: a] :
              ( comple4887499456419720421f_real
              @ ( image_real_nat_real
                @ ^ [I4: real > nat] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) ) ) ).

% borel_measurable_cINF_real
thf(fact_997_borel__measurable__cINF__real,axiom,
    ! [I3: set_real_b,F4: ( real > b ) > a > real,M: sigma_measure_a] :
      ( ( counta6639396087987402821real_b @ I3 )
     => ( ! [I2: real > b] :
            ( ( member_real_b @ I2 @ I3 )
           => ( member_a_real @ ( F4 @ I2 ) @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) )
       => ( member_a_real
          @ ^ [X4: a] :
              ( comple4887499456419720421f_real
              @ ( image_real_b_real
                @ ^ [I4: real > b] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) ) ) ).

% borel_measurable_cINF_real
thf(fact_998_borel__measurable__cINF__real,axiom,
    ! [I3: set_real_a,F4: ( real > a ) > a > real,M: sigma_measure_a] :
      ( ( counta6639396083684174020real_a @ I3 )
     => ( ! [I2: real > a] :
            ( ( member_real_a @ I2 @ I3 )
           => ( member_a_real @ ( F4 @ I2 ) @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) )
       => ( member_a_real
          @ ^ [X4: a] :
              ( comple4887499456419720421f_real
              @ ( image_real_a_real
                @ ^ [I4: real > a] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) ) ) ).

% borel_measurable_cINF_real
thf(fact_999_borel__measurable__cINF__real,axiom,
    ! [I3: set_a_complex,F4: ( a > complex ) > a > real,M: sigma_measure_a] :
      ( ( counta599731762510375256omplex @ I3 )
     => ( ! [I2: a > complex] :
            ( ( member_a_complex @ I2 @ I3 )
           => ( member_a_real @ ( F4 @ I2 ) @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) )
       => ( member_a_real
          @ ^ [X4: a] :
              ( comple4887499456419720421f_real
              @ ( image_a_complex_real
                @ ^ [I4: a > complex] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) ) ) ).

% borel_measurable_cINF_real
thf(fact_1000_borel__measurable__cINF__real,axiom,
    ! [I3: set_a_real,F4: ( a > real ) > a > real,M: sigma_measure_a] :
      ( ( counta6122129581416836822a_real @ I3 )
     => ( ! [I2: a > real] :
            ( ( member_a_real @ I2 @ I3 )
           => ( member_a_real @ ( F4 @ I2 ) @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) )
       => ( member_a_real
          @ ^ [X4: a] :
              ( comple4887499456419720421f_real
              @ ( image_a_real_real
                @ ^ [I4: a > real] : ( F4 @ I4 @ X4 )
                @ I3 ) )
          @ ( sigma_9116425665531756122a_real @ M @ borel_5078946678739801102l_real ) ) ) ) ).

% borel_measurable_cINF_real
thf(fact_1001_measurable__Sup__measurable,axiom,
    ! [F: real > b,N: sigma_measure_real,A: set_b] :
      ( ( member_real_b @ F
        @ ( pi_real_b @ ( sigma_space_real @ N )
          @ ^ [Uu: real] : A ) )
     => ( member_real_b @ F
        @ ( sigma_523072396149930113real_b @ N
          @ ( comple2239804596439124687sure_b
            @ ( collec3051732625303252049sure_b
              @ ^ [M3: sigma_measure_b] :
                  ( ( ( sigma_space_b @ M3 )
                    = A )
                  & ( member_real_b @ F @ ( sigma_523072396149930113real_b @ N @ M3 ) ) ) ) ) ) ) ) ).

% measurable_Sup_measurable
thf(fact_1002_measurable__Sup__measurable,axiom,
    ! [F: real > real,N: sigma_measure_real,A: set_real] :
      ( ( member_real_real @ F
        @ ( pi_real_real @ ( sigma_space_real @ N )
          @ ^ [Uu: real] : A ) )
     => ( member_real_real @ F
        @ ( sigma_5267869275261027754l_real @ N
          @ ( comple1433435454551854066e_real
            @ ( collec7224749146907561712e_real
              @ ^ [M3: sigma_measure_real] :
                  ( ( ( sigma_space_real @ M3 )
                    = A )
                  & ( member_real_real @ F @ ( sigma_5267869275261027754l_real @ N @ M3 ) ) ) ) ) ) ) ) ).

% measurable_Sup_measurable
thf(fact_1003_measurable__Sup__measurable,axiom,
    ! [F: real > $o,N: sigma_measure_real,A: set_o] :
      ( ( member_real_o @ F
        @ ( pi_real_o @ ( sigma_space_real @ N )
          @ ^ [Uu: real] : A ) )
     => ( member_real_o @ F
        @ ( sigma_3939073009482781210real_o @ N
          @ ( comple8691778902212741480sure_o
            @ ( collec7312474603106749418sure_o
              @ ^ [M3: sigma_measure_o] :
                  ( ( ( sigma_space_o @ M3 )
                    = A )
                  & ( member_real_o @ F @ ( sigma_3939073009482781210real_o @ N @ M3 ) ) ) ) ) ) ) ) ).

% measurable_Sup_measurable
thf(fact_1004_measurable__Sup__measurable,axiom,
    ! [F: real > extend8495563244428889912nnreal,N: sigma_measure_real,A: set_Ex3793607809372303086nnreal] :
      ( ( member2919562650594848410nnreal @ F
        @ ( pi_rea7198910874028739761nnreal @ ( sigma_space_real @ N )
          @ ^ [Uu: real] : A ) )
     => ( member2919562650594848410nnreal @ F
        @ ( sigma_9017504469962657078nnreal @ N
          @ ( comple2394123286901040126nnreal
            @ ( collec8236033019726599676nnreal
              @ ^ [M3: sigma_7234349610311085201nnreal] :
                  ( ( ( sigma_3147302497200244656nnreal @ M3 )
                    = A )
                  & ( member2919562650594848410nnreal @ F @ ( sigma_9017504469962657078nnreal @ N @ M3 ) ) ) ) ) ) ) ) ).

% measurable_Sup_measurable
thf(fact_1005_measurable__Sup__measurable,axiom,
    ! [F: nat > real,N: sigma_measure_nat,A: set_real] :
      ( ( member_nat_real @ F
        @ ( pi_nat_real @ ( sigma_space_nat @ N )
          @ ^ [Uu: nat] : A ) )
     => ( member_nat_real @ F
        @ ( sigma_1747752005702207822t_real @ N
          @ ( comple1433435454551854066e_real
            @ ( collec7224749146907561712e_real
              @ ^ [M3: sigma_measure_real] :
                  ( ( ( sigma_space_real @ M3 )
                    = A )
                  & ( member_nat_real @ F @ ( sigma_1747752005702207822t_real @ N @ M3 ) ) ) ) ) ) ) ) ).

% measurable_Sup_measurable
thf(fact_1006_measurable__Sup__measurable,axiom,
    ! [F: nat > nat,N: sigma_measure_nat,A: set_nat] :
      ( ( member_nat_nat @ F
        @ ( pi_nat_nat @ ( sigma_space_nat @ N )
          @ ^ [Uu: nat] : A ) )
     => ( member_nat_nat @ F
        @ ( sigma_4350458207664084850at_nat @ N
          @ ( comple1344625017055687830re_nat
            @ ( collec4653854238239757972re_nat
              @ ^ [M3: sigma_measure_nat] :
                  ( ( ( sigma_space_nat @ M3 )
                    = A )
                  & ( member_nat_nat @ F @ ( sigma_4350458207664084850at_nat @ N @ M3 ) ) ) ) ) ) ) ) ).

% measurable_Sup_measurable
thf(fact_1007_measurable__Sup__measurable,axiom,
    ! [F: nat > $o,N: sigma_measure_nat,A: set_o] :
      ( ( member_nat_o @ F
        @ ( pi_nat_o @ ( sigma_space_nat @ N )
          @ ^ [Uu: nat] : A ) )
     => ( member_nat_o @ F
        @ ( sigma_5101835498682829686_nat_o @ N
          @ ( comple8691778902212741480sure_o
            @ ( collec7312474603106749418sure_o
              @ ^ [M3: sigma_measure_o] :
                  ( ( ( sigma_space_o @ M3 )
                    = A )
                  & ( member_nat_o @ F @ ( sigma_5101835498682829686_nat_o @ N @ M3 ) ) ) ) ) ) ) ) ).

% measurable_Sup_measurable
thf(fact_1008_measurable__Sup__measurable,axiom,
    ! [F: nat > extend8495563244428889912nnreal,N: sigma_measure_nat,A: set_Ex3793607809372303086nnreal] :
      ( ( member8283130129095025342nnreal @ F
        @ ( pi_nat6594671786139111381nnreal @ ( sigma_space_nat @ N )
          @ ^ [Uu: nat] : A ) )
     => ( member8283130129095025342nnreal @ F
        @ ( sigma_6306161311797543642nnreal @ N
          @ ( comple2394123286901040126nnreal
            @ ( collec8236033019726599676nnreal
              @ ^ [M3: sigma_7234349610311085201nnreal] :
                  ( ( ( sigma_3147302497200244656nnreal @ M3 )
                    = A )
                  & ( member8283130129095025342nnreal @ F @ ( sigma_6306161311797543642nnreal @ N @ M3 ) ) ) ) ) ) ) ) ).

% measurable_Sup_measurable
thf(fact_1009_measurable__Sup__measurable,axiom,
    ! [F: $o > real,N: sigma_measure_o,A: set_real] :
      ( ( member_o_real @ F
        @ ( pi_o_real @ ( sigma_space_o @ N )
          @ ^ [Uu: $o] : A ) )
     => ( member_o_real @ F
        @ ( sigma_2430008634441611636o_real @ N
          @ ( comple1433435454551854066e_real
            @ ( collec7224749146907561712e_real
              @ ^ [M3: sigma_measure_real] :
                  ( ( ( sigma_space_real @ M3 )
                    = A )
                  & ( member_o_real @ F @ ( sigma_2430008634441611636o_real @ N @ M3 ) ) ) ) ) ) ) ) ).

% measurable_Sup_measurable
thf(fact_1010_measurable__Sup__measurable,axiom,
    ! [F: $o > nat,N: sigma_measure_o,A: set_nat] :
      ( ( member_o_nat @ F
        @ ( pi_o_nat @ ( sigma_space_o @ N )
          @ ^ [Uu: $o] : A ) )
     => ( member_o_nat @ F
        @ ( sigma_1999164137574644376_o_nat @ N
          @ ( comple1344625017055687830re_nat
            @ ( collec4653854238239757972re_nat
              @ ^ [M3: sigma_measure_nat] :
                  ( ( ( sigma_space_nat @ M3 )
                    = A )
                  & ( member_o_nat @ F @ ( sigma_1999164137574644376_o_nat @ N @ M3 ) ) ) ) ) ) ) ) ).

% measurable_Sup_measurable
thf(fact_1011_Pi__cong__sets,axiom,
    ! [I3: set_real,J2: set_real,M: real > set_a,N: real > set_a] :
      ( ( I3 = J2 )
     => ( ! [X2: real] :
            ( ( member_real @ X2 @ I3 )
           => ( ( M @ X2 )
              = ( N @ X2 ) ) )
       => ( ( pi_real_a @ I3 @ M )
          = ( pi_real_a @ J2 @ N ) ) ) ) ).

% Pi_cong_sets
thf(fact_1012_Pi__cong,axiom,
    ! [A: set_real,F: real > nat,G: real > nat,B2: real > set_nat] :
      ( ! [W: real] :
          ( ( member_real @ W @ A )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_real_nat @ F @ ( pi_real_nat @ A @ B2 ) )
        = ( member_real_nat @ G @ ( pi_real_nat @ A @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_1013_Pi__cong,axiom,
    ! [A: set_real,F: real > b,G: real > b,B2: real > set_b] :
      ( ! [W: real] :
          ( ( member_real @ W @ A )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_real_b @ F @ ( pi_real_b @ A @ B2 ) )
        = ( member_real_b @ G @ ( pi_real_b @ A @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_1014_Pi__cong,axiom,
    ! [A: set_real,F: real > a,G: real > a,B2: real > set_a] :
      ( ! [W: real] :
          ( ( member_real @ W @ A )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_real_a @ F @ ( pi_real_a @ A @ B2 ) )
        = ( member_real_a @ G @ ( pi_real_a @ A @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_1015_Pi__cong,axiom,
    ! [A: set_a,F: a > complex,G: a > complex,B2: a > set_complex] :
      ( ! [W: a] :
          ( ( member_a @ W @ A )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_a_complex @ F @ ( pi_a_complex @ A @ B2 ) )
        = ( member_a_complex @ G @ ( pi_a_complex @ A @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_1016_Pi__cong,axiom,
    ! [A: set_a,F: a > real,G: a > real,B2: a > set_real] :
      ( ! [W: a] :
          ( ( member_a @ W @ A )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_a_real @ F @ ( pi_a_real @ A @ B2 ) )
        = ( member_a_real @ G @ ( pi_a_real @ A @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_1017_Pi__cong,axiom,
    ! [A: set_a,F: a > $o,G: a > $o,B2: a > set_o] :
      ( ! [W: a] :
          ( ( member_a @ W @ A )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_a_o @ F @ ( pi_a_o @ A @ B2 ) )
        = ( member_a_o @ G @ ( pi_a_o @ A @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_1018_Pi__cong,axiom,
    ! [A: set_a,F: a > nat,G: a > nat,B2: a > set_nat] :
      ( ! [W: a] :
          ( ( member_a @ W @ A )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_a_nat @ F @ ( pi_a_nat @ A @ B2 ) )
        = ( member_a_nat @ G @ ( pi_a_nat @ A @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_1019_Pi__cong,axiom,
    ! [A: set_a,F: a > a,G: a > a,B2: a > set_a] :
      ( ! [W: a] :
          ( ( member_a @ W @ A )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_a_a @ F @ ( pi_a_a @ A @ B2 ) )
        = ( member_a_a @ G @ ( pi_a_a @ A @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_1020_Pi__mem,axiom,
    ! [F: nat > nat,A: set_nat,B2: nat > set_nat,X: nat] :
      ( ( member_nat_nat @ F @ ( pi_nat_nat @ A @ B2 ) )
     => ( ( member_nat @ X @ A )
       => ( member_nat @ ( F @ X ) @ ( B2 @ X ) ) ) ) ).

% Pi_mem
thf(fact_1021_Pi__mem,axiom,
    ! [F: nat > a,A: set_nat,B2: nat > set_a,X: nat] :
      ( ( member_nat_a @ F @ ( pi_nat_a @ A @ B2 ) )
     => ( ( member_nat @ X @ A )
       => ( member_a @ ( F @ X ) @ ( B2 @ X ) ) ) ) ).

% Pi_mem
thf(fact_1022_Pi__mem,axiom,
    ! [F: real > nat,A: set_real,B2: real > set_nat,X: real] :
      ( ( member_real_nat @ F @ ( pi_real_nat @ A @ B2 ) )
     => ( ( member_real @ X @ A )
       => ( member_nat @ ( F @ X ) @ ( B2 @ X ) ) ) ) ).

% Pi_mem
thf(fact_1023_Pi__mem,axiom,
    ! [F: real > b,A: set_real,B2: real > set_b,X: real] :
      ( ( member_real_b @ F @ ( pi_real_b @ A @ B2 ) )
     => ( ( member_real @ X @ A )
       => ( member_b @ ( F @ X ) @ ( B2 @ X ) ) ) ) ).

% Pi_mem
thf(fact_1024_Pi__mem,axiom,
    ! [F: real > a,A: set_real,B2: real > set_a,X: real] :
      ( ( member_real_a @ F @ ( pi_real_a @ A @ B2 ) )
     => ( ( member_real @ X @ A )
       => ( member_a @ ( F @ X ) @ ( B2 @ X ) ) ) ) ).

% Pi_mem
thf(fact_1025_Pi__mem,axiom,
    ! [F: a > complex,A: set_a,B2: a > set_complex,X: a] :
      ( ( member_a_complex @ F @ ( pi_a_complex @ A @ B2 ) )
     => ( ( member_a @ X @ A )
       => ( member_complex @ ( F @ X ) @ ( B2 @ X ) ) ) ) ).

% Pi_mem
thf(fact_1026_Pi__mem,axiom,
    ! [F: a > real,A: set_a,B2: a > set_real,X: a] :
      ( ( member_a_real @ F @ ( pi_a_real @ A @ B2 ) )
     => ( ( member_a @ X @ A )
       => ( member_real @ ( F @ X ) @ ( B2 @ X ) ) ) ) ).

% Pi_mem
thf(fact_1027_Pi__mem,axiom,
    ! [F: a > $o,A: set_a,B2: a > set_o,X: a] :
      ( ( member_a_o @ F @ ( pi_a_o @ A @ B2 ) )
     => ( ( member_a @ X @ A )
       => ( member_o @ ( F @ X ) @ ( B2 @ X ) ) ) ) ).

% Pi_mem
thf(fact_1028_Pi__mem,axiom,
    ! [F: a > nat,A: set_a,B2: a > set_nat,X: a] :
      ( ( member_a_nat @ F @ ( pi_a_nat @ A @ B2 ) )
     => ( ( member_a @ X @ A )
       => ( member_nat @ ( F @ X ) @ ( B2 @ X ) ) ) ) ).

% Pi_mem
thf(fact_1029_Pi__mem,axiom,
    ! [F: a > a,A: set_a,B2: a > set_a,X: a] :
      ( ( member_a_a @ F @ ( pi_a_a @ A @ B2 ) )
     => ( ( member_a @ X @ A )
       => ( member_a @ ( F @ X ) @ ( B2 @ X ) ) ) ) ).

% Pi_mem
thf(fact_1030_Pi__iff,axiom,
    ! [F: real > nat,I3: set_real,X5: real > set_nat] :
      ( ( member_real_nat @ F @ ( pi_real_nat @ I3 @ X5 ) )
      = ( ! [X4: real] :
            ( ( member_real @ X4 @ I3 )
           => ( member_nat @ ( F @ X4 ) @ ( X5 @ X4 ) ) ) ) ) ).

% Pi_iff
thf(fact_1031_Pi__iff,axiom,
    ! [F: real > b,I3: set_real,X5: real > set_b] :
      ( ( member_real_b @ F @ ( pi_real_b @ I3 @ X5 ) )
      = ( ! [X4: real] :
            ( ( member_real @ X4 @ I3 )
           => ( member_b @ ( F @ X4 ) @ ( X5 @ X4 ) ) ) ) ) ).

% Pi_iff
thf(fact_1032_Pi__iff,axiom,
    ! [F: real > a,I3: set_real,X5: real > set_a] :
      ( ( member_real_a @ F @ ( pi_real_a @ I3 @ X5 ) )
      = ( ! [X4: real] :
            ( ( member_real @ X4 @ I3 )
           => ( member_a @ ( F @ X4 ) @ ( X5 @ X4 ) ) ) ) ) ).

% Pi_iff
thf(fact_1033_Pi__iff,axiom,
    ! [F: a > complex,I3: set_a,X5: a > set_complex] :
      ( ( member_a_complex @ F @ ( pi_a_complex @ I3 @ X5 ) )
      = ( ! [X4: a] :
            ( ( member_a @ X4 @ I3 )
           => ( member_complex @ ( F @ X4 ) @ ( X5 @ X4 ) ) ) ) ) ).

% Pi_iff
thf(fact_1034_Pi__iff,axiom,
    ! [F: a > real,I3: set_a,X5: a > set_real] :
      ( ( member_a_real @ F @ ( pi_a_real @ I3 @ X5 ) )
      = ( ! [X4: a] :
            ( ( member_a @ X4 @ I3 )
           => ( member_real @ ( F @ X4 ) @ ( X5 @ X4 ) ) ) ) ) ).

% Pi_iff
thf(fact_1035_Pi__iff,axiom,
    ! [F: a > $o,I3: set_a,X5: a > set_o] :
      ( ( member_a_o @ F @ ( pi_a_o @ I3 @ X5 ) )
      = ( ! [X4: a] :
            ( ( member_a @ X4 @ I3 )
           => ( member_o @ ( F @ X4 ) @ ( X5 @ X4 ) ) ) ) ) ).

% Pi_iff
thf(fact_1036_Pi__iff,axiom,
    ! [F: a > nat,I3: set_a,X5: a > set_nat] :
      ( ( member_a_nat @ F @ ( pi_a_nat @ I3 @ X5 ) )
      = ( ! [X4: a] :
            ( ( member_a @ X4 @ I3 )
           => ( member_nat @ ( F @ X4 ) @ ( X5 @ X4 ) ) ) ) ) ).

% Pi_iff
thf(fact_1037_Pi__iff,axiom,
    ! [F: a > a,I3: set_a,X5: a > set_a] :
      ( ( member_a_a @ F @ ( pi_a_a @ I3 @ X5 ) )
      = ( ! [X4: a] :
            ( ( member_a @ X4 @ I3 )
           => ( member_a @ ( F @ X4 ) @ ( X5 @ X4 ) ) ) ) ) ).

% Pi_iff
thf(fact_1038_Pi__I_H,axiom,
    ! [A: set_real,F: real > b,B2: real > set_b] :
      ( ! [X2: real] :
          ( ( member_real @ X2 @ A )
         => ( member_b @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_real_b @ F @ ( pi_real_b @ A @ B2 ) ) ) ).

% Pi_I'
thf(fact_1039_Pi__I_H,axiom,
    ! [A: set_real,F: real > nat,B2: real > set_nat] :
      ( ! [X2: real] :
          ( ( member_real @ X2 @ A )
         => ( member_nat @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_real_nat @ F @ ( pi_real_nat @ A @ B2 ) ) ) ).

% Pi_I'
thf(fact_1040_Pi__I_H,axiom,
    ! [A: set_real,F: real > a,B2: real > set_a] :
      ( ! [X2: real] :
          ( ( member_real @ X2 @ A )
         => ( member_a @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_real_a @ F @ ( pi_real_a @ A @ B2 ) ) ) ).

% Pi_I'
thf(fact_1041_Pi__I_H,axiom,
    ! [A: set_nat,F: nat > nat,B2: nat > set_nat] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_nat @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_nat_nat @ F @ ( pi_nat_nat @ A @ B2 ) ) ) ).

% Pi_I'
thf(fact_1042_Pi__I_H,axiom,
    ! [A: set_nat,F: nat > a,B2: nat > set_a] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_a @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_nat_a @ F @ ( pi_nat_a @ A @ B2 ) ) ) ).

% Pi_I'
thf(fact_1043_Pi__I_H,axiom,
    ! [A: set_a,F: a > complex,B2: a > set_complex] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_complex @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_a_complex @ F @ ( pi_a_complex @ A @ B2 ) ) ) ).

% Pi_I'
thf(fact_1044_Pi__I_H,axiom,
    ! [A: set_a,F: a > real,B2: a > set_real] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_real @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_a_real @ F @ ( pi_a_real @ A @ B2 ) ) ) ).

% Pi_I'
thf(fact_1045_Pi__I_H,axiom,
    ! [A: set_a,F: a > $o,B2: a > set_o] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_o @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_a_o @ F @ ( pi_a_o @ A @ B2 ) ) ) ).

% Pi_I'
thf(fact_1046_Pi__I_H,axiom,
    ! [A: set_a,F: a > nat,B2: a > set_nat] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_nat @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_a_nat @ F @ ( pi_a_nat @ A @ B2 ) ) ) ).

% Pi_I'
thf(fact_1047_Pi__I_H,axiom,
    ! [A: set_a,F: a > a,B2: a > set_a] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_a @ ( F @ X2 ) @ ( B2 @ X2 ) ) )
     => ( member_a_a @ F @ ( pi_a_a @ A @ B2 ) ) ) ).

% Pi_I'
thf(fact_1048_PiE,axiom,
    ! [F: nat > nat,A: set_nat,B2: nat > set_nat,X: nat] :
      ( ( member_nat_nat @ F @ ( pi_nat_nat @ A @ B2 ) )
     => ( ~ ( member_nat @ ( F @ X ) @ ( B2 @ X ) )
       => ~ ( member_nat @ X @ A ) ) ) ).

% PiE
thf(fact_1049_PiE,axiom,
    ! [F: nat > a,A: set_nat,B2: nat > set_a,X: nat] :
      ( ( member_nat_a @ F @ ( pi_nat_a @ A @ B2 ) )
     => ( ~ ( member_a @ ( F @ X ) @ ( B2 @ X ) )
       => ~ ( member_nat @ X @ A ) ) ) ).

% PiE
thf(fact_1050_PiE,axiom,
    ! [F: real > nat,A: set_real,B2: real > set_nat,X: real] :
      ( ( member_real_nat @ F @ ( pi_real_nat @ A @ B2 ) )
     => ( ~ ( member_nat @ ( F @ X ) @ ( B2 @ X ) )
       => ~ ( member_real @ X @ A ) ) ) ).

% PiE
thf(fact_1051_PiE,axiom,
    ! [F: real > b,A: set_real,B2: real > set_b,X: real] :
      ( ( member_real_b @ F @ ( pi_real_b @ A @ B2 ) )
     => ( ~ ( member_b @ ( F @ X ) @ ( B2 @ X ) )
       => ~ ( member_real @ X @ A ) ) ) ).

% PiE
thf(fact_1052_PiE,axiom,
    ! [F: real > a,A: set_real,B2: real > set_a,X: real] :
      ( ( member_real_a @ F @ ( pi_real_a @ A @ B2 ) )
     => ( ~ ( member_a @ ( F @ X ) @ ( B2 @ X ) )
       => ~ ( member_real @ X @ A ) ) ) ).

% PiE
thf(fact_1053_PiE,axiom,
    ! [F: a > complex,A: set_a,B2: a > set_complex,X: a] :
      ( ( member_a_complex @ F @ ( pi_a_complex @ A @ B2 ) )
     => ( ~ ( member_complex @ ( F @ X ) @ ( B2 @ X ) )
       => ~ ( member_a @ X @ A ) ) ) ).

% PiE
thf(fact_1054_PiE,axiom,
    ! [F: a > real,A: set_a,B2: a > set_real,X: a] :
      ( ( member_a_real @ F @ ( pi_a_real @ A @ B2 ) )
     => ( ~ ( member_real @ ( F @ X ) @ ( B2 @ X ) )
       => ~ ( member_a @ X @ A ) ) ) ).

% PiE
thf(fact_1055_PiE,axiom,
    ! [F: a > $o,A: set_a,B2: a > set_o,X: a] :
      ( ( member_a_o @ F @ ( pi_a_o @ A @ B2 ) )
     => ( ~ ( member_o @ ( F @ X ) @ ( B2 @ X ) )
       => ~ ( member_a @ X @ A ) ) ) ).

% PiE
thf(fact_1056_PiE,axiom,
    ! [F: a > nat,A: set_a,B2: a > set_nat,X: a] :
      ( ( member_a_nat @ F @ ( pi_a_nat @ A @ B2 ) )
     => ( ~ ( member_nat @ ( F @ X ) @ ( B2 @ X ) )
       => ~ ( member_a @ X @ A ) ) ) ).

% PiE
thf(fact_1057_PiE,axiom,
    ! [F: a > a,A: set_a,B2: a > set_a,X: a] :
      ( ( member_a_a @ F @ ( pi_a_a @ A @ B2 ) )
     => ( ~ ( member_a @ ( F @ X ) @ ( B2 @ X ) )
       => ~ ( member_a @ X @ A ) ) ) ).

% PiE
thf(fact_1058_funcset__mem,axiom,
    ! [F: nat > nat,A: set_nat,B2: set_nat,X: nat] :
      ( ( member_nat_nat @ F
        @ ( pi_nat_nat @ A
          @ ^ [Uu: nat] : B2 ) )
     => ( ( member_nat @ X @ A )
       => ( member_nat @ ( F @ X ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_1059_funcset__mem,axiom,
    ! [F: nat > a,A: set_nat,B2: set_a,X: nat] :
      ( ( member_nat_a @ F
        @ ( pi_nat_a @ A
          @ ^ [Uu: nat] : B2 ) )
     => ( ( member_nat @ X @ A )
       => ( member_a @ ( F @ X ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_1060_funcset__mem,axiom,
    ! [F: real > nat,A: set_real,B2: set_nat,X: real] :
      ( ( member_real_nat @ F
        @ ( pi_real_nat @ A
          @ ^ [Uu: real] : B2 ) )
     => ( ( member_real @ X @ A )
       => ( member_nat @ ( F @ X ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_1061_funcset__mem,axiom,
    ! [F: real > b,A: set_real,B2: set_b,X: real] :
      ( ( member_real_b @ F
        @ ( pi_real_b @ A
          @ ^ [Uu: real] : B2 ) )
     => ( ( member_real @ X @ A )
       => ( member_b @ ( F @ X ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_1062_funcset__mem,axiom,
    ! [F: real > a,A: set_real,B2: set_a,X: real] :
      ( ( member_real_a @ F
        @ ( pi_real_a @ A
          @ ^ [Uu: real] : B2 ) )
     => ( ( member_real @ X @ A )
       => ( member_a @ ( F @ X ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_1063_funcset__mem,axiom,
    ! [F: a > complex,A: set_a,B2: set_complex,X: a] :
      ( ( member_a_complex @ F
        @ ( pi_a_complex @ A
          @ ^ [Uu: a] : B2 ) )
     => ( ( member_a @ X @ A )
       => ( member_complex @ ( F @ X ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_1064_funcset__mem,axiom,
    ! [F: a > real,A: set_a,B2: set_real,X: a] :
      ( ( member_a_real @ F
        @ ( pi_a_real @ A
          @ ^ [Uu: a] : B2 ) )
     => ( ( member_a @ X @ A )
       => ( member_real @ ( F @ X ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_1065_funcset__mem,axiom,
    ! [F: a > $o,A: set_a,B2: set_o,X: a] :
      ( ( member_a_o @ F
        @ ( pi_a_o @ A
          @ ^ [Uu: a] : B2 ) )
     => ( ( member_a @ X @ A )
       => ( member_o @ ( F @ X ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_1066_funcset__mem,axiom,
    ! [F: a > nat,A: set_a,B2: set_nat,X: a] :
      ( ( member_a_nat @ F
        @ ( pi_a_nat @ A
          @ ^ [Uu: a] : B2 ) )
     => ( ( member_a @ X @ A )
       => ( member_nat @ ( F @ X ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_1067_funcset__mem,axiom,
    ! [F: a > a,A: set_a,B2: set_a,X: a] :
      ( ( member_a_a @ F
        @ ( pi_a_a @ A
          @ ^ [Uu: a] : B2 ) )
     => ( ( member_a @ X @ A )
       => ( member_a @ ( F @ X ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_1068_funcset__id,axiom,
    ! [A: set_a] :
      ( member_a_a
      @ ^ [X4: a] : X4
      @ ( pi_a_a @ A
        @ ^ [Uu: a] : A ) ) ).

% funcset_id
thf(fact_1069_funcsetI,axiom,
    ! [A: set_real,F: real > b,B2: set_b] :
      ( ! [X2: real] :
          ( ( member_real @ X2 @ A )
         => ( member_b @ ( F @ X2 ) @ B2 ) )
     => ( member_real_b @ F
        @ ( pi_real_b @ A
          @ ^ [Uu: real] : B2 ) ) ) ).

% funcsetI
thf(fact_1070_funcsetI,axiom,
    ! [A: set_real,F: real > nat,B2: set_nat] :
      ( ! [X2: real] :
          ( ( member_real @ X2 @ A )
         => ( member_nat @ ( F @ X2 ) @ B2 ) )
     => ( member_real_nat @ F
        @ ( pi_real_nat @ A
          @ ^ [Uu: real] : B2 ) ) ) ).

% funcsetI
thf(fact_1071_funcsetI,axiom,
    ! [A: set_real,F: real > a,B2: set_a] :
      ( ! [X2: real] :
          ( ( member_real @ X2 @ A )
         => ( member_a @ ( F @ X2 ) @ B2 ) )
     => ( member_real_a @ F
        @ ( pi_real_a @ A
          @ ^ [Uu: real] : B2 ) ) ) ).

% funcsetI
thf(fact_1072_funcsetI,axiom,
    ! [A: set_nat,F: nat > nat,B2: set_nat] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_nat @ ( F @ X2 ) @ B2 ) )
     => ( member_nat_nat @ F
        @ ( pi_nat_nat @ A
          @ ^ [Uu: nat] : B2 ) ) ) ).

% funcsetI
thf(fact_1073_funcsetI,axiom,
    ! [A: set_nat,F: nat > a,B2: set_a] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_a @ ( F @ X2 ) @ B2 ) )
     => ( member_nat_a @ F
        @ ( pi_nat_a @ A
          @ ^ [Uu: nat] : B2 ) ) ) ).

% funcsetI
thf(fact_1074_funcsetI,axiom,
    ! [A: set_a,F: a > complex,B2: set_complex] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_complex @ ( F @ X2 ) @ B2 ) )
     => ( member_a_complex @ F
        @ ( pi_a_complex @ A
          @ ^ [Uu: a] : B2 ) ) ) ).

% funcsetI
thf(fact_1075_funcsetI,axiom,
    ! [A: set_a,F: a > real,B2: set_real] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_real @ ( F @ X2 ) @ B2 ) )
     => ( member_a_real @ F
        @ ( pi_a_real @ A
          @ ^ [Uu: a] : B2 ) ) ) ).

% funcsetI
thf(fact_1076_funcsetI,axiom,
    ! [A: set_a,F: a > $o,B2: set_o] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_o @ ( F @ X2 ) @ B2 ) )
     => ( member_a_o @ F
        @ ( pi_a_o @ A
          @ ^ [Uu: a] : B2 ) ) ) ).

% funcsetI
thf(fact_1077_funcsetI,axiom,
    ! [A: set_a,F: a > nat,B2: set_nat] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_nat @ ( F @ X2 ) @ B2 ) )
     => ( member_a_nat @ F
        @ ( pi_a_nat @ A
          @ ^ [Uu: a] : B2 ) ) ) ).

% funcsetI
thf(fact_1078_funcsetI,axiom,
    ! [A: set_a,F: a > a,B2: set_a] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_a @ ( F @ X2 ) @ B2 ) )
     => ( member_a_a @ F
        @ ( pi_a_a @ A
          @ ^ [Uu: a] : B2 ) ) ) ).

% funcsetI
thf(fact_1079_Sup__UNIV,axiom,
    ( ( comple6814414086264997003nnreal @ top_to7994903218803871134nnreal )
    = top_to1496364449551166952nnreal ) ).

% Sup_UNIV
thf(fact_1080_Sup__UNIV,axiom,
    ( ( complete_Sup_Sup_o @ top_top_set_o )
    = top_top_o ) ).

% Sup_UNIV
thf(fact_1081_Sup__UNIV,axiom,
    ( ( comple4226387801268262977nnreal @ top_to3356475028079756884nnreal )
    = top_to7994903218803871134nnreal ) ).

% Sup_UNIV
thf(fact_1082_Sup__UNIV,axiom,
    ( ( comple8424636186594484919omplex @ top_to4650676778325599690omplex )
    = top_top_set_complex ) ).

% Sup_UNIV
thf(fact_1083_Sup__UNIV,axiom,
    ( ( comple3096694443085538997t_real @ top_top_set_set_real )
    = top_top_set_real ) ).

% Sup_UNIV
thf(fact_1084_Sup__UNIV,axiom,
    ( ( comple90263536869209701_set_o @ top_top_set_set_o )
    = top_top_set_o ) ).

% Sup_UNIV
thf(fact_1085_Sup__UNIV,axiom,
    ( ( comple7399068483239264473et_nat @ top_top_set_set_nat )
    = top_top_set_nat ) ).

% Sup_UNIV
thf(fact_1086_Sup__UNIV,axiom,
    ( ( comple2307003609928055243_set_a @ top_top_set_set_a )
    = top_top_set_a ) ).

% Sup_UNIV
thf(fact_1087_Sup__UNIV,axiom,
    ( ( comple2307003614231284044_set_b @ top_top_set_set_b )
    = top_top_set_b ) ).

% Sup_UNIV
thf(fact_1088_Sup__UNIV,axiom,
    ( ( comple4225921873958597590real_a @ top_to8684641019652371353real_a )
    = top_top_set_real_a ) ).

% Sup_UNIV
thf(fact_1089_INF__apply,axiom,
    ! [F: a > real > nat,A: set_a,X: real] :
      ( ( comple284232062038725972al_nat @ ( image_a_real_nat @ F @ A ) @ X )
      = ( complete_Inf_Inf_nat
        @ ( image_a_nat
          @ ^ [Y2: a] : ( F @ Y2 @ X )
          @ A ) ) ) ).

% INF_apply
thf(fact_1090_INF__identity__eq,axiom,
    ! [A: set_o] :
      ( ( complete_Inf_Inf_o
        @ ( image_o_o
          @ ^ [X4: $o] : X4
          @ A ) )
      = ( complete_Inf_Inf_o @ A ) ) ).

% INF_identity_eq
thf(fact_1091_INF__identity__eq,axiom,
    ! [A: set_nat] :
      ( ( complete_Inf_Inf_nat
        @ ( image_nat_nat
          @ ^ [X4: nat] : X4
          @ A ) )
      = ( complete_Inf_Inf_nat @ A ) ) ).

% INF_identity_eq
thf(fact_1092_INF__identity__eq,axiom,
    ! [A: set_real] :
      ( ( comple4887499456419720421f_real
        @ ( image_real_real
          @ ^ [X4: real] : X4
          @ A ) )
      = ( comple4887499456419720421f_real @ A ) ) ).

% INF_identity_eq
thf(fact_1093_SUP__apply,axiom,
    ! [F: a > real > nat,A: set_a,X: real] :
      ( ( comple5752178096987194350al_nat @ ( image_a_real_nat @ F @ A ) @ X )
      = ( complete_Sup_Sup_nat
        @ ( image_a_nat
          @ ^ [Y2: a] : ( F @ Y2 @ X )
          @ A ) ) ) ).

% SUP_apply
thf(fact_1094_SUP__identity__eq,axiom,
    ! [A: set_o] :
      ( ( complete_Sup_Sup_o
        @ ( image_o_o
          @ ^ [X4: $o] : X4
          @ A ) )
      = ( complete_Sup_Sup_o @ A ) ) ).

% SUP_identity_eq
thf(fact_1095_SUP__identity__eq,axiom,
    ! [A: set_nat] :
      ( ( complete_Sup_Sup_nat
        @ ( image_nat_nat
          @ ^ [X4: nat] : X4
          @ A ) )
      = ( complete_Sup_Sup_nat @ A ) ) ).

% SUP_identity_eq
thf(fact_1096_SUP__identity__eq,axiom,
    ! [A: set_real] :
      ( ( comple1385675409528146559p_real
        @ ( image_real_real
          @ ^ [X4: real] : X4
          @ A ) )
      = ( comple1385675409528146559p_real @ A ) ) ).

% SUP_identity_eq
thf(fact_1097_Union__iff,axiom,
    ! [A: nat,C2: set_set_nat] :
      ( ( member_nat @ A @ ( comple7399068483239264473et_nat @ C2 ) )
      = ( ? [X4: set_nat] :
            ( ( member_set_nat @ X4 @ C2 )
            & ( member_nat @ A @ X4 ) ) ) ) ).

% Union_iff
thf(fact_1098_Union__iff,axiom,
    ! [A: real > nat,C2: set_set_real_nat] :
      ( ( member_real_nat @ A @ ( comple266511651042094116al_nat @ C2 ) )
      = ( ? [X4: set_real_nat] :
            ( ( member_set_real_nat @ X4 @ C2 )
            & ( member_real_nat @ A @ X4 ) ) ) ) ).

% Union_iff
thf(fact_1099_Union__iff,axiom,
    ! [A: real > b,C2: set_set_real_b] :
      ( ( member_real_b @ A @ ( comple4296955914004943575real_b @ C2 ) )
      = ( ? [X4: set_real_b] :
            ( ( member_set_real_b @ X4 @ C2 )
            & ( member_real_b @ A @ X4 ) ) ) ) ).

% Union_iff
thf(fact_1100_Union__iff,axiom,
    ! [A: real > a,C2: set_set_real_a] :
      ( ( member_real_a @ A @ ( comple4225921873958597590real_a @ C2 ) )
      = ( ? [X4: set_real_a] :
            ( ( member_set_real_a @ X4 @ C2 )
            & ( member_real_a @ A @ X4 ) ) ) ) ).

% Union_iff
thf(fact_1101_Union__iff,axiom,
    ! [A: a,C2: set_set_a] :
      ( ( member_a @ A @ ( comple2307003609928055243_set_a @ C2 ) )
      = ( ? [X4: set_a] :
            ( ( member_set_a @ X4 @ C2 )
            & ( member_a @ A @ X4 ) ) ) ) ).

% Union_iff
thf(fact_1102_Union__iff,axiom,
    ! [A: a > complex,C2: set_set_a_complex] :
      ( ( member_a_complex @ A @ ( comple8696354750574632938omplex @ C2 ) )
      = ( ? [X4: set_a_complex] :
            ( ( member_set_a_complex @ X4 @ C2 )
            & ( member_a_complex @ A @ X4 ) ) ) ) ).

% Union_iff
thf(fact_1103_Union__iff,axiom,
    ! [A: a > real,C2: set_set_a_real] :
      ( ( member_a_real @ A @ ( comple1817482458065178856a_real @ C2 ) )
      = ( ? [X4: set_a_real] :
            ( ( member_set_a_real @ X4 @ C2 )
            & ( member_a_real @ A @ X4 ) ) ) ) ).

% Union_iff
thf(fact_1104_Union__iff,axiom,
    ! [A: a > $o,C2: set_set_a_o] :
      ( ( member_a_o @ A @ ( comple3956969172160116872et_a_o @ C2 ) )
      = ( ? [X4: set_a_o] :
            ( ( member_set_a_o @ X4 @ C2 )
            & ( member_a_o @ A @ X4 ) ) ) ) ).

% Union_iff
thf(fact_1105_Union__iff,axiom,
    ! [A: a > nat,C2: set_set_a_nat] :
      ( ( member_a_nat @ A @ ( comple4286861423968083212_a_nat @ C2 ) )
      = ( ? [X4: set_a_nat] :
            ( ( member_set_a_nat @ X4 @ C2 )
            & ( member_a_nat @ A @ X4 ) ) ) ) ).

% Union_iff
thf(fact_1106_Union__iff,axiom,
    ! [A: a > a,C2: set_set_a_a] :
      ( ( member_a_a @ A @ ( comple6518619711525350638et_a_a @ C2 ) )
      = ( ? [X4: set_a_a] :
            ( ( member_set_a_a @ X4 @ C2 )
            & ( member_a_a @ A @ X4 ) ) ) ) ).

% Union_iff
thf(fact_1107_UnionI,axiom,
    ! [X5: set_nat,C2: set_set_nat,A: nat] :
      ( ( member_set_nat @ X5 @ C2 )
     => ( ( member_nat @ A @ X5 )
       => ( member_nat @ A @ ( comple7399068483239264473et_nat @ C2 ) ) ) ) ).

% UnionI
thf(fact_1108_UnionI,axiom,
    ! [X5: set_real_nat,C2: set_set_real_nat,A: real > nat] :
      ( ( member_set_real_nat @ X5 @ C2 )
     => ( ( member_real_nat @ A @ X5 )
       => ( member_real_nat @ A @ ( comple266511651042094116al_nat @ C2 ) ) ) ) ).

% UnionI
thf(fact_1109_UnionI,axiom,
    ! [X5: set_real_b,C2: set_set_real_b,A: real > b] :
      ( ( member_set_real_b @ X5 @ C2 )
     => ( ( member_real_b @ A @ X5 )
       => ( member_real_b @ A @ ( comple4296955914004943575real_b @ C2 ) ) ) ) ).

% UnionI
thf(fact_1110_UnionI,axiom,
    ! [X5: set_real_a,C2: set_set_real_a,A: real > a] :
      ( ( member_set_real_a @ X5 @ C2 )
     => ( ( member_real_a @ A @ X5 )
       => ( member_real_a @ A @ ( comple4225921873958597590real_a @ C2 ) ) ) ) ).

% UnionI
thf(fact_1111_UnionI,axiom,
    ! [X5: set_a,C2: set_set_a,A: a] :
      ( ( member_set_a @ X5 @ C2 )
     => ( ( member_a @ A @ X5 )
       => ( member_a @ A @ ( comple2307003609928055243_set_a @ C2 ) ) ) ) ).

% UnionI
thf(fact_1112_UnionI,axiom,
    ! [X5: set_a_complex,C2: set_set_a_complex,A: a > complex] :
      ( ( member_set_a_complex @ X5 @ C2 )
     => ( ( member_a_complex @ A @ X5 )
       => ( member_a_complex @ A @ ( comple8696354750574632938omplex @ C2 ) ) ) ) ).

% UnionI
thf(fact_1113_UnionI,axiom,
    ! [X5: set_a_real,C2: set_set_a_real,A: a > real] :
      ( ( member_set_a_real @ X5 @ C2 )
     => ( ( member_a_real @ A @ X5 )
       => ( member_a_real @ A @ ( comple1817482458065178856a_real @ C2 ) ) ) ) ).

% UnionI
thf(fact_1114_UnionI,axiom,
    ! [X5: set_a_o,C2: set_set_a_o,A: a > $o] :
      ( ( member_set_a_o @ X5 @ C2 )
     => ( ( member_a_o @ A @ X5 )
       => ( member_a_o @ A @ ( comple3956969172160116872et_a_o @ C2 ) ) ) ) ).

% UnionI
thf(fact_1115_UnionI,axiom,
    ! [X5: set_a_nat,C2: set_set_a_nat,A: a > nat] :
      ( ( member_set_a_nat @ X5 @ C2 )
     => ( ( member_a_nat @ A @ X5 )
       => ( member_a_nat @ A @ ( comple4286861423968083212_a_nat @ C2 ) ) ) ) ).

% UnionI
thf(fact_1116_UnionI,axiom,
    ! [X5: set_a_a,C2: set_set_a_a,A: a > a] :
      ( ( member_set_a_a @ X5 @ C2 )
     => ( ( member_a_a @ A @ X5 )
       => ( member_a_a @ A @ ( comple6518619711525350638et_a_a @ C2 ) ) ) ) ).

% UnionI
thf(fact_1117_Inter__iff,axiom,
    ! [A: nat,C2: set_set_nat] :
      ( ( member_nat @ A @ ( comple7806235888213564991et_nat @ C2 ) )
      = ( ! [X4: set_nat] :
            ( ( member_set_nat @ X4 @ C2 )
           => ( member_nat @ A @ X4 ) ) ) ) ).

% Inter_iff
thf(fact_1118_Inter__iff,axiom,
    ! [A: real > nat,C2: set_set_real_nat] :
      ( ( member_real_nat @ A @ ( comple8071895948329575818al_nat @ C2 ) )
      = ( ! [X4: set_real_nat] :
            ( ( member_set_real_nat @ X4 @ C2 )
           => ( member_real_nat @ A @ X4 ) ) ) ) ).

% Inter_iff
thf(fact_1119_Inter__iff,axiom,
    ! [A: real > b,C2: set_set_real_b] :
      ( ( member_real_b @ A @ ( comple7721903285369235185real_b @ C2 ) )
      = ( ! [X4: set_real_b] :
            ( ( member_set_real_b @ X4 @ C2 )
           => ( member_real_b @ A @ X4 ) ) ) ) ).

% Inter_iff
thf(fact_1120_Inter__iff,axiom,
    ! [A: real > a,C2: set_set_real_a] :
      ( ( member_real_a @ A @ ( comple7650869245322889200real_a @ C2 ) )
      = ( ! [X4: set_real_a] :
            ( ( member_set_real_a @ X4 @ C2 )
           => ( member_real_a @ A @ X4 ) ) ) ) ).

% Inter_iff
thf(fact_1121_Inter__iff,axiom,
    ! [A: a,C2: set_set_a] :
      ( ( member_a @ A @ ( comple6135023378680113637_set_a @ C2 ) )
      = ( ! [X4: set_a] :
            ( ( member_set_a @ X4 @ C2 )
           => ( member_a @ A @ X4 ) ) ) ) ).

% Inter_iff
thf(fact_1122_Inter__iff,axiom,
    ! [A: a > complex,C2: set_set_a_complex] :
      ( ( member_a_complex @ A @ ( comple987388759867256068omplex @ C2 ) )
      = ( ! [X4: set_a_complex] :
            ( ( member_set_a_complex @ X4 @ C2 )
           => ( member_a_complex @ A @ X4 ) ) ) ) ).

% Inter_iff
thf(fact_1123_Inter__iff,axiom,
    ! [A: a > real,C2: set_set_a_real] :
      ( ( member_a_real @ A @ ( comple5242429829429470466a_real @ C2 ) )
      = ( ! [X4: set_a_real] :
            ( ( member_set_a_real @ X4 @ C2 )
           => ( member_a_real @ A @ X4 ) ) ) ) ).

% Inter_iff
thf(fact_1124_Inter__iff,axiom,
    ! [A: a > $o,C2: set_set_a_o] :
      ( ( member_a_o @ A @ ( comple8115264379980766446et_a_o @ C2 ) )
      = ( ! [X4: set_a_o] :
            ( ( member_set_a_o @ X4 @ C2 )
           => ( member_a_o @ A @ X4 ) ) ) ) ).

% Inter_iff
thf(fact_1125_Inter__iff,axiom,
    ! [A: a > nat,C2: set_set_a_nat] :
      ( ( member_a_nat @ A @ ( comple4385993935590776358_a_nat @ C2 ) )
      = ( ! [X4: set_a_nat] :
            ( ( member_set_a_nat @ X4 @ C2 )
           => ( member_a_nat @ A @ X4 ) ) ) ) ).

% Inter_iff
thf(fact_1126_Inter__iff,axiom,
    ! [A: a > a,C2: set_set_a_a] :
      ( ( member_a_a @ A @ ( comple1050673676576882260et_a_a @ C2 ) )
      = ( ! [X4: set_a_a] :
            ( ( member_set_a_a @ X4 @ C2 )
           => ( member_a_a @ A @ X4 ) ) ) ) ).

% Inter_iff
thf(fact_1127_InterI,axiom,
    ! [C2: set_set_nat,A: nat] :
      ( ! [X6: set_nat] :
          ( ( member_set_nat @ X6 @ C2 )
         => ( member_nat @ A @ X6 ) )
     => ( member_nat @ A @ ( comple7806235888213564991et_nat @ C2 ) ) ) ).

% InterI
thf(fact_1128_InterI,axiom,
    ! [C2: set_set_real_nat,A: real > nat] :
      ( ! [X6: set_real_nat] :
          ( ( member_set_real_nat @ X6 @ C2 )
         => ( member_real_nat @ A @ X6 ) )
     => ( member_real_nat @ A @ ( comple8071895948329575818al_nat @ C2 ) ) ) ).

% InterI
thf(fact_1129_InterI,axiom,
    ! [C2: set_set_real_b,A: real > b] :
      ( ! [X6: set_real_b] :
          ( ( member_set_real_b @ X6 @ C2 )
         => ( member_real_b @ A @ X6 ) )
     => ( member_real_b @ A @ ( comple7721903285369235185real_b @ C2 ) ) ) ).

% InterI
thf(fact_1130_InterI,axiom,
    ! [C2: set_set_real_a,A: real > a] :
      ( ! [X6: set_real_a] :
          ( ( member_set_real_a @ X6 @ C2 )
         => ( member_real_a @ A @ X6 ) )
     => ( member_real_a @ A @ ( comple7650869245322889200real_a @ C2 ) ) ) ).

% InterI
thf(fact_1131_InterI,axiom,
    ! [C2: set_set_a,A: a] :
      ( ! [X6: set_a] :
          ( ( member_set_a @ X6 @ C2 )
         => ( member_a @ A @ X6 ) )
     => ( member_a @ A @ ( comple6135023378680113637_set_a @ C2 ) ) ) ).

% InterI
thf(fact_1132_InterI,axiom,
    ! [C2: set_set_a_complex,A: a > complex] :
      ( ! [X6: set_a_complex] :
          ( ( member_set_a_complex @ X6 @ C2 )
         => ( member_a_complex @ A @ X6 ) )
     => ( member_a_complex @ A @ ( comple987388759867256068omplex @ C2 ) ) ) ).

% InterI
thf(fact_1133_InterI,axiom,
    ! [C2: set_set_a_real,A: a > real] :
      ( ! [X6: set_a_real] :
          ( ( member_set_a_real @ X6 @ C2 )
         => ( member_a_real @ A @ X6 ) )
     => ( member_a_real @ A @ ( comple5242429829429470466a_real @ C2 ) ) ) ).

% InterI
thf(fact_1134_InterI,axiom,
    ! [C2: set_set_a_o,A: a > $o] :
      ( ! [X6: set_a_o] :
          ( ( member_set_a_o @ X6 @ C2 )
         => ( member_a_o @ A @ X6 ) )
     => ( member_a_o @ A @ ( comple8115264379980766446et_a_o @ C2 ) ) ) ).

% InterI
thf(fact_1135_InterI,axiom,
    ! [C2: set_set_a_nat,A: a > nat] :
      ( ! [X6: set_a_nat] :
          ( ( member_set_a_nat @ X6 @ C2 )
         => ( member_a_nat @ A @ X6 ) )
     => ( member_a_nat @ A @ ( comple4385993935590776358_a_nat @ C2 ) ) ) ).

% InterI
thf(fact_1136_InterI,axiom,
    ! [C2: set_set_a_a,A: a > a] :
      ( ! [X6: set_a_a] :
          ( ( member_set_a_a @ X6 @ C2 )
         => ( member_a_a @ A @ X6 ) )
     => ( member_a_a @ A @ ( comple1050673676576882260et_a_a @ C2 ) ) ) ).

% InterI
thf(fact_1137_Inf__top__conv_I1_J,axiom,
    ! [A: set_o] :
      ( ( ( complete_Inf_Inf_o @ A )
        = top_top_o )
      = ( ! [X4: $o] :
            ( ( member_o @ X4 @ A )
           => ( X4 = top_top_o ) ) ) ) ).

% Inf_top_conv(1)
thf(fact_1138_Inf__top__conv_I1_J,axiom,
    ! [A: set_se4580700918925141924nnreal] :
      ( ( ( comple5724520875574609319nnreal @ A )
        = top_to7994903218803871134nnreal )
      = ( ! [X4: set_Ex3793607809372303086nnreal] :
            ( ( member603777416030116741nnreal @ X4 @ A )
           => ( X4 = top_to7994903218803871134nnreal ) ) ) ) ).

% Inf_top_conv(1)
thf(fact_1139_Inf__top__conv_I1_J,axiom,
    ! [A: set_set_complex] :
      ( ( ( comple2956690151646016541omplex @ A )
        = top_top_set_complex )
      = ( ! [X4: set_complex] :
            ( ( member_set_complex @ X4 @ A )
           => ( X4 = top_top_set_complex ) ) ) ) ).

% Inf_top_conv(1)
thf(fact_1140_Inf__top__conv_I1_J,axiom,
    ! [A: set_set_real] :
      ( ( ( comple8289635161444856091t_real @ A )
        = top_top_set_real )
      = ( ! [X4: set_real] :
            ( ( member_set_real @ X4 @ A )
           => ( X4 = top_top_set_real ) ) ) ) ).

% Inf_top_conv(1)
thf(fact_1141_Inf__top__conv_I1_J,axiom,
    ! [A: set_set_o] :
      ( ( ( comple3063163877087187839_set_o @ A )
        = top_top_set_o )
      = ( ! [X4: set_o] :
            ( ( member_set_o @ X4 @ A )
           => ( X4 = top_top_set_o ) ) ) ) ).

% Inf_top_conv(1)
thf(fact_1142_Inf__top__conv_I1_J,axiom,
    ! [A: set_set_nat] :
      ( ( ( comple7806235888213564991et_nat @ A )
        = top_top_set_nat )
      = ( ! [X4: set_nat] :
            ( ( member_set_nat @ X4 @ A )
           => ( X4 = top_top_set_nat ) ) ) ) ).

% Inf_top_conv(1)
thf(fact_1143_Inf__top__conv_I1_J,axiom,
    ! [A: set_set_a] :
      ( ( ( comple6135023378680113637_set_a @ A )
        = top_top_set_a )
      = ( ! [X4: set_a] :
            ( ( member_set_a @ X4 @ A )
           => ( X4 = top_top_set_a ) ) ) ) ).

% Inf_top_conv(1)
thf(fact_1144_Inf__top__conv_I1_J,axiom,
    ! [A: set_set_b] :
      ( ( ( comple6135023382983342438_set_b @ A )
        = top_top_set_b )
      = ( ! [X4: set_b] :
            ( ( member_set_b @ X4 @ A )
           => ( X4 = top_top_set_b ) ) ) ) ).

% Inf_top_conv(1)
thf(fact_1145_Inf__top__conv_I1_J,axiom,
    ! [A: set_set_real_a] :
      ( ( ( comple7650869245322889200real_a @ A )
        = top_top_set_real_a )
      = ( ! [X4: set_real_a] :
            ( ( member_set_real_a @ X4 @ A )
           => ( X4 = top_top_set_real_a ) ) ) ) ).

% Inf_top_conv(1)
thf(fact_1146_Inf__top__conv_I1_J,axiom,
    ! [A: set_set_real_b] :
      ( ( ( comple7721903285369235185real_b @ A )
        = top_top_set_real_b )
      = ( ! [X4: set_real_b] :
            ( ( member_set_real_b @ X4 @ A )
           => ( X4 = top_top_set_real_b ) ) ) ) ).

% Inf_top_conv(1)
thf(fact_1147_Inf__top__conv_I2_J,axiom,
    ! [A: set_o] :
      ( ( top_top_o
        = ( complete_Inf_Inf_o @ A ) )
      = ( ! [X4: $o] :
            ( ( member_o @ X4 @ A )
           => ( X4 = top_top_o ) ) ) ) ).

% Inf_top_conv(2)
thf(fact_1148_Inf__top__conv_I2_J,axiom,
    ! [A: set_se4580700918925141924nnreal] :
      ( ( top_to7994903218803871134nnreal
        = ( comple5724520875574609319nnreal @ A ) )
      = ( ! [X4: set_Ex3793607809372303086nnreal] :
            ( ( member603777416030116741nnreal @ X4 @ A )
           => ( X4 = top_to7994903218803871134nnreal ) ) ) ) ).

% Inf_top_conv(2)
thf(fact_1149_Inf__top__conv_I2_J,axiom,
    ! [A: set_set_complex] :
      ( ( top_top_set_complex
        = ( comple2956690151646016541omplex @ A ) )
      = ( ! [X4: set_complex] :
            ( ( member_set_complex @ X4 @ A )
           => ( X4 = top_top_set_complex ) ) ) ) ).

% Inf_top_conv(2)
thf(fact_1150_Inf__top__conv_I2_J,axiom,
    ! [A: set_set_real] :
      ( ( top_top_set_real
        = ( comple8289635161444856091t_real @ A ) )
      = ( ! [X4: set_real] :
            ( ( member_set_real @ X4 @ A )
           => ( X4 = top_top_set_real ) ) ) ) ).

% Inf_top_conv(2)
thf(fact_1151_Inf__top__conv_I2_J,axiom,
    ! [A: set_set_o] :
      ( ( top_top_set_o
        = ( comple3063163877087187839_set_o @ A ) )
      = ( ! [X4: set_o] :
            ( ( member_set_o @ X4 @ A )
           => ( X4 = top_top_set_o ) ) ) ) ).

% Inf_top_conv(2)
thf(fact_1152_Inf__top__conv_I2_J,axiom,
    ! [A: set_set_nat] :
      ( ( top_top_set_nat
        = ( comple7806235888213564991et_nat @ A ) )
      = ( ! [X4: set_nat] :
            ( ( member_set_nat @ X4 @ A )
           => ( X4 = top_top_set_nat ) ) ) ) ).

% Inf_top_conv(2)
thf(fact_1153_Inf__top__conv_I2_J,axiom,
    ! [A: set_set_a] :
      ( ( top_top_set_a
        = ( comple6135023378680113637_set_a @ A ) )
      = ( ! [X4: set_a] :
            ( ( member_set_a @ X4 @ A )
           => ( X4 = top_top_set_a ) ) ) ) ).

% Inf_top_conv(2)
thf(fact_1154_Inf__top__conv_I2_J,axiom,
    ! [A: set_set_b] :
      ( ( top_top_set_b
        = ( comple6135023382983342438_set_b @ A ) )
      = ( ! [X4: set_b] :
            ( ( member_set_b @ X4 @ A )
           => ( X4 = top_top_set_b ) ) ) ) ).

% Inf_top_conv(2)
thf(fact_1155_Inf__top__conv_I2_J,axiom,
    ! [A: set_set_real_a] :
      ( ( top_top_set_real_a
        = ( comple7650869245322889200real_a @ A ) )
      = ( ! [X4: set_real_a] :
            ( ( member_set_real_a @ X4 @ A )
           => ( X4 = top_top_set_real_a ) ) ) ) ).

% Inf_top_conv(2)
thf(fact_1156_Inf__top__conv_I2_J,axiom,
    ! [A: set_set_real_b] :
      ( ( top_top_set_real_b
        = ( comple7721903285369235185real_b @ A ) )
      = ( ! [X4: set_real_b] :
            ( ( member_set_real_b @ X4 @ A )
           => ( X4 = top_top_set_real_b ) ) ) ) ).

% Inf_top_conv(2)
thf(fact_1157_Inter__UNIV__conv_I1_J,axiom,
    ! [A: set_se4580700918925141924nnreal] :
      ( ( ( comple5724520875574609319nnreal @ A )
        = top_to7994903218803871134nnreal )
      = ( ! [X4: set_Ex3793607809372303086nnreal] :
            ( ( member603777416030116741nnreal @ X4 @ A )
           => ( X4 = top_to7994903218803871134nnreal ) ) ) ) ).

% Inter_UNIV_conv(1)
thf(fact_1158_Inter__UNIV__conv_I1_J,axiom,
    ! [A: set_set_complex] :
      ( ( ( comple2956690151646016541omplex @ A )
        = top_top_set_complex )
      = ( ! [X4: set_complex] :
            ( ( member_set_complex @ X4 @ A )
           => ( X4 = top_top_set_complex ) ) ) ) ).

% Inter_UNIV_conv(1)
thf(fact_1159_Inter__UNIV__conv_I1_J,axiom,
    ! [A: set_set_real] :
      ( ( ( comple8289635161444856091t_real @ A )
        = top_top_set_real )
      = ( ! [X4: set_real] :
            ( ( member_set_real @ X4 @ A )
           => ( X4 = top_top_set_real ) ) ) ) ).

% Inter_UNIV_conv(1)
thf(fact_1160_Inter__UNIV__conv_I1_J,axiom,
    ! [A: set_set_o] :
      ( ( ( comple3063163877087187839_set_o @ A )
        = top_top_set_o )
      = ( ! [X4: set_o] :
            ( ( member_set_o @ X4 @ A )
           => ( X4 = top_top_set_o ) ) ) ) ).

% Inter_UNIV_conv(1)
thf(fact_1161_Inter__UNIV__conv_I1_J,axiom,
    ! [A: set_set_nat] :
      ( ( ( comple7806235888213564991et_nat @ A )
        = top_top_set_nat )
      = ( ! [X4: set_nat] :
            ( ( member_set_nat @ X4 @ A )
           => ( X4 = top_top_set_nat ) ) ) ) ).

% Inter_UNIV_conv(1)
thf(fact_1162_Inter__UNIV__conv_I1_J,axiom,
    ! [A: set_set_a] :
      ( ( ( comple6135023378680113637_set_a @ A )
        = top_top_set_a )
      = ( ! [X4: set_a] :
            ( ( member_set_a @ X4 @ A )
           => ( X4 = top_top_set_a ) ) ) ) ).

% Inter_UNIV_conv(1)
thf(fact_1163_Inter__UNIV__conv_I1_J,axiom,
    ! [A: set_set_b] :
      ( ( ( comple6135023382983342438_set_b @ A )
        = top_top_set_b )
      = ( ! [X4: set_b] :
            ( ( member_set_b @ X4 @ A )
           => ( X4 = top_top_set_b ) ) ) ) ).

% Inter_UNIV_conv(1)
thf(fact_1164_Inter__UNIV__conv_I1_J,axiom,
    ! [A: set_set_real_a] :
      ( ( ( comple7650869245322889200real_a @ A )
        = top_top_set_real_a )
      = ( ! [X4: set_real_a] :
            ( ( member_set_real_a @ X4 @ A )
           => ( X4 = top_top_set_real_a ) ) ) ) ).

% Inter_UNIV_conv(1)
thf(fact_1165_Inter__UNIV__conv_I1_J,axiom,
    ! [A: set_set_real_b] :
      ( ( ( comple7721903285369235185real_b @ A )
        = top_top_set_real_b )
      = ( ! [X4: set_real_b] :
            ( ( member_set_real_b @ X4 @ A )
           => ( X4 = top_top_set_real_b ) ) ) ) ).

% Inter_UNIV_conv(1)
thf(fact_1166_Inter__UNIV__conv_I1_J,axiom,
    ! [A: set_set_real_nat] :
      ( ( ( comple8071895948329575818al_nat @ A )
        = top_top_set_real_nat )
      = ( ! [X4: set_real_nat] :
            ( ( member_set_real_nat @ X4 @ A )
           => ( X4 = top_top_set_real_nat ) ) ) ) ).

% Inter_UNIV_conv(1)
thf(fact_1167_Inter__UNIV__conv_I2_J,axiom,
    ! [A: set_se4580700918925141924nnreal] :
      ( ( top_to7994903218803871134nnreal
        = ( comple5724520875574609319nnreal @ A ) )
      = ( ! [X4: set_Ex3793607809372303086nnreal] :
            ( ( member603777416030116741nnreal @ X4 @ A )
           => ( X4 = top_to7994903218803871134nnreal ) ) ) ) ).

% Inter_UNIV_conv(2)
thf(fact_1168_Inter__UNIV__conv_I2_J,axiom,
    ! [A: set_set_complex] :
      ( ( top_top_set_complex
        = ( comple2956690151646016541omplex @ A ) )
      = ( ! [X4: set_complex] :
            ( ( member_set_complex @ X4 @ A )
           => ( X4 = top_top_set_complex ) ) ) ) ).

% Inter_UNIV_conv(2)
thf(fact_1169_Inter__UNIV__conv_I2_J,axiom,
    ! [A: set_set_real] :
      ( ( top_top_set_real
        = ( comple8289635161444856091t_real @ A ) )
      = ( ! [X4: set_real] :
            ( ( member_set_real @ X4 @ A )
           => ( X4 = top_top_set_real ) ) ) ) ).

% Inter_UNIV_conv(2)
thf(fact_1170_Inter__UNIV__conv_I2_J,axiom,
    ! [A: set_set_o] :
      ( ( top_top_set_o
        = ( comple3063163877087187839_set_o @ A ) )
      = ( ! [X4: set_o] :
            ( ( member_set_o @ X4 @ A )
           => ( X4 = top_top_set_o ) ) ) ) ).

% Inter_UNIV_conv(2)
thf(fact_1171_Inter__UNIV__conv_I2_J,axiom,
    ! [A: set_set_nat] :
      ( ( top_top_set_nat
        = ( comple7806235888213564991et_nat @ A ) )
      = ( ! [X4: set_nat] :
            ( ( member_set_nat @ X4 @ A )
           => ( X4 = top_top_set_nat ) ) ) ) ).

% Inter_UNIV_conv(2)
thf(fact_1172_Inter__UNIV__conv_I2_J,axiom,
    ! [A: set_set_a] :
      ( ( top_top_set_a
        = ( comple6135023378680113637_set_a @ A ) )
      = ( ! [X4: set_a] :
            ( ( member_set_a @ X4 @ A )
           => ( X4 = top_top_set_a ) ) ) ) ).

% Inter_UNIV_conv(2)
thf(fact_1173_Inter__UNIV__conv_I2_J,axiom,
    ! [A: set_set_b] :
      ( ( top_top_set_b
        = ( comple6135023382983342438_set_b @ A ) )
      = ( ! [X4: set_b] :
            ( ( member_set_b @ X4 @ A )
           => ( X4 = top_top_set_b ) ) ) ) ).

% Inter_UNIV_conv(2)
thf(fact_1174_Inter__UNIV__conv_I2_J,axiom,
    ! [A: set_set_real_a] :
      ( ( top_top_set_real_a
        = ( comple7650869245322889200real_a @ A ) )
      = ( ! [X4: set_real_a] :
            ( ( member_set_real_a @ X4 @ A )
           => ( X4 = top_top_set_real_a ) ) ) ) ).

% Inter_UNIV_conv(2)
thf(fact_1175_Inter__UNIV__conv_I2_J,axiom,
    ! [A: set_set_real_b] :
      ( ( top_top_set_real_b
        = ( comple7721903285369235185real_b @ A ) )
      = ( ! [X4: set_real_b] :
            ( ( member_set_real_b @ X4 @ A )
           => ( X4 = top_top_set_real_b ) ) ) ) ).

% Inter_UNIV_conv(2)
thf(fact_1176_Inter__UNIV__conv_I2_J,axiom,
    ! [A: set_set_real_nat] :
      ( ( top_top_set_real_nat
        = ( comple8071895948329575818al_nat @ A ) )
      = ( ! [X4: set_real_nat] :
            ( ( member_set_real_nat @ X4 @ A )
           => ( X4 = top_top_set_real_nat ) ) ) ) ).

% Inter_UNIV_conv(2)
thf(fact_1177_UN__I,axiom,
    ! [A3: nat,A: set_nat,B: nat,B2: nat > set_nat] :
      ( ( member_nat @ A3 @ A )
     => ( ( member_nat @ B @ ( B2 @ A3 ) )
       => ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B2 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1178_UN__I,axiom,
    ! [A3: nat,A: set_nat,B: a,B2: nat > set_a] :
      ( ( member_nat @ A3 @ A )
     => ( ( member_a @ B @ ( B2 @ A3 ) )
       => ( member_a @ B @ ( comple2307003609928055243_set_a @ ( image_nat_set_a @ B2 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1179_UN__I,axiom,
    ! [A3: a,A: set_a,B: nat,B2: a > set_nat] :
      ( ( member_a @ A3 @ A )
     => ( ( member_nat @ B @ ( B2 @ A3 ) )
       => ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_a_set_nat @ B2 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1180_UN__I,axiom,
    ! [A3: a,A: set_a,B: a,B2: a > set_a] :
      ( ( member_a @ A3 @ A )
     => ( ( member_a @ B @ ( B2 @ A3 ) )
       => ( member_a @ B @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ B2 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1181_UN__I,axiom,
    ! [A3: nat,A: set_nat,B: real > nat,B2: nat > set_real_nat] :
      ( ( member_nat @ A3 @ A )
     => ( ( member_real_nat @ B @ ( B2 @ A3 ) )
       => ( member_real_nat @ B @ ( comple266511651042094116al_nat @ ( image_6900357751826779304al_nat @ B2 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1182_UN__I,axiom,
    ! [A3: nat,A: set_nat,B: real > b,B2: nat > set_real_b] :
      ( ( member_nat @ A3 @ A )
     => ( ( member_real_b @ B @ ( B2 @ A3 ) )
       => ( member_real_b @ B @ ( comple4296955914004943575real_b @ ( image_nat_set_real_b @ B2 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1183_UN__I,axiom,
    ! [A3: nat,A: set_nat,B: real > a,B2: nat > set_real_a] :
      ( ( member_nat @ A3 @ A )
     => ( ( member_real_a @ B @ ( B2 @ A3 ) )
       => ( member_real_a @ B @ ( comple4225921873958597590real_a @ ( image_nat_set_real_a @ B2 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1184_UN__I,axiom,
    ! [A3: nat,A: set_nat,B: a > complex,B2: nat > set_a_complex] :
      ( ( member_nat @ A3 @ A )
     => ( ( member_a_complex @ B @ ( B2 @ A3 ) )
       => ( member_a_complex @ B @ ( comple8696354750574632938omplex @ ( image_3591888402735308390omplex @ B2 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1185_UN__I,axiom,
    ! [A3: nat,A: set_nat,B: a > real,B2: nat > set_a_real] :
      ( ( member_nat @ A3 @ A )
     => ( ( member_a_real @ B @ ( B2 @ A3 ) )
       => ( member_a_real @ B @ ( comple1817482458065178856a_real @ ( image_nat_set_a_real @ B2 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1186_UN__I,axiom,
    ! [A3: nat,A: set_nat,B: a > $o,B2: nat > set_a_o] :
      ( ( member_nat @ A3 @ A )
     => ( ( member_a_o @ B @ ( B2 @ A3 ) )
       => ( member_a_o @ B @ ( comple3956969172160116872et_a_o @ ( image_nat_set_a_o @ B2 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1187_INT__I,axiom,
    ! [A: set_nat,B: nat,B2: nat > set_nat] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_nat @ B @ ( B2 @ X2 ) ) )
     => ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B2 @ A ) ) ) ) ).

% INT_I
thf(fact_1188_INT__I,axiom,
    ! [A: set_nat,B: a,B2: nat > set_a] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_a @ B @ ( B2 @ X2 ) ) )
     => ( member_a @ B @ ( comple6135023378680113637_set_a @ ( image_nat_set_a @ B2 @ A ) ) ) ) ).

% INT_I
thf(fact_1189_INT__I,axiom,
    ! [A: set_a,B: nat,B2: a > set_nat] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_nat @ B @ ( B2 @ X2 ) ) )
     => ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_a_set_nat @ B2 @ A ) ) ) ) ).

% INT_I
thf(fact_1190_INT__I,axiom,
    ! [A: set_a,B: a,B2: a > set_a] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_a @ B @ ( B2 @ X2 ) ) )
     => ( member_a @ B @ ( comple6135023378680113637_set_a @ ( image_a_set_a @ B2 @ A ) ) ) ) ).

% INT_I
thf(fact_1191_INT__I,axiom,
    ! [A: set_nat,B: real > nat,B2: nat > set_real_nat] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_real_nat @ B @ ( B2 @ X2 ) ) )
     => ( member_real_nat @ B @ ( comple8071895948329575818al_nat @ ( image_6900357751826779304al_nat @ B2 @ A ) ) ) ) ).

% INT_I
thf(fact_1192_INT__I,axiom,
    ! [A: set_nat,B: real > b,B2: nat > set_real_b] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_real_b @ B @ ( B2 @ X2 ) ) )
     => ( member_real_b @ B @ ( comple7721903285369235185real_b @ ( image_nat_set_real_b @ B2 @ A ) ) ) ) ).

% INT_I
thf(fact_1193_INT__I,axiom,
    ! [A: set_nat,B: real > a,B2: nat > set_real_a] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_real_a @ B @ ( B2 @ X2 ) ) )
     => ( member_real_a @ B @ ( comple7650869245322889200real_a @ ( image_nat_set_real_a @ B2 @ A ) ) ) ) ).

% INT_I
thf(fact_1194_INT__I,axiom,
    ! [A: set_nat,B: a > complex,B2: nat > set_a_complex] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_a_complex @ B @ ( B2 @ X2 ) ) )
     => ( member_a_complex @ B @ ( comple987388759867256068omplex @ ( image_3591888402735308390omplex @ B2 @ A ) ) ) ) ).

% INT_I
thf(fact_1195_INT__I,axiom,
    ! [A: set_nat,B: a > real,B2: nat > set_a_real] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_a_real @ B @ ( B2 @ X2 ) ) )
     => ( member_a_real @ B @ ( comple5242429829429470466a_real @ ( image_nat_set_a_real @ B2 @ A ) ) ) ) ).

% INT_I
thf(fact_1196_INT__I,axiom,
    ! [A: set_nat,B: a > $o,B2: nat > set_a_o] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A )
         => ( member_a_o @ B @ ( B2 @ X2 ) ) )
     => ( member_a_o @ B @ ( comple8115264379980766446et_a_o @ ( image_nat_set_a_o @ B2 @ A ) ) ) ) ).

% INT_I
thf(fact_1197_uncountable__UNIV__complex,axiom,
    ~ ( counta5113917769705169331omplex @ top_top_set_complex ) ).

% uncountable_UNIV_complex
thf(fact_1198_Sup__set__def,axiom,
    ( comple266511651042094116al_nat
    = ( ^ [A2: set_set_real_nat] :
          ( collect_real_nat
          @ ^ [X4: real > nat] : ( complete_Sup_Sup_o @ ( image_set_real_nat_o @ ( member_real_nat @ X4 ) @ A2 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1199_Sup__set__def,axiom,
    ( comple4296955914004943575real_b
    = ( ^ [A2: set_set_real_b] :
          ( collect_real_b
          @ ^ [X4: real > b] : ( complete_Sup_Sup_o @ ( image_set_real_b_o @ ( member_real_b @ X4 ) @ A2 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1200_Sup__set__def,axiom,
    ( comple4225921873958597590real_a
    = ( ^ [A2: set_set_real_a] :
          ( collect_real_a
          @ ^ [X4: real > a] : ( complete_Sup_Sup_o @ ( image_set_real_a_o @ ( member_real_a @ X4 ) @ A2 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1201_Sup__set__def,axiom,
    ( comple2307003609928055243_set_a
    = ( ^ [A2: set_set_a] :
          ( collect_a
          @ ^ [X4: a] : ( complete_Sup_Sup_o @ ( image_set_a_o @ ( member_a @ X4 ) @ A2 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1202_Sup__set__def,axiom,
    ( comple8696354750574632938omplex
    = ( ^ [A2: set_set_a_complex] :
          ( collect_a_complex
          @ ^ [X4: a > complex] : ( complete_Sup_Sup_o @ ( image_5240558645659804640plex_o @ ( member_a_complex @ X4 ) @ A2 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1203_Sup__set__def,axiom,
    ( comple1817482458065178856a_real
    = ( ^ [A2: set_set_a_real] :
          ( collect_a_real
          @ ^ [X4: a > real] : ( complete_Sup_Sup_o @ ( image_set_a_real_o @ ( member_a_real @ X4 ) @ A2 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1204_Sup__set__def,axiom,
    ( comple3956969172160116872et_a_o
    = ( ^ [A2: set_set_a_o] :
          ( collect_a_o
          @ ^ [X4: a > $o] : ( complete_Sup_Sup_o @ ( image_set_a_o_o @ ( member_a_o @ X4 ) @ A2 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1205_Sup__set__def,axiom,
    ( comple4286861423968083212_a_nat
    = ( ^ [A2: set_set_a_nat] :
          ( collect_a_nat
          @ ^ [X4: a > nat] : ( complete_Sup_Sup_o @ ( image_set_a_nat_o @ ( member_a_nat @ X4 ) @ A2 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1206_Sup__set__def,axiom,
    ( comple6518619711525350638et_a_a
    = ( ^ [A2: set_set_a_a] :
          ( collect_a_a
          @ ^ [X4: a > a] : ( complete_Sup_Sup_o @ ( image_set_a_a_o @ ( member_a_a @ X4 ) @ A2 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1207_Sup__set__def,axiom,
    ( comple7399068483239264473et_nat
    = ( ^ [A2: set_set_nat] :
          ( collect_nat
          @ ^ [X4: nat] : ( complete_Sup_Sup_o @ ( image_set_nat_o @ ( member_nat @ X4 ) @ A2 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1208_Inf__set__def,axiom,
    ( comple8071895948329575818al_nat
    = ( ^ [A2: set_set_real_nat] :
          ( collect_real_nat
          @ ^ [X4: real > nat] : ( complete_Inf_Inf_o @ ( image_set_real_nat_o @ ( member_real_nat @ X4 ) @ A2 ) ) ) ) ) ).

% Inf_set_def
thf(fact_1209_Inf__set__def,axiom,
    ( comple7721903285369235185real_b
    = ( ^ [A2: set_set_real_b] :
          ( collect_real_b
          @ ^ [X4: real > b] : ( complete_Inf_Inf_o @ ( image_set_real_b_o @ ( member_real_b @ X4 ) @ A2 ) ) ) ) ) ).

% Inf_set_def
thf(fact_1210_Inf__set__def,axiom,
    ( comple7650869245322889200real_a
    = ( ^ [A2: set_set_real_a] :
          ( collect_real_a
          @ ^ [X4: real > a] : ( complete_Inf_Inf_o @ ( image_set_real_a_o @ ( member_real_a @ X4 ) @ A2 ) ) ) ) ) ).

% Inf_set_def
thf(fact_1211_Inf__set__def,axiom,
    ( comple6135023378680113637_set_a
    = ( ^ [A2: set_set_a] :
          ( collect_a
          @ ^ [X4: a] : ( complete_Inf_Inf_o @ ( image_set_a_o @ ( member_a @ X4 ) @ A2 ) ) ) ) ) ).

% Inf_set_def
thf(fact_1212_Inf__set__def,axiom,
    ( comple987388759867256068omplex
    = ( ^ [A2: set_set_a_complex] :
          ( collect_a_complex
          @ ^ [X4: a > complex] : ( complete_Inf_Inf_o @ ( image_5240558645659804640plex_o @ ( member_a_complex @ X4 ) @ A2 ) ) ) ) ) ).

% Inf_set_def
thf(fact_1213_Inf__set__def,axiom,
    ( comple5242429829429470466a_real
    = ( ^ [A2: set_set_a_real] :
          ( collect_a_real
          @ ^ [X4: a > real] : ( complete_Inf_Inf_o @ ( image_set_a_real_o @ ( member_a_real @ X4 ) @ A2 ) ) ) ) ) ).

% Inf_set_def
thf(fact_1214_Inf__set__def,axiom,
    ( comple8115264379980766446et_a_o
    = ( ^ [A2: set_set_a_o] :
          ( collect_a_o
          @ ^ [X4: a > $o] : ( complete_Inf_Inf_o @ ( image_set_a_o_o @ ( member_a_o @ X4 ) @ A2 ) ) ) ) ) ).

% Inf_set_def
thf(fact_1215_Inf__set__def,axiom,
    ( comple4385993935590776358_a_nat
    = ( ^ [A2: set_set_a_nat] :
          ( collect_a_nat
          @ ^ [X4: a > nat] : ( complete_Inf_Inf_o @ ( image_set_a_nat_o @ ( member_a_nat @ X4 ) @ A2 ) ) ) ) ) ).

% Inf_set_def
thf(fact_1216_Inf__set__def,axiom,
    ( comple1050673676576882260et_a_a
    = ( ^ [A2: set_set_a_a] :
          ( collect_a_a
          @ ^ [X4: a > a] : ( complete_Inf_Inf_o @ ( image_set_a_a_o @ ( member_a_a @ X4 ) @ A2 ) ) ) ) ) ).

% Inf_set_def
thf(fact_1217_Inf__set__def,axiom,
    ( comple7806235888213564991et_nat
    = ( ^ [A2: set_set_nat] :
          ( collect_nat
          @ ^ [X4: nat] : ( complete_Inf_Inf_o @ ( image_set_nat_o @ ( member_nat @ X4 ) @ A2 ) ) ) ) ) ).

% Inf_set_def
thf(fact_1218_INT__E,axiom,
    ! [B: nat,B2: nat > set_nat,A: set_nat,A3: nat] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B2 @ A ) ) )
     => ( ~ ( member_nat @ B @ ( B2 @ A3 ) )
       => ~ ( member_nat @ A3 @ A ) ) ) ).

% INT_E
thf(fact_1219_INT__E,axiom,
    ! [B: nat,B2: a > set_nat,A: set_a,A3: a] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_a_set_nat @ B2 @ A ) ) )
     => ( ~ ( member_nat @ B @ ( B2 @ A3 ) )
       => ~ ( member_a @ A3 @ A ) ) ) ).

% INT_E
thf(fact_1220_INT__E,axiom,
    ! [B: a,B2: nat > set_a,A: set_nat,A3: nat] :
      ( ( member_a @ B @ ( comple6135023378680113637_set_a @ ( image_nat_set_a @ B2 @ A ) ) )
     => ( ~ ( member_a @ B @ ( B2 @ A3 ) )
       => ~ ( member_nat @ A3 @ A ) ) ) ).

% INT_E
thf(fact_1221_INT__E,axiom,
    ! [B: a,B2: a > set_a,A: set_a,A3: a] :
      ( ( member_a @ B @ ( comple6135023378680113637_set_a @ ( image_a_set_a @ B2 @ A ) ) )
     => ( ~ ( member_a @ B @ ( B2 @ A3 ) )
       => ~ ( member_a @ A3 @ A ) ) ) ).

% INT_E
thf(fact_1222_INT__E,axiom,
    ! [B: nat,B2: ( real > nat ) > set_nat,A: set_real_nat,A3: real > nat] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_9082491048595935784et_nat @ B2 @ A ) ) )
     => ( ~ ( member_nat @ B @ ( B2 @ A3 ) )
       => ~ ( member_real_nat @ A3 @ A ) ) ) ).

% INT_E
thf(fact_1223_INT__E,axiom,
    ! [B: nat,B2: ( real > b ) > set_nat,A: set_real_b,A3: real > b] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_real_b_set_nat @ B2 @ A ) ) )
     => ( ~ ( member_nat @ B @ ( B2 @ A3 ) )
       => ~ ( member_real_b @ A3 @ A ) ) ) ).

% INT_E
thf(fact_1224_INT__E,axiom,
    ! [B: nat,B2: ( real > a ) > set_nat,A: set_real_a,A3: real > a] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_real_a_set_nat @ B2 @ A ) ) )
     => ( ~ ( member_nat @ B @ ( B2 @ A3 ) )
       => ~ ( member_real_a @ A3 @ A ) ) ) ).

% INT_E
thf(fact_1225_INT__E,axiom,
    ! [B: nat,B2: ( a > complex ) > set_nat,A: set_a_complex,A3: a > complex] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_5756905062129988830et_nat @ B2 @ A ) ) )
     => ( ~ ( member_nat @ B @ ( B2 @ A3 ) )
       => ~ ( member_a_complex @ A3 @ A ) ) ) ).

% INT_E
thf(fact_1226_INT__E,axiom,
    ! [B: nat,B2: ( a > real ) > set_nat,A: set_a_real,A3: a > real] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_a_real_set_nat @ B2 @ A ) ) )
     => ( ~ ( member_nat @ B @ ( B2 @ A3 ) )
       => ~ ( member_a_real @ A3 @ A ) ) ) ).

% INT_E
thf(fact_1227_INT__E,axiom,
    ! [B: nat,B2: ( a > $o ) > set_nat,A: set_a_o,A3: a > $o] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_a_o_set_nat @ B2 @ A ) ) )
     => ( ~ ( member_nat @ B @ ( B2 @ A3 ) )
       => ~ ( member_a_o @ A3 @ A ) ) ) ).

% INT_E
thf(fact_1228_INT__D,axiom,
    ! [B: nat,B2: nat > set_nat,A: set_nat,A3: nat] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B2 @ A ) ) )
     => ( ( member_nat @ A3 @ A )
       => ( member_nat @ B @ ( B2 @ A3 ) ) ) ) ).

% INT_D
thf(fact_1229_INT__D,axiom,
    ! [B: nat,B2: a > set_nat,A: set_a,A3: a] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_a_set_nat @ B2 @ A ) ) )
     => ( ( member_a @ A3 @ A )
       => ( member_nat @ B @ ( B2 @ A3 ) ) ) ) ).

% INT_D
thf(fact_1230_INT__D,axiom,
    ! [B: a,B2: nat > set_a,A: set_nat,A3: nat] :
      ( ( member_a @ B @ ( comple6135023378680113637_set_a @ ( image_nat_set_a @ B2 @ A ) ) )
     => ( ( member_nat @ A3 @ A )
       => ( member_a @ B @ ( B2 @ A3 ) ) ) ) ).

% INT_D
thf(fact_1231_INT__D,axiom,
    ! [B: a,B2: a > set_a,A: set_a,A3: a] :
      ( ( member_a @ B @ ( comple6135023378680113637_set_a @ ( image_a_set_a @ B2 @ A ) ) )
     => ( ( member_a @ A3 @ A )
       => ( member_a @ B @ ( B2 @ A3 ) ) ) ) ).

% INT_D
thf(fact_1232_INT__D,axiom,
    ! [B: nat,B2: ( real > nat ) > set_nat,A: set_real_nat,A3: real > nat] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_9082491048595935784et_nat @ B2 @ A ) ) )
     => ( ( member_real_nat @ A3 @ A )
       => ( member_nat @ B @ ( B2 @ A3 ) ) ) ) ).

% INT_D
thf(fact_1233_INT__D,axiom,
    ! [B: nat,B2: ( real > b ) > set_nat,A: set_real_b,A3: real > b] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_real_b_set_nat @ B2 @ A ) ) )
     => ( ( member_real_b @ A3 @ A )
       => ( member_nat @ B @ ( B2 @ A3 ) ) ) ) ).

% INT_D
thf(fact_1234_INT__D,axiom,
    ! [B: nat,B2: ( real > a ) > set_nat,A: set_real_a,A3: real > a] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_real_a_set_nat @ B2 @ A ) ) )
     => ( ( member_real_a @ A3 @ A )
       => ( member_nat @ B @ ( B2 @ A3 ) ) ) ) ).

% INT_D
thf(fact_1235_INT__D,axiom,
    ! [B: nat,B2: ( a > complex ) > set_nat,A: set_a_complex,A3: a > complex] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_5756905062129988830et_nat @ B2 @ A ) ) )
     => ( ( member_a_complex @ A3 @ A )
       => ( member_nat @ B @ ( B2 @ A3 ) ) ) ) ).

% INT_D
thf(fact_1236_INT__D,axiom,
    ! [B: nat,B2: ( a > real ) > set_nat,A: set_a_real,A3: a > real] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_a_real_set_nat @ B2 @ A ) ) )
     => ( ( member_a_real @ A3 @ A )
       => ( member_nat @ B @ ( B2 @ A3 ) ) ) ) ).

% INT_D
thf(fact_1237_INT__D,axiom,
    ! [B: nat,B2: ( a > $o ) > set_nat,A: set_a_o,A3: a > $o] :
      ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_a_o_set_nat @ B2 @ A ) ) )
     => ( ( member_a_o @ A3 @ A )
       => ( member_nat @ B @ ( B2 @ A3 ) ) ) ) ).

% INT_D
thf(fact_1238_UN__E,axiom,
    ! [B: nat,B2: nat > set_nat,A: set_nat] :
      ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B2 @ A ) ) )
     => ~ ! [X2: nat] :
            ( ( member_nat @ X2 @ A )
           => ~ ( member_nat @ B @ ( B2 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1239_UN__E,axiom,
    ! [B: nat,B2: a > set_nat,A: set_a] :
      ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_a_set_nat @ B2 @ A ) ) )
     => ~ ! [X2: a] :
            ( ( member_a @ X2 @ A )
           => ~ ( member_nat @ B @ ( B2 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1240_UN__E,axiom,
    ! [B: a,B2: nat > set_a,A: set_nat] :
      ( ( member_a @ B @ ( comple2307003609928055243_set_a @ ( image_nat_set_a @ B2 @ A ) ) )
     => ~ ! [X2: nat] :
            ( ( member_nat @ X2 @ A )
           => ~ ( member_a @ B @ ( B2 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1241_UN__E,axiom,
    ! [B: a,B2: a > set_a,A: set_a] :
      ( ( member_a @ B @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ B2 @ A ) ) )
     => ~ ! [X2: a] :
            ( ( member_a @ X2 @ A )
           => ~ ( member_a @ B @ ( B2 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1242_UN__E,axiom,
    ! [B: nat,B2: ( real > nat ) > set_nat,A: set_real_nat] :
      ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_9082491048595935784et_nat @ B2 @ A ) ) )
     => ~ ! [X2: real > nat] :
            ( ( member_real_nat @ X2 @ A )
           => ~ ( member_nat @ B @ ( B2 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1243_UN__E,axiom,
    ! [B: nat,B2: ( real > b ) > set_nat,A: set_real_b] :
      ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_real_b_set_nat @ B2 @ A ) ) )
     => ~ ! [X2: real > b] :
            ( ( member_real_b @ X2 @ A )
           => ~ ( member_nat @ B @ ( B2 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1244_UN__E,axiom,
    ! [B: nat,B2: ( real > a ) > set_nat,A: set_real_a] :
      ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_real_a_set_nat @ B2 @ A ) ) )
     => ~ ! [X2: real > a] :
            ( ( member_real_a @ X2 @ A )
           => ~ ( member_nat @ B @ ( B2 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1245_UN__E,axiom,
    ! [B: nat,B2: ( a > complex ) > set_nat,A: set_a_complex] :
      ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_5756905062129988830et_nat @ B2 @ A ) ) )
     => ~ ! [X2: a > complex] :
            ( ( member_a_complex @ X2 @ A )
           => ~ ( member_nat @ B @ ( B2 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1246_UN__E,axiom,
    ! [B: nat,B2: ( a > real ) > set_nat,A: set_a_real] :
      ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_a_real_set_nat @ B2 @ A ) ) )
     => ~ ! [X2: a > real] :
            ( ( member_a_real @ X2 @ A )
           => ~ ( member_nat @ B @ ( B2 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1247_UN__E,axiom,
    ! [B: nat,B2: ( a > $o ) > set_nat,A: set_a_o] :
      ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_a_o_set_nat @ B2 @ A ) ) )
     => ~ ! [X2: a > $o] :
            ( ( member_a_o @ X2 @ A )
           => ~ ( member_nat @ B @ ( B2 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1248_Sup__SUP__eq,axiom,
    ( comple4070330114094914769_nat_o
    = ( ^ [S2: set_a_nat_o,X4: a > nat] : ( member_a_nat @ X4 @ ( comple4286861423968083212_a_nat @ ( image_7293232773405579610_a_nat @ collect_a_nat @ S2 ) ) ) ) ) ).

% Sup_SUP_eq
thf(fact_1249_Sup__SUP__eq,axiom,
    ( comple2105534466620790551_a_a_o
    = ( ^ [S2: set_a_a_o,X4: a > a] : ( member_a_a @ X4 @ ( comple6518619711525350638et_a_a @ ( image_a_a_o_set_a_a @ collect_a_a @ S2 ) ) ) ) ) ).

% Sup_SUP_eq
thf(fact_1250_Sup__SUP__eq,axiom,
    ( comple8317665133742190828_nat_o
    = ( ^ [S2: set_nat_o,X4: nat] : ( member_nat @ X4 @ ( comple7399068483239264473et_nat @ ( image_nat_o_set_nat @ collect_nat @ S2 ) ) ) ) ) ).

% Sup_SUP_eq
thf(fact_1251_Sup__bool__def,axiom,
    ( complete_Sup_Sup_o
    = ( member_o @ $true ) ) ).

% Sup_bool_def
thf(fact_1252_Inf__bool__def,axiom,
    ( complete_Inf_Inf_o
    = ( ^ [A2: set_o] :
          ~ ( member_o @ $false @ A2 ) ) ) ).

% Inf_bool_def
thf(fact_1253_Inf__nat__def,axiom,
    ( complete_Inf_Inf_nat
    = ( ^ [X7: set_nat] :
          ( ord_Least_nat
          @ ^ [N4: nat] : ( member_nat @ N4 @ X7 ) ) ) ) ).

% Inf_nat_def
thf(fact_1254_Inf__nat__def1,axiom,
    ! [K2: set_nat] :
      ( ( K2 != bot_bot_set_nat )
     => ( member_nat @ ( complete_Inf_Inf_nat @ K2 ) @ K2 ) ) ).

% Inf_nat_def1
thf(fact_1255_infinite__UNIV__nat,axiom,
    ~ ( finite_finite_nat @ top_top_set_nat ) ).

% infinite_UNIV_nat
thf(fact_1256_real__of__nat__Sup,axiom,
    ! [A: set_nat] :
      ( ( A != bot_bot_set_nat )
     => ( ( condit2214826472909112428ve_nat @ A )
       => ( ( semiri5074537144036343181t_real @ ( complete_Sup_Sup_nat @ A ) )
          = ( comple1385675409528146559p_real @ ( image_nat_real @ semiri5074537144036343181t_real @ A ) ) ) ) ) ).

% real_of_nat_Sup
thf(fact_1257_nat__not__finite,axiom,
    ~ ( finite_finite_nat @ top_top_set_nat ) ).

% nat_not_finite
thf(fact_1258_Inf__real__def,axiom,
    ( comple4887499456419720421f_real
    = ( ^ [X7: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X7 ) ) ) ) ) ).

% Inf_real_def
thf(fact_1259_ennreal__minus__eq__top,axiom,
    ! [A3: extend8495563244428889912nnreal,B: extend8495563244428889912nnreal] :
      ( ( ( minus_8429688780609304081nnreal @ A3 @ B )
        = top_to1496364449551166952nnreal )
      = ( A3 = top_to1496364449551166952nnreal ) ) ).

% ennreal_minus_eq_top
thf(fact_1260_ennreal__top__minus,axiom,
    ! [X: extend8495563244428889912nnreal] :
      ( ( minus_8429688780609304081nnreal @ top_to1496364449551166952nnreal @ X )
      = top_to1496364449551166952nnreal ) ).

% ennreal_top_minus
thf(fact_1261_finite__Collect__less__nat,axiom,
    ! [K: nat] :
      ( finite_finite_nat
      @ ( collect_nat
        @ ^ [N4: nat] : ( ord_less_nat @ N4 @ K ) ) ) ).

% finite_Collect_less_nat
thf(fact_1262_diff__less__top__ennreal,axiom,
    ! [A3: extend8495563244428889912nnreal,B: extend8495563244428889912nnreal] :
      ( ( ord_le7381754540660121996nnreal @ ( minus_8429688780609304081nnreal @ A3 @ B ) @ top_to1496364449551166952nnreal )
      = ( ord_le7381754540660121996nnreal @ A3 @ top_to1496364449551166952nnreal ) ) ).

% diff_less_top_ennreal
thf(fact_1263_real_Ocountable__space__discrete,axiom,
    ( ( counta7319604579010473777e_real @ ( sigma_space_real @ borel_5078946678739801102l_real ) )
   => ( ( sigma_sets_real @ borel_5078946678739801102l_real )
      = ( sigma_sets_real @ ( sigma_8508918144308765139e_real @ ( sigma_space_real @ borel_5078946678739801102l_real ) ) ) ) ) ).

% real.countable_space_discrete
thf(fact_1264_bool_Ocountable__space__discrete,axiom,
    ( ( counta5976203206615340371able_o @ ( sigma_space_o @ borel_5500255247093592246orel_o ) )
   => ( ( sigma_sets_o @ borel_5500255247093592246orel_o )
      = ( sigma_sets_o @ ( sigma_count_space_o @ ( sigma_space_o @ borel_5500255247093592246orel_o ) ) ) ) ) ).

% bool.countable_space_discrete
thf(fact_1265_nat_Ocountable__space__discrete,axiom,
    ( ( counta1168086296615599829le_nat @ ( sigma_space_nat @ borel_8449730974584783410el_nat ) )
   => ( ( sigma_sets_nat @ borel_8449730974584783410el_nat )
      = ( sigma_sets_nat @ ( sigma_7685844798829912695ce_nat @ ( sigma_space_nat @ borel_8449730974584783410el_nat ) ) ) ) ) ).

% nat.countable_space_discrete
thf(fact_1266_ennreal_Osingleton__sets,axiom,
    ! [X: extend8495563244428889912nnreal] :
      ( ( member7908768830364227535nnreal @ X @ ( sigma_3147302497200244656nnreal @ borel_6524799422816628122nnreal ) )
     => ( member603777416030116741nnreal @ ( insert7407984058720857448nnreal @ X @ bot_bo4854962954004695426nnreal ) @ ( sigma_5465916536984168985nnreal @ borel_6524799422816628122nnreal ) ) ) ).

% ennreal.singleton_sets
thf(fact_1267_ennreal_Ocountable__space__discrete,axiom,
    ( ( counta8439243037236335165nnreal @ ( sigma_3147302497200244656nnreal @ borel_6524799422816628122nnreal ) )
   => ( ( sigma_5465916536984168985nnreal @ borel_6524799422816628122nnreal )
      = ( sigma_5465916536984168985nnreal @ ( sigma_7204664791115113951nnreal @ ( sigma_3147302497200244656nnreal @ borel_6524799422816628122nnreal ) ) ) ) ) ).

% ennreal.countable_space_discrete
thf(fact_1268_ennreal_Ospace__UNIV,axiom,
    ( ( sigma_3147302497200244656nnreal @ borel_6524799422816628122nnreal )
    = top_to7994903218803871134nnreal ) ).

% ennreal.space_UNIV
thf(fact_1269_UNIV__bool,axiom,
    ( top_top_set_o
    = ( insert_o @ $false @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).

% UNIV_bool
thf(fact_1270_real_Osingleton__sets,axiom,
    ! [X: real] :
      ( ( member_real @ X @ ( sigma_space_real @ borel_5078946678739801102l_real ) )
     => ( member_set_real @ ( insert_real @ X @ bot_bot_set_real ) @ ( sigma_sets_real @ borel_5078946678739801102l_real ) ) ) ).

% real.singleton_sets
thf(fact_1271_bool_Osingleton__sets,axiom,
    ! [X: $o] :
      ( ( member_o @ X @ ( sigma_space_o @ borel_5500255247093592246orel_o ) )
     => ( member_set_o @ ( insert_o @ X @ bot_bot_set_o ) @ ( sigma_sets_o @ borel_5500255247093592246orel_o ) ) ) ).

% bool.singleton_sets
thf(fact_1272_nat_Osingleton__sets,axiom,
    ! [X: nat] :
      ( ( member_nat @ X @ ( sigma_space_nat @ borel_8449730974584783410el_nat ) )
     => ( member_set_nat @ ( insert_nat @ X @ bot_bot_set_nat ) @ ( sigma_sets_nat @ borel_8449730974584783410el_nat ) ) ) ).

% nat.singleton_sets
thf(fact_1273_finite__M__bounded__by__nat,axiom,
    ! [P: nat > $o,I: nat] :
      ( finite_finite_nat
      @ ( collect_nat
        @ ^ [K3: nat] :
            ( ( P @ K3 )
            & ( ord_less_nat @ K3 @ I ) ) ) ) ).

% finite_M_bounded_by_nat
thf(fact_1274_separate__measurable,axiom,
    ! [P: real > nat] :
      ( ! [I2: nat] : ( member_set_real @ ( vimage_real_nat @ P @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) @ ( sigma_sets_real @ borel_5078946678739801102l_real ) )
     => ( member_real_nat @ P @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ borel_8449730974584783410el_nat ) ) ) ).

% separate_measurable
thf(fact_1275_measurable__separate,axiom,
    ! [P: real > nat,I: nat] :
      ( ( member_real_nat @ P @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ borel_8449730974584783410el_nat ) )
     => ( member_set_real @ ( vimage_real_nat @ P @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ ( sigma_sets_real @ borel_5078946678739801102l_real ) ) ) ).

% measurable_separate

% Conjectures (1)
thf(conj_0,conjecture,
    member_real_a @ p @ ( sigma_523072396149930112real_a @ borel_5078946678739801102l_real @ ( sigma_count_space_a @ ( image_real_a @ p @ top_top_set_real ) ) ) ).

%------------------------------------------------------------------------------