TPTP Problem File: SLH0934^1.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/0009_Monad_QuasiBorel/prob_00475_020793__15408692_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1927 ( 516 unt; 633 typ;   0 def)
%            Number of atoms       : 3945 (1130 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 12586 ( 371   ~;  31   |; 293   &;10541   @)
%                                         (   0 <=>;1350  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :  103 ( 102 usr)
%            Number of type conns  : 4112 (4112   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  534 ( 531 usr;  29 con; 0-4 aty)
%            Number of variables   : 4247 ( 727   ^;3459   !;  61   ?;4247   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 14:10:45.031
%------------------------------------------------------------------------------
% Could-be-implicit typings (102)
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thf(ty_n_t__Set__Oset_It__Set__Oset_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mtf__b_J_J_J,type,
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thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
    set_re3580165118909042347pace_b: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_J,type,
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thf(ty_n_t__QuasiBorel__Oquasi____borel_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
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thf(ty_n_t__QuasiBorel__Oquasi____borel_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J,type,
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thf(ty_n_t__Product____Type__Oprod_I_062_Itf__a_Mt__Set__Oset_Itf__b_J_J_M_062_Itf__a_Mt__Set__Oset_Itf__b_J_J_J,type,
    produc1616453953277916653_set_b: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__b_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
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thf(ty_n_t__Set__Oset_I_062_Itf__b_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_J,type,
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thf(ty_n_t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
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thf(ty_n_t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_J,type,
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thf(ty_n_t__Set__Oset_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_Mtf__b_J_J,type,
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thf(ty_n_t__Set__Oset_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mtf__b_J_J,type,
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thf(ty_n_t__Set__Oset_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mtf__a_J_J,type,
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thf(ty_n_t__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
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thf(ty_n_t__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J,type,
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thf(ty_n_t__Product____Type__Oprod_I_062_Itf__a_Mtf__b_J_M_062_Itf__a_Mtf__b_J_J,type,
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thf(ty_n_t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
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thf(ty_n_t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J,type,
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thf(ty_n_t__Set__Oset_I_062_I_062_Itf__a_Mtf__b_J_M_062_Itf__a_Mtf__b_J_J_J,type,
    set_a_b_a_b: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_062_Itf__a_Mtf__b_J_J_J,type,
    set_real_a_b: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_062_Itf__a_Mtf__b_J_J,type,
    quasi_borel_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_062_Itf__a_Mtf__b_J_J_J,type,
    set_set_a_b: $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__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__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__Real__Oreal_J,type,
    set_real: $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__Real__Oreal,type,
    real: $tType ).

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

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

% Explicit typings (531)
thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
    comple3236514525185195311pace_b: set_se4320058886960055698pace_b > set_Pr7742364250814120412pace_b ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mtf__b_J_J,type,
    comple2201105612168094190ce_a_b: set_se3219625108814215889ce_a_b > set_Pr8041968334489646747ce_a_b ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J_J,type,
    comple1483613879995724273pace_b: set_se5218783146767645012pace_b > set_a_5989463605624649374pace_b ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_J,type,
    comple9167635969721739439pace_a: set_se6007621025939403026pace_a > set_a_5785126655188516188pace_a ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
    comple6646451451432703792pace_b: set_se5848838506614550291pace_b > set_a_3263942136899480541pace_b ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_Itf__a_Mtf__b_J_J,type,
    comple6589653751571696623et_a_b: set_set_a_b > set_a_b ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_Itf__b_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
    comple3219233233111103983pace_b: set_se2718600146793341522pace_b > set_b_9060095955432656540pace_b ).

thf(sy_c_Finite__Product__Measure_Omerge_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
    finite5780851627059721263pace_b: set_Pr8456636223741192351pace_a > set_Pr8456636223741192351pace_a > produc2113741087038843565pace_b > probab4737552673497767871pace_a > probab4737552677800996672pace_b ).

thf(sy_c_Finite__Product__Measure_Omerge_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001t__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
    finite2812723535947976847pace_b: set_Pr8456636223741192351pace_a > set_Pr8456636223741192351pace_a > produc4378702480952713069pace_b > probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b ).

thf(sy_c_Finite__Product__Measure_Omerge_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001t__Set__Oset_Itf__b_J,type,
    finite4108965814801126606_set_b: set_Pr8456636223741192351pace_a > set_Pr8456636223741192351pace_a > produc4507326589786375019_set_b > probab4737552673497767871pace_a > set_b ).

thf(sy_c_Finite__Product__Measure_Omerge_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001tf__b,type,
    finite3957753199828097006ce_a_b: set_Pr8456636223741192351pace_a > set_Pr8456636223741192351pace_a > produc2422889851104496043ce_a_b > probab4737552673497767871pace_a > b ).

thf(sy_c_Finite__Product__Measure_Omerge_001tf__a_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
    finite4354535354149943921pace_b: set_a > set_a > produc2134183119093696817pace_b > a > probab8624551251471354625pace_b ).

thf(sy_c_Finite__Product__Measure_Omerge_001tf__a_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J,type,
    finite6055857896737165103pace_a: set_a > set_a > produc6714447585088131501pace_a > a > probab4737552673497767871pace_a ).

thf(sy_c_Finite__Product__Measure_Omerge_001tf__a_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
    finite6055857901040393904pace_b: set_a > set_a > produc6642715939417409839pace_b > a > probab4737552677800996672pace_b ).

thf(sy_c_Finite__Product__Measure_Omerge_001tf__a_001t__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
    finite3412154840674873937pace_b: set_a > set_a > produc7758990284346961137pace_b > a > set_Pr2974436765678502625pace_b ).

thf(sy_c_Finite__Product__Measure_Omerge_001tf__a_001t__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J,type,
    finite8390634798700271631pace_a: set_a > set_a > produc4521791571825303405pace_a > a > set_Pr8456636223741192351pace_a ).

thf(sy_c_Finite__Product__Measure_Omerge_001tf__a_001t__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
    finite8461668838746617616pace_b: set_a > set_a > produc7960666857113055727pace_b > a > set_Pr8527670263787538336pace_b ).

thf(sy_c_Finite__Product__Measure_Omerge_001tf__a_001t__Set__Oset_Itf__b_J,type,
    finite1260387632014723919_set_b: set_a > set_a > produc1616453953277916653_set_b > a > set_b ).

thf(sy_c_Finite__Product__Measure_Omerge_001tf__a_001tf__b,type,
    finite2735608678046798447ge_a_b: set_a > set_a > product_prod_a_b_a_b > a > b ).

thf(sy_c_Finite__Product__Measure_Omerge_001tf__b_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
    finite283199583066403055pace_b: set_b > set_b > produc3920177095362909229pace_b > b > probab4737552677800996672pace_b ).

thf(sy_c_Finite__Product__Measure_Omerge_001tf__b_001t__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
    finite2633747095815736655pace_b: set_b > set_b > produc4050322596820764909pace_b > b > set_Pr8527670263787538336pace_b ).

thf(sy_c_Fun_Ocomp_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001t__Real__Oreal,type,
    comp_P2386351730793452623a_real: ( probab4737552673497767871pace_a > probab4737552673497767871pace_a ) > ( real > probab4737552673497767871pace_a ) > real > probab4737552673497767871pace_a ).

thf(sy_c_Fun_Ocomp_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_001t__Real__Oreal,type,
    comp_P8831019459788205904b_real: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > ( real > probab4737552673497767871pace_a ) > real > probab4737552677800996672pace_b ).

thf(sy_c_Fun_Ocomp_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001tf__b_001t__Real__Oreal,type,
    comp_P3348619169354409871b_real: ( probab4737552673497767871pace_a > b ) > ( real > probab4737552673497767871pace_a ) > real > b ).

thf(sy_c_Fun_Ocomp_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001tf__b_001tf__a,type,
    comp_P9206150651643741019_a_b_a: ( probab4737552673497767871pace_a > b ) > ( a > probab4737552673497767871pace_a ) > a > b ).

thf(sy_c_Fun_Ocomp_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001t__Real__Oreal,type,
    comp_P3681088572523203470a_real: ( probab4737552677800996672pace_b > probab4737552673497767871pace_a ) > ( real > probab4737552677800996672pace_b ) > real > probab4737552673497767871pace_a ).

thf(sy_c_Fun_Ocomp_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_001t__Real__Oreal,type,
    comp_P902384264663180943b_real: ( probab4737552677800996672pace_b > probab4737552677800996672pace_b ) > ( real > probab4737552677800996672pace_b ) > real > probab4737552677800996672pace_b ).

thf(sy_c_Fun_Ocomp_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_001tf__b_001tf__a,type,
    comp_P6427446343783718492_b_b_a: ( probab4737552677800996672pace_b > b ) > ( a > probab4737552677800996672pace_b ) > a > b ).

thf(sy_c_Fun_Ocomp_001tf__a_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_001t__Real__Oreal,type,
    comp_a6393136188637473938b_real: ( a > probab8624551251471354625pace_b ) > ( real > a ) > real > probab8624551251471354625pace_b ).

thf(sy_c_Fun_Ocomp_001tf__a_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001t__Real__Oreal,type,
    comp_a423948744115472976a_real: ( a > probab4737552673497767871pace_a ) > ( real > a ) > real > probab4737552673497767871pace_a ).

thf(sy_c_Fun_Ocomp_001tf__a_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001tf__a,type,
    comp_a7340621667389922906ce_a_a: ( a > probab4737552673497767871pace_a ) > ( a > a ) > a > probab4737552673497767871pace_a ).

thf(sy_c_Fun_Ocomp_001tf__a_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_001t__Real__Oreal,type,
    comp_a6868616473110226257b_real: ( a > probab4737552677800996672pace_b ) > ( real > a ) > real > probab4737552677800996672pace_b ).

thf(sy_c_Fun_Ocomp_001tf__a_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_001tf__a,type,
    comp_a6704972666784936217ce_b_a: ( a > probab4737552677800996672pace_b ) > ( a > a ) > a > probab4737552677800996672pace_b ).

thf(sy_c_Fun_Ocomp_001tf__a_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_001tf__b,type,
    comp_a6704972666784936218ce_b_b: ( a > probab4737552677800996672pace_b ) > ( b > a ) > b > probab4737552677800996672pace_b ).

thf(sy_c_Fun_Ocomp_001tf__a_001tf__b_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J,type,
    comp_a3666068046325000155pace_a: ( a > b ) > ( probab4737552673497767871pace_a > a ) > probab4737552673497767871pace_a > b ).

thf(sy_c_Fun_Ocomp_001tf__a_001tf__b_001t__Real__Oreal,type,
    comp_a_b_real: ( a > b ) > ( real > a ) > real > b ).

thf(sy_c_Fun_Ocomp_001tf__a_001tf__b_001tf__a,type,
    comp_a_b_a: ( a > b ) > ( a > a ) > a > b ).

thf(sy_c_Fun_Ocomp_001tf__b_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_001t__Real__Oreal,type,
    comp_b4925389053965159440b_real: ( b > probab4737552677800996672pace_b ) > ( real > b ) > real > probab4737552677800996672pace_b ).

thf(sy_c_Fun_Ocomp_001tf__b_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_001tf__b,type,
    comp_b6576235760933465243ce_b_b: ( b > probab4737552677800996672pace_b ) > ( b > b ) > b > probab4737552677800996672pace_b ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__b_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J,type,
    comp_b3537331140473529180pace_a: ( b > b ) > ( probab4737552673497767871pace_a > b ) > probab4737552673497767871pace_a > b ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__b_001tf__a,type,
    comp_b_b_a: ( b > b ) > ( a > b ) > a > b ).

thf(sy_c_Fun_Oid_001_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
    id_Pro8631783166541050741pace_b: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > probab4737552673497767871pace_a > probab4737552677800996672pace_b ).

thf(sy_c_Fun_Oid_001_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mtf__b_J,type,
    id_Pro5186492747891939252ce_a_b: ( probab4737552673497767871pace_a > b ) > probab4737552673497767871pace_a > b ).

thf(sy_c_Fun_Oid_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
    id_a_P2005203185063471415pace_b: ( a > probab8624551251471354625pace_b ) > a > probab8624551251471354625pace_b ).

thf(sy_c_Fun_Oid_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J,type,
    id_a_P7447643778571857653pace_a: ( a > probab4737552673497767871pace_a ) > a > probab4737552673497767871pace_a ).

thf(sy_c_Fun_Oid_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
    id_a_P7518677818618203638pace_b: ( a > probab4737552677800996672pace_b ) > a > probab4737552677800996672pace_b ).

thf(sy_c_Fun_Oid_001_062_Itf__a_Mtf__b_J,type,
    id_a_b: ( a > b ) > a > b ).

thf(sy_c_Fun_Oid_001_062_Itf__b_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
    id_b_P1746019500644212789pace_b: ( b > probab4737552677800996672pace_b ) > b > probab4737552677800996672pace_b ).

thf(sy_c_Fun_Oid_001tf__a,type,
    id_a: a > a ).

thf(sy_c_Fun_Oid_001tf__b,type,
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    inf_in4158870736502718360_a_b_o: ( ( probab4737552673497767871pace_a > b ) > $o ) > ( ( probab4737552673497767871pace_a > b ) > $o ) > ( probab4737552673497767871pace_a > b ) > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J_M_Eo_J,type,
    inf_in1454270903699293013ce_b_o: ( ( a > probab8624551251471354625pace_b ) > $o ) > ( ( a > probab8624551251471354625pace_b ) > $o ) > ( a > probab8624551251471354625pace_b ) > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_M_Eo_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_M_Eo_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_Itf__a_Mtf__b_J_M_Eo_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_Itf__b_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_M_Eo_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mtf__b_J_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_It__Real__Oreal_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_It__Real__Oreal_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_Itf__a_Mtf__b_J_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_Itf__b_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
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thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__b_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_M_Eo_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mtf__b_J_M_Eo_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J_M_Eo_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_M_Eo_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_M_Eo_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_Itf__a_Mtf__b_J_M_Eo_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001t__QuasiBorel__Oquasi____borel_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001t__QuasiBorel__Oquasi____borel_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mtf__b_J_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_Itf__a_Mtf__b_J_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J,type,
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thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__b_J,type,
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thf(sy_c_Monad__QuasiBorel_Oin__MPx_001tf__a,type,
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thf(sy_c_Monad__QuasiBorel_Oin__MPx_001tf__b,type,
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thf(sy_c_Monad__QuasiBorel_Oin__Px_001tf__a,type,
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thf(sy_c_Monad__QuasiBorel_Oin__Px_001tf__b,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs_001tf__a,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs_001tf__b,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs__MPx_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs__MPx_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs__MPx_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs__MPx_001tf__a,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs__MPx_001tf__b,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs__Px_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs__Px_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs__Px_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs__Px_001tf__a,type,
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thf(sy_c_Monad__QuasiBorel_OmonadP__qbs__Px_001tf__b,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__closed1_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J,type,
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thf(sy_c_QuasiBorel_Oqbs__closed1_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
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thf(sy_c_QuasiBorel_Oqbs__closed2_001_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
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thf(sy_c_QuasiBorel_Oqbs__closed2_001_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mtf__b_J,type,
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thf(sy_c_QuasiBorel_Oqbs__closed2_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J,type,
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thf(sy_c_QuasiBorel_Oqbs__closed2_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
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thf(sy_c_QuasiBorel_Oqbs__closed2_001_062_Itf__a_Mtf__b_J,type,
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thf(sy_c_QuasiBorel_Oqbs__closed2_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
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thf(sy_c_QuasiBorel_Oqbs__closed3_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J,type,
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thf(sy_c_QuasiBorel_Oqbs__morphism_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001tf__a,type,
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thf(sy_c_QuasiBorel_Oqbs__morphism_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_001tf__b,type,
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thf(sy_c_QuasiBorel_Oqbs__morphism_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
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thf(sy_c_QuasiBorel_Oqbs__morphism_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_001tf__b,type,
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thf(sy_c_QuasiBorel_Oqbs__morphism_001tf__a_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
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thf(sy_c_QuasiBorel_Oqbs__morphism_001tf__a_001tf__a,type,
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thf(sy_c_QuasiBorel_Oqbs__morphism_001tf__a_001tf__b,type,
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thf(sy_c_QuasiBorel_Oqbs__morphism_001tf__b_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
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thf(sy_c_QuasiBorel_Oqbs__morphism_001tf__b_001tf__a,type,
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thf(sy_c_QuasiBorel_Oqbs__morphism_001tf__b_001tf__b,type,
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thf(sy_c_member_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_J,type,
    member2562354099133141246pace_a: ( a > probab8553517211425008640pace_a ) > set_a_6148246124949502109pace_a > $o ).

thf(sy_c_member_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
    member41169580844105599pace_b: ( a > probab8624551251471354625pace_b ) > set_a_5989463605624649374pace_b > $o ).

thf(sy_c_member_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J,type,
    member7269867574344811837pace_a: ( a > probab4737552673497767871pace_a ) > set_a_5785126655188516188pace_a > $o ).

thf(sy_c_member_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
    member7340901614391157822pace_b: ( a > probab4737552677800996672pace_b ) > set_a_3263942136899480541pace_b > $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__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
    member6868725278929494462pace_b: ( b > probab8624551251471354625pace_b ) > set_b_5065340218742860125pace_b > $o ).

thf(sy_c_member_001_062_Itf__b_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J,type,
    member1497209256370820988pace_a: ( b > probab4737552673497767871pace_a ) > set_b_2357908436866916379pace_a > $o ).

thf(sy_c_member_001_062_Itf__b_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
    member1568243296417166973pace_b: ( b > probab4737552677800996672pace_b ) > set_b_9060095955432656540pace_b > $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_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J,type,
    member7462078926031725098pace_b: probab8624551251471354625pace_b > set_Pr2974436765678502625pace_b > $o ).

thf(sy_c_member_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J,type,
    member6485455074645559016pace_a: probab4737552673497767871pace_a > set_Pr8456636223741192351pace_a > $o ).

thf(sy_c_member_001t__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J,type,
    member6485455078948787817pace_b: probab4737552677800996672pace_b > set_Pr8527670263787538336pace_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_Mt__Set__Oset_I_062_It__Real__Oreal_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_J_J,type,
    member640087230083980059pace_a: produc5176701162915795698pace_a > set_Pr3107357357746732882pace_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_Mt__Set__Oset_I_062_It__Real__Oreal_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J_J,type,
    member2497209941670631003pace_b: produc7033823874502446642pace_b > set_Pr232608783647758994pace_b > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
    member3909763555603355763pace_b: set_Pr7742364250814120412pace_b > set_se4320058886960055698pace_b > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mtf__b_J_J,type,
    member6295589911677730098ce_a_b: set_Pr8041968334489646747ce_a_b > set_se3219625108814215889ce_a_b > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J_J,type,
    member2156862910413884725pace_b: set_a_5989463605624649374pace_b > set_se5218783146767645012pace_b > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_J,type,
    member4038748232376599539pace_a: set_a_5785126655188516188pace_a > set_se6007621025939403026pace_a > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
    member1517563714087563892pace_b: set_a_3263942136899480541pace_b > set_se5848838506614550291pace_b > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_Itf__a_Mtf__b_J_J,type,
    member_set_a_b: set_a_b > set_set_a_b > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_Itf__b_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_J,type,
    member7313717532620739891pace_b: set_b_9060095955432656540pace_b > set_se2718600146793341522pace_b > $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_X,type,
    x: quasi_borel_a ).

thf(sy_v_Y,type,
    y: quasi_borel_b ).

thf(sy_v_f,type,
    f: a > probab4737552677800996672pace_b ).

% Relevant facts (1278)
thf(fact_0_assms,axiom,
    member7340901614391157822pace_b @ f @ ( qbs_mo6277074943135278010pace_b @ x @ ( monad_monadP_qbs_b @ y ) ) ).

% assms
thf(fact_1_qbs__return__morphism_H,axiom,
    ! [F: a > b,X: quasi_borel_a,Y: quasi_borel_b] :
      ( ( member_a_b @ F @ ( qbs_morphism_a_b @ X @ Y ) )
     => ( member7340901614391157822pace_b
        @ ^ [X2: a] : ( monad_qbs_return_b @ Y @ ( F @ X2 ) )
        @ ( qbs_mo6277074943135278010pace_b @ X @ ( monad_monadP_qbs_b @ Y ) ) ) ) ).

% qbs_return_morphism'
thf(fact_2_qbs__return__morphism_H,axiom,
    ! [F: a > probab4737552677800996672pace_b,X: quasi_borel_a,Y: quasi_3431323906171122406pace_b] :
      ( ( member7340901614391157822pace_b @ F @ ( qbs_mo6277074943135278010pace_b @ X @ Y ) )
     => ( member41169580844105599pace_b
        @ ^ [X2: a] : ( monad_5097244483053731721pace_b @ Y @ ( F @ X2 ) )
        @ ( qbs_mo7666231875222642555pace_b @ X @ ( monad_1549008831671149082pace_b @ Y ) ) ) ) ).

% qbs_return_morphism'
thf(fact_3_qbs__return__morphism_H,axiom,
    ! [F: probab4737552673497767871pace_a > b,X: quasi_3360289866124776421pace_a,Y: quasi_borel_b] :
      ( ( member5008716543664893436ce_a_b @ F @ ( qbs_mo4178970241922981112ce_a_b @ X @ Y ) )
     => ( member6667749562321684925pace_b
        @ ^ [X2: probab4737552673497767871pace_a] : ( monad_qbs_return_b @ Y @ ( F @ X2 ) )
        @ ( qbs_mo9092548148132419897pace_b @ X @ ( monad_monadP_qbs_b @ Y ) ) ) ) ).

% qbs_return_morphism'
thf(fact_4_qbs__return__morphism_H,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,X: quasi_3360289866124776421pace_a,Y: quasi_3431323906171122406pace_b] :
      ( ( member6667749562321684925pace_b @ F @ ( qbs_mo9092548148132419897pace_b @ X @ Y ) )
     => ( member2122011575714886910pace_b
        @ ^ [X2: probab4737552673497767871pace_a] : ( monad_5097244483053731721pace_b @ Y @ ( F @ X2 ) )
        @ ( qbs_mo2822951220955735290pace_b @ X @ ( monad_1549008831671149082pace_b @ Y ) ) ) ) ).

% qbs_return_morphism'
thf(fact_5_qbs__return__morphism_H,axiom,
    ! [F: b > b,X: quasi_borel_b,Y: quasi_borel_b] :
      ( ( member_b_b @ F @ ( qbs_morphism_b_b @ X @ Y ) )
     => ( member1568243296417166973pace_b
        @ ^ [X2: b] : ( monad_qbs_return_b @ Y @ ( F @ X2 ) )
        @ ( qbs_mo504416625161287161pace_b @ X @ ( monad_monadP_qbs_b @ Y ) ) ) ) ).

% qbs_return_morphism'
thf(fact_6_qbs__return__morphism_H,axiom,
    ! [F: a > a,X: quasi_borel_a,Y: quasi_borel_a] :
      ( ( member_a_a @ F @ ( qbs_morphism_a_a @ X @ Y ) )
     => ( member7269867574344811837pace_a
        @ ^ [X2: a] : ( monad_qbs_return_a @ Y @ ( F @ X2 ) )
        @ ( qbs_mo6277074938832049209pace_a @ X @ ( monad_monadP_qbs_a @ Y ) ) ) ) ).

% qbs_return_morphism'
thf(fact_7_qbs__return__morphism_H,axiom,
    ! [F: a > probab4737552673497767871pace_a,X: quasi_borel_a,Y: quasi_3360289866124776421pace_a] :
      ( ( member7269867574344811837pace_a @ F @ ( qbs_mo6277074938832049209pace_a @ X @ Y ) )
     => ( member2562354099133141246pace_a
        @ ^ [X2: a] : ( monad_5097244478750502920pace_a @ Y @ ( F @ X2 ) )
        @ ( qbs_mo7595197835176296570pace_a @ X @ ( monad_1549008827367920281pace_a @ Y ) ) ) ) ).

% qbs_return_morphism'
thf(fact_8_qbs__return__morphism_H,axiom,
    ! [F: b > probab4737552677800996672pace_b,X: quasi_borel_b,Y: quasi_3431323906171122406pace_b] :
      ( ( member1568243296417166973pace_b @ F @ ( qbs_mo504416625161287161pace_b @ X @ Y ) )
     => ( member6868725278929494462pace_b
        @ ^ [X2: b] : ( monad_5097244483053731721pace_b @ Y @ ( F @ X2 ) )
        @ ( qbs_mo5270415536453255610pace_b @ X @ ( monad_1549008831671149082pace_b @ Y ) ) ) ) ).

% qbs_return_morphism'
thf(fact_9_qbs__return__morphism_H,axiom,
    ! [F: a > probab8624551251471354625pace_b,X: quasi_borel_a,Y: quasi_5637586813637594663pace_b] :
      ( ( member41169580844105599pace_b @ F @ ( qbs_mo7666231875222642555pace_b @ X @ Y ) )
     => ( member2238741843251964480pace_b
        @ ^ [X2: a] : ( monad_2576622430688152394pace_b @ Y @ ( F @ X2 ) )
        @ ( qbs_mo6214013345488546492pace_b @ X @ ( monad_6019819981739679195pace_b @ Y ) ) ) ) ).

% qbs_return_morphism'
thf(fact_10_qbs__return__morphism_H,axiom,
    ! [F: b > a,X: quasi_borel_b,Y: quasi_borel_a] :
      ( ( member_b_a @ F @ ( qbs_morphism_b_a @ X @ Y ) )
     => ( member1497209256370820988pace_a
        @ ^ [X2: b] : ( monad_qbs_return_a @ Y @ ( F @ X2 ) )
        @ ( qbs_mo504416620858058360pace_a @ X @ ( monad_monadP_qbs_a @ Y ) ) ) ) ).

% qbs_return_morphism'
thf(fact_11_qbs__return__morphism,axiom,
    ! [X: quasi_3360289866124776421pace_a] : ( member4643196094003922557pace_a @ ( monad_5097244478750502920pace_a @ X ) @ ( qbs_mo2751917180909389305pace_a @ X @ ( monad_1549008827367920281pace_a @ X ) ) ) ).

% qbs_return_morphism
thf(fact_12_qbs__return__morphism,axiom,
    ! [X: quasi_5637586813637594663pace_b] : ( member5735377712513227005pace_b @ ( monad_2576622430688152394pace_b @ X ) @ ( qbs_mo7218912178804963705pace_b @ X @ ( monad_6019819981739679195pace_b @ X ) ) ) ).

% qbs_return_morphism
thf(fact_13_qbs__return__morphism,axiom,
    ! [X: quasi_3431323906171122406pace_b] : ( member1197888188833097661pace_b @ ( monad_5097244483053731721pace_b @ X ) @ ( qbs_mo1898827834073946041pace_b @ X @ ( monad_1549008831671149082pace_b @ X ) ) ) ).

% qbs_return_morphism
thf(fact_14_qbs__return__morphism,axiom,
    ! [X: quasi_borel_a] : ( member7269867574344811837pace_a @ ( monad_qbs_return_a @ X ) @ ( qbs_mo6277074938832049209pace_a @ X @ ( monad_monadP_qbs_a @ X ) ) ) ).

% qbs_return_morphism
thf(fact_15_qbs__return__morphism,axiom,
    ! [X: quasi_borel_b] : ( member1568243296417166973pace_b @ ( monad_qbs_return_b @ X ) @ ( qbs_mo504416625161287161pace_b @ X @ ( monad_monadP_qbs_b @ X ) ) ) ).

% qbs_return_morphism
thf(fact_16_qbs__morphism__ident_H,axiom,
    ! [X: quasi_borel_b] :
      ( member_b_b
      @ ^ [X2: b] : X2
      @ ( qbs_morphism_b_b @ X @ X ) ) ).

% qbs_morphism_ident'
thf(fact_17_qbs__morphism__ident_H,axiom,
    ! [X: quasi_borel_a] :
      ( member_a_a
      @ ^ [X2: a] : X2
      @ ( qbs_morphism_a_a @ X @ X ) ) ).

% qbs_morphism_ident'
thf(fact_18_monadP__qbs__Mx,axiom,
    ! [X: quasi_3360289866124776421pace_a] :
      ( ( qbs_Mx7393067164300094327pace_a @ ( monad_1549008827367920281pace_a @ X ) )
      = ( monad_2041073077907995374pace_a @ X ) ) ).

% monadP_qbs_Mx
thf(fact_19_monadP__qbs__Mx,axiom,
    ! [X: quasi_5637586813637594663pace_b] :
      ( ( qbs_Mx7979775613117285817pace_b @ ( monad_6019819981739679195pace_b @ X ) )
      = ( monad_2480142628005426736pace_b @ X ) ) ).

% monadP_qbs_Mx
thf(fact_20_monadP__qbs__Mx,axiom,
    ! [X: quasi_3431323906171122406pace_b] :
      ( ( qbs_Mx7464101204346440312pace_b @ ( monad_1549008831671149082pace_b @ X ) )
      = ( monad_2041073082211224175pace_b @ X ) ) ).

% monadP_qbs_Mx
thf(fact_21_monadP__qbs__Mx,axiom,
    ! [X: quasi_borel_a] :
      ( ( qbs_Mx4221877616140324662pace_a @ ( monad_monadP_qbs_a @ X ) )
      = ( monad_4223963853064302125_MPx_a @ X ) ) ).

% monadP_qbs_Mx
thf(fact_22_monadP__qbs__Mx,axiom,
    ! [X: quasi_borel_b] :
      ( ( qbs_Mx4221877620443553463pace_b @ ( monad_monadP_qbs_b @ X ) )
      = ( monad_4223963853064302126_MPx_b @ X ) ) ).

% monadP_qbs_Mx
thf(fact_23_monadP__qbs__space,axiom,
    ! [X: quasi_3360289866124776421pace_a] :
      ( ( qbs_sp8664130063403789110pace_a @ ( monad_1549008827367920281pace_a @ X ) )
      = ( monad_8082909349986334129pace_a @ X ) ) ).

% monadP_qbs_space
thf(fact_24_monadP__qbs__space,axiom,
    ! [X: quasi_5637586813637594663pace_b] :
      ( ( qbs_sp6026744849438692728pace_b @ ( monad_6019819981739679195pace_b @ X ) )
      = ( monad_8832862858680975603pace_b @ X ) ) ).

% monadP_qbs_space
thf(fact_25_monadP__qbs__space,axiom,
    ! [X: quasi_3431323906171122406pace_b] :
      ( ( qbs_sp8735164103450135095pace_b @ ( monad_1549008831671149082pace_b @ X ) )
      = ( monad_8082909354289562930pace_b @ X ) ) ).

% monadP_qbs_space
thf(fact_26_monadP__qbs__space,axiom,
    ! [X: quasi_borel_a] :
      ( ( qbs_sp9192884683601510133pace_a @ ( monad_monadP_qbs_a @ X ) )
      = ( monad_3932415646498543856s_Px_a @ X ) ) ).

% monadP_qbs_space
thf(fact_27_monadP__qbs__space,axiom,
    ! [X: quasi_borel_b] :
      ( ( qbs_sp9192884687904738934pace_b @ ( monad_monadP_qbs_b @ X ) )
      = ( monad_3932415646498543857s_Px_b @ X ) ) ).

% monadP_qbs_space
thf(fact_28_qbs__morphism__const,axiom,
    ! [Y2: probab4737552677800996672pace_b,Y: quasi_3431323906171122406pace_b,X: quasi_borel_a] :
      ( ( member6485455078948787817pace_b @ Y2 @ ( qbs_sp9192884687904738934pace_b @ Y ) )
     => ( member7340901614391157822pace_b
        @ ^ [Uu: a] : Y2
        @ ( qbs_mo6277074943135278010pace_b @ X @ Y ) ) ) ).

% qbs_morphism_const
thf(fact_29_qbs__morphism__const,axiom,
    ! [Y2: probab4737552677800996672pace_b,Y: quasi_3431323906171122406pace_b,X: quasi_3360289866124776421pace_a] :
      ( ( member6485455078948787817pace_b @ Y2 @ ( qbs_sp9192884687904738934pace_b @ Y ) )
     => ( member6667749562321684925pace_b
        @ ^ [Uu: probab4737552673497767871pace_a] : Y2
        @ ( qbs_mo9092548148132419897pace_b @ X @ Y ) ) ) ).

% qbs_morphism_const
thf(fact_30_qbs__morphism__const,axiom,
    ! [Y2: b,Y: quasi_borel_b,X: quasi_borel_a] :
      ( ( member_b @ Y2 @ ( qbs_space_b @ Y ) )
     => ( member_a_b
        @ ^ [Uu: a] : Y2
        @ ( qbs_morphism_a_b @ X @ Y ) ) ) ).

% qbs_morphism_const
thf(fact_31_qbs__morphism__const,axiom,
    ! [Y2: b,Y: quasi_borel_b,X: quasi_3360289866124776421pace_a] :
      ( ( member_b @ Y2 @ ( qbs_space_b @ Y ) )
     => ( member5008716543664893436ce_a_b
        @ ^ [Uu: probab4737552673497767871pace_a] : Y2
        @ ( qbs_mo4178970241922981112ce_a_b @ X @ Y ) ) ) ).

% qbs_morphism_const
thf(fact_32_qbs__morphism__const,axiom,
    ! [Y2: probab4737552677800996672pace_b,Y: quasi_3431323906171122406pace_b,X: quasi_borel_b] :
      ( ( member6485455078948787817pace_b @ Y2 @ ( qbs_sp9192884687904738934pace_b @ Y ) )
     => ( member1568243296417166973pace_b
        @ ^ [Uu: b] : Y2
        @ ( qbs_mo504416625161287161pace_b @ X @ Y ) ) ) ).

% qbs_morphism_const
thf(fact_33_qbs__morphism__const,axiom,
    ! [Y2: probab4737552673497767871pace_a,Y: quasi_3360289866124776421pace_a,X: quasi_borel_a] :
      ( ( member6485455074645559016pace_a @ Y2 @ ( qbs_sp9192884683601510133pace_a @ Y ) )
     => ( member7269867574344811837pace_a
        @ ^ [Uu: a] : Y2
        @ ( qbs_mo6277074938832049209pace_a @ X @ Y ) ) ) ).

% qbs_morphism_const
thf(fact_34_qbs__morphism__const,axiom,
    ! [Y2: probab8624551251471354625pace_b,Y: quasi_5637586813637594663pace_b,X: quasi_borel_a] :
      ( ( member7462078926031725098pace_b @ Y2 @ ( qbs_sp8735164103450135095pace_b @ Y ) )
     => ( member41169580844105599pace_b
        @ ^ [Uu: a] : Y2
        @ ( qbs_mo7666231875222642555pace_b @ X @ Y ) ) ) ).

% qbs_morphism_const
thf(fact_35_qbs__morphism__const,axiom,
    ! [Y2: b,Y: quasi_borel_b,X: quasi_borel_b] :
      ( ( member_b @ Y2 @ ( qbs_space_b @ Y ) )
     => ( member_b_b
        @ ^ [Uu: b] : Y2
        @ ( qbs_morphism_b_b @ X @ Y ) ) ) ).

% qbs_morphism_const
thf(fact_36_qbs__morphism__const,axiom,
    ! [Y2: a,Y: quasi_borel_a,X: quasi_borel_b] :
      ( ( member_a @ Y2 @ ( qbs_space_a @ Y ) )
     => ( member_b_a
        @ ^ [Uu: b] : Y2
        @ ( qbs_morphism_b_a @ X @ Y ) ) ) ).

% qbs_morphism_const
thf(fact_37_qbs__morphism__const,axiom,
    ! [Y2: a,Y: quasi_borel_a,X: quasi_borel_a] :
      ( ( member_a @ Y2 @ ( qbs_space_a @ Y ) )
     => ( member_a_a
        @ ^ [Uu: a] : Y2
        @ ( qbs_morphism_a_a @ X @ Y ) ) ) ).

% qbs_morphism_const
thf(fact_38_qbs__morphism__ident,axiom,
    ! [X: quasi_2250266780261042646pace_b] : ( member4572553558456976002pace_b @ id_b_P1746019500644212789pace_b @ ( qbs_mo8448350875971007814pace_b @ X @ X ) ) ).

% qbs_morphism_ident
thf(fact_39_qbs__morphism__ident,axiom,
    ! [X: quasi_3272867757783880152pace_b] : ( member3715463284693178246pace_b @ id_a_P2005203185063471415pace_b @ ( qbs_mo3679909306002000714pace_b @ X @ X ) ) ).

% qbs_morphism_ident
thf(fact_40_qbs__morphism__ident,axiom,
    ! [X: quasi_5677484998582642455pace_b] : ( member7295092402511476612pace_b @ id_a_P7518677818618203638pace_b @ ( qbs_mo4292957782823123656pace_b @ X @ X ) ) ).

% qbs_morphism_ident
thf(fact_41_qbs__morphism__ident,axiom,
    ! [X: quasi_8198669516871678102pace_a] : ( member7366824048182198274pace_a @ id_a_P7447643778571857653pace_a @ ( qbs_mo1772470870158463686pace_a @ X @ X ) ) ).

% qbs_morphism_ident
thf(fact_42_qbs__morphism__ident,axiom,
    ! [X: quasi_borel_a_b] : ( member_a_b_a_b @ id_a_b @ ( qbs_morphism_a_b_a_b @ X @ X ) ) ).

% qbs_morphism_ident
thf(fact_43_qbs__morphism__ident,axiom,
    ! [X: quasi_borel_b] : ( member_b_b @ id_b @ ( qbs_morphism_b_b @ X @ X ) ) ).

% qbs_morphism_ident
thf(fact_44_qbs__morphism__ident,axiom,
    ! [X: quasi_borel_a] : ( member_a_a @ id_a @ ( qbs_morphism_a_a @ X @ X ) ) ).

% qbs_morphism_ident
thf(fact_45_qbs__morphism__comp,axiom,
    ! [F: a > a,X: quasi_borel_a,Y: quasi_borel_a,G: a > b,Z: quasi_borel_b] :
      ( ( member_a_a @ F @ ( qbs_morphism_a_a @ X @ Y ) )
     => ( ( member_a_b @ G @ ( qbs_morphism_a_b @ Y @ Z ) )
       => ( member_a_b @ ( comp_a_b_a @ G @ F ) @ ( qbs_morphism_a_b @ X @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_46_qbs__morphism__comp,axiom,
    ! [F: a > b,X: quasi_borel_a,Y: quasi_borel_b,G: b > b,Z: quasi_borel_b] :
      ( ( member_a_b @ F @ ( qbs_morphism_a_b @ X @ Y ) )
     => ( ( member_b_b @ G @ ( qbs_morphism_b_b @ Y @ Z ) )
       => ( member_a_b @ ( comp_b_b_a @ G @ F ) @ ( qbs_morphism_a_b @ X @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_47_qbs__morphism__comp,axiom,
    ! [F: a > a,X: quasi_borel_a,Y: quasi_borel_a,G: a > probab4737552677800996672pace_b,Z: quasi_3431323906171122406pace_b] :
      ( ( member_a_a @ F @ ( qbs_morphism_a_a @ X @ Y ) )
     => ( ( member7340901614391157822pace_b @ G @ ( qbs_mo6277074943135278010pace_b @ Y @ Z ) )
       => ( member7340901614391157822pace_b @ ( comp_a6704972666784936217ce_b_a @ G @ F ) @ ( qbs_mo6277074943135278010pace_b @ X @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_48_qbs__morphism__comp,axiom,
    ! [F: b > a,X: quasi_borel_b,Y: quasi_borel_a,G: a > probab4737552677800996672pace_b,Z: quasi_3431323906171122406pace_b] :
      ( ( member_b_a @ F @ ( qbs_morphism_b_a @ X @ Y ) )
     => ( ( member7340901614391157822pace_b @ G @ ( qbs_mo6277074943135278010pace_b @ Y @ Z ) )
       => ( member1568243296417166973pace_b @ ( comp_a6704972666784936218ce_b_b @ G @ F ) @ ( qbs_mo504416625161287161pace_b @ X @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_49_qbs__morphism__comp,axiom,
    ! [F: b > b,X: quasi_borel_b,Y: quasi_borel_b,G: b > probab4737552677800996672pace_b,Z: quasi_3431323906171122406pace_b] :
      ( ( member_b_b @ F @ ( qbs_morphism_b_b @ X @ Y ) )
     => ( ( member1568243296417166973pace_b @ G @ ( qbs_mo504416625161287161pace_b @ Y @ Z ) )
       => ( member1568243296417166973pace_b @ ( comp_b6576235760933465243ce_b_b @ G @ F ) @ ( qbs_mo504416625161287161pace_b @ X @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_50_qbs__morphism__comp,axiom,
    ! [F: a > a,X: quasi_borel_a,Y: quasi_borel_a,G: a > probab4737552673497767871pace_a,Z: quasi_3360289866124776421pace_a] :
      ( ( member_a_a @ F @ ( qbs_morphism_a_a @ X @ Y ) )
     => ( ( member7269867574344811837pace_a @ G @ ( qbs_mo6277074938832049209pace_a @ Y @ Z ) )
       => ( member7269867574344811837pace_a @ ( comp_a7340621667389922906ce_a_a @ G @ F ) @ ( qbs_mo6277074938832049209pace_a @ X @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_51_qbs__morphism__comp,axiom,
    ! [F: probab4737552673497767871pace_a > a,X: quasi_3360289866124776421pace_a,Y: quasi_borel_a,G: a > b,Z: quasi_borel_b] :
      ( ( member5008716539361664635ce_a_a @ F @ ( qbs_mo4178970241922981111ce_a_a @ X @ Y ) )
     => ( ( member_a_b @ G @ ( qbs_morphism_a_b @ Y @ Z ) )
       => ( member5008716543664893436ce_a_b @ ( comp_a3666068046325000155pace_a @ G @ F ) @ ( qbs_mo4178970241922981112ce_a_b @ X @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_52_qbs__morphism__comp,axiom,
    ! [F: a > probab4737552677800996672pace_b,X: quasi_borel_a,Y: quasi_3431323906171122406pace_b,G: probab4737552677800996672pace_b > b,Z: quasi_borel_b] :
      ( ( member7340901614391157822pace_b @ F @ ( qbs_mo6277074943135278010pace_b @ X @ Y ) )
     => ( ( member4373067543059906747ce_b_b @ G @ ( qbs_mo3543321241317994423ce_b_b @ Y @ Z ) )
       => ( member_a_b @ ( comp_P6427446343783718492_b_b_a @ G @ F ) @ ( qbs_morphism_a_b @ X @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_53_qbs__morphism__comp,axiom,
    ! [F: probab4737552673497767871pace_a > b,X: quasi_3360289866124776421pace_a,Y: quasi_borel_b,G: b > b,Z: quasi_borel_b] :
      ( ( member5008716543664893436ce_a_b @ F @ ( qbs_mo4178970241922981112ce_a_b @ X @ Y ) )
     => ( ( member_b_b @ G @ ( qbs_morphism_b_b @ Y @ Z ) )
       => ( member5008716543664893436ce_a_b @ ( comp_b3537331140473529180pace_a @ G @ F ) @ ( qbs_mo4178970241922981112ce_a_b @ X @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_54_qbs__morphism__comp,axiom,
    ! [F: a > probab4737552673497767871pace_a,X: quasi_borel_a,Y: quasi_3360289866124776421pace_a,G: probab4737552673497767871pace_a > b,Z: quasi_borel_b] :
      ( ( member7269867574344811837pace_a @ F @ ( qbs_mo6277074938832049209pace_a @ X @ Y ) )
     => ( ( member5008716543664893436ce_a_b @ G @ ( qbs_mo4178970241922981112ce_a_b @ Y @ Z ) )
       => ( member_a_b @ ( comp_P9206150651643741019_a_b_a @ G @ F ) @ ( qbs_morphism_a_b @ X @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_55_qbs__morphismE_I2_J,axiom,
    ! [F: a > b,X: quasi_borel_a,Y: quasi_borel_b,X3: a] :
      ( ( member_a_b @ F @ ( qbs_morphism_a_b @ X @ Y ) )
     => ( ( member_a @ X3 @ ( qbs_space_a @ X ) )
       => ( member_b @ ( F @ X3 ) @ ( qbs_space_b @ Y ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_56_qbs__morphismE_I2_J,axiom,
    ! [F: a > probab4737552677800996672pace_b,X: quasi_borel_a,Y: quasi_3431323906171122406pace_b,X3: a] :
      ( ( member7340901614391157822pace_b @ F @ ( qbs_mo6277074943135278010pace_b @ X @ Y ) )
     => ( ( member_a @ X3 @ ( qbs_space_a @ X ) )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( qbs_sp9192884687904738934pace_b @ Y ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_57_qbs__morphismE_I2_J,axiom,
    ! [F: probab4737552673497767871pace_a > b,X: quasi_3360289866124776421pace_a,Y: quasi_borel_b,X3: probab4737552673497767871pace_a] :
      ( ( member5008716543664893436ce_a_b @ F @ ( qbs_mo4178970241922981112ce_a_b @ X @ Y ) )
     => ( ( member6485455074645559016pace_a @ X3 @ ( qbs_sp9192884683601510133pace_a @ X ) )
       => ( member_b @ ( F @ X3 ) @ ( qbs_space_b @ Y ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_58_qbs__morphismE_I2_J,axiom,
    ! [F: b > probab4737552677800996672pace_b,X: quasi_borel_b,Y: quasi_3431323906171122406pace_b,X3: b] :
      ( ( member1568243296417166973pace_b @ F @ ( qbs_mo504416625161287161pace_b @ X @ Y ) )
     => ( ( member_b @ X3 @ ( qbs_space_b @ X ) )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( qbs_sp9192884687904738934pace_b @ Y ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_59_qbs__morphismE_I2_J,axiom,
    ! [F: a > probab4737552673497767871pace_a,X: quasi_borel_a,Y: quasi_3360289866124776421pace_a,X3: a] :
      ( ( member7269867574344811837pace_a @ F @ ( qbs_mo6277074938832049209pace_a @ X @ Y ) )
     => ( ( member_a @ X3 @ ( qbs_space_a @ X ) )
       => ( member6485455074645559016pace_a @ ( F @ X3 ) @ ( qbs_sp9192884683601510133pace_a @ Y ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_60_qbs__morphismE_I2_J,axiom,
    ! [F: probab4737552677800996672pace_b > probab4737552677800996672pace_b,X: quasi_3431323906171122406pace_b,Y: quasi_3431323906171122406pace_b,X3: probab4737552677800996672pace_b] :
      ( ( member3240531344000085116pace_b @ F @ ( qbs_mo5665329929810820088pace_b @ X @ Y ) )
     => ( ( member6485455078948787817pace_b @ X3 @ ( qbs_sp9192884687904738934pace_b @ X ) )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( qbs_sp9192884687904738934pace_b @ Y ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_61_qbs__morphismE_I2_J,axiom,
    ! [F: probab4737552677800996672pace_b > probab4737552673497767871pace_a,X: quasi_3431323906171122406pace_b,Y: quasi_3360289866124776421pace_a,X3: probab4737552677800996672pace_b] :
      ( ( member3169497303953739131pace_a @ F @ ( qbs_mo5665329925507591287pace_a @ X @ Y ) )
     => ( ( member6485455078948787817pace_b @ X3 @ ( qbs_sp9192884687904738934pace_b @ X ) )
       => ( member6485455074645559016pace_a @ ( F @ X3 ) @ ( qbs_sp9192884683601510133pace_a @ Y ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_62_qbs__morphismE_I2_J,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552673497767871pace_a,X: quasi_3360289866124776421pace_a,Y: quasi_3360289866124776421pace_a,X3: probab4737552673497767871pace_a] :
      ( ( member6596715522275338940pace_a @ F @ ( qbs_mo9092548143829191096pace_a @ X @ Y ) )
     => ( ( member6485455074645559016pace_a @ X3 @ ( qbs_sp9192884683601510133pace_a @ X ) )
       => ( member6485455074645559016pace_a @ ( F @ X3 ) @ ( qbs_sp9192884683601510133pace_a @ Y ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_63_qbs__morphismE_I2_J,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,X: quasi_3360289866124776421pace_a,Y: quasi_3431323906171122406pace_b,X3: probab4737552673497767871pace_a] :
      ( ( member6667749562321684925pace_b @ F @ ( qbs_mo9092548148132419897pace_b @ X @ Y ) )
     => ( ( member6485455074645559016pace_a @ X3 @ ( qbs_sp9192884683601510133pace_a @ X ) )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( qbs_sp9192884687904738934pace_b @ Y ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_64_qbs__morphismE_I2_J,axiom,
    ! [F: a > probab8624551251471354625pace_b,X: quasi_borel_a,Y: quasi_5637586813637594663pace_b,X3: a] :
      ( ( member41169580844105599pace_b @ F @ ( qbs_mo7666231875222642555pace_b @ X @ Y ) )
     => ( ( member_a @ X3 @ ( qbs_space_a @ X ) )
       => ( member7462078926031725098pace_b @ ( F @ X3 ) @ ( qbs_sp8735164103450135095pace_b @ Y ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_65_qbs__morphism__cong,axiom,
    ! [X: quasi_borel_a,F: a > b,G: a > b,Y: quasi_borel_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ ( qbs_space_a @ X ) )
         => ( ( F @ X4 )
            = ( G @ X4 ) ) )
     => ( ( member_a_b @ F @ ( qbs_morphism_a_b @ X @ Y ) )
       => ( member_a_b @ G @ ( qbs_morphism_a_b @ X @ Y ) ) ) ) ).

% qbs_morphism_cong
thf(fact_66_qbs__morphism__cong,axiom,
    ! [X: quasi_borel_a,F: a > probab4737552677800996672pace_b,G: a > probab4737552677800996672pace_b,Y: quasi_3431323906171122406pace_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ ( qbs_space_a @ X ) )
         => ( ( F @ X4 )
            = ( G @ X4 ) ) )
     => ( ( member7340901614391157822pace_b @ F @ ( qbs_mo6277074943135278010pace_b @ X @ Y ) )
       => ( member7340901614391157822pace_b @ G @ ( qbs_mo6277074943135278010pace_b @ X @ Y ) ) ) ) ).

% qbs_morphism_cong
thf(fact_67_qbs__morphism__cong,axiom,
    ! [X: quasi_3360289866124776421pace_a,F: probab4737552673497767871pace_a > b,G: probab4737552673497767871pace_a > b,Y: quasi_borel_b] :
      ( ! [X4: probab4737552673497767871pace_a] :
          ( ( member6485455074645559016pace_a @ X4 @ ( qbs_sp9192884683601510133pace_a @ X ) )
         => ( ( F @ X4 )
            = ( G @ X4 ) ) )
     => ( ( member5008716543664893436ce_a_b @ F @ ( qbs_mo4178970241922981112ce_a_b @ X @ Y ) )
       => ( member5008716543664893436ce_a_b @ G @ ( qbs_mo4178970241922981112ce_a_b @ X @ Y ) ) ) ) ).

% qbs_morphism_cong
thf(fact_68_qbs__morphism__cong,axiom,
    ! [X: quasi_borel_b,F: b > probab4737552677800996672pace_b,G: b > probab4737552677800996672pace_b,Y: quasi_3431323906171122406pace_b] :
      ( ! [X4: b] :
          ( ( member_b @ X4 @ ( qbs_space_b @ X ) )
         => ( ( F @ X4 )
            = ( G @ X4 ) ) )
     => ( ( member1568243296417166973pace_b @ F @ ( qbs_mo504416625161287161pace_b @ X @ Y ) )
       => ( member1568243296417166973pace_b @ G @ ( qbs_mo504416625161287161pace_b @ X @ Y ) ) ) ) ).

% qbs_morphism_cong
thf(fact_69_qbs__morphism__cong,axiom,
    ! [X: quasi_borel_a,F: a > probab4737552673497767871pace_a,G: a > probab4737552673497767871pace_a,Y: quasi_3360289866124776421pace_a] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ ( qbs_space_a @ X ) )
         => ( ( F @ X4 )
            = ( G @ X4 ) ) )
     => ( ( member7269867574344811837pace_a @ F @ ( qbs_mo6277074938832049209pace_a @ X @ Y ) )
       => ( member7269867574344811837pace_a @ G @ ( qbs_mo6277074938832049209pace_a @ X @ Y ) ) ) ) ).

% qbs_morphism_cong
thf(fact_70_qbs__morphism__cong,axiom,
    ! [X: quasi_3360289866124776421pace_a,F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,G: probab4737552673497767871pace_a > probab4737552677800996672pace_b,Y: quasi_3431323906171122406pace_b] :
      ( ! [X4: probab4737552673497767871pace_a] :
          ( ( member6485455074645559016pace_a @ X4 @ ( qbs_sp9192884683601510133pace_a @ X ) )
         => ( ( F @ X4 )
            = ( G @ X4 ) ) )
     => ( ( member6667749562321684925pace_b @ F @ ( qbs_mo9092548148132419897pace_b @ X @ Y ) )
       => ( member6667749562321684925pace_b @ G @ ( qbs_mo9092548148132419897pace_b @ X @ Y ) ) ) ) ).

% qbs_morphism_cong
thf(fact_71_qbs__morphism__cong,axiom,
    ! [X: quasi_borel_a,F: a > probab8624551251471354625pace_b,G: a > probab8624551251471354625pace_b,Y: quasi_5637586813637594663pace_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ ( qbs_space_a @ X ) )
         => ( ( F @ X4 )
            = ( G @ X4 ) ) )
     => ( ( member41169580844105599pace_b @ F @ ( qbs_mo7666231875222642555pace_b @ X @ Y ) )
       => ( member41169580844105599pace_b @ G @ ( qbs_mo7666231875222642555pace_b @ X @ Y ) ) ) ) ).

% qbs_morphism_cong
thf(fact_72_qbs__morphism__cong,axiom,
    ! [X: quasi_borel_b,F: b > b,G: b > b,Y: quasi_borel_b] :
      ( ! [X4: b] :
          ( ( member_b @ X4 @ ( qbs_space_b @ X ) )
         => ( ( F @ X4 )
            = ( G @ X4 ) ) )
     => ( ( member_b_b @ F @ ( qbs_morphism_b_b @ X @ Y ) )
       => ( member_b_b @ G @ ( qbs_morphism_b_b @ X @ Y ) ) ) ) ).

% qbs_morphism_cong
thf(fact_73_qbs__morphism__cong,axiom,
    ! [X: quasi_borel_b,F: b > a,G: b > a,Y: quasi_borel_a] :
      ( ! [X4: b] :
          ( ( member_b @ X4 @ ( qbs_space_b @ X ) )
         => ( ( F @ X4 )
            = ( G @ X4 ) ) )
     => ( ( member_b_a @ F @ ( qbs_morphism_b_a @ X @ Y ) )
       => ( member_b_a @ G @ ( qbs_morphism_b_a @ X @ Y ) ) ) ) ).

% qbs_morphism_cong
thf(fact_74_qbs__morphism__cong,axiom,
    ! [X: quasi_borel_a,F: a > a,G: a > a,Y: quasi_borel_a] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ ( qbs_space_a @ X ) )
         => ( ( F @ X4 )
            = ( G @ X4 ) ) )
     => ( ( member_a_a @ F @ ( qbs_morphism_a_a @ X @ Y ) )
       => ( member_a_a @ G @ ( qbs_morphism_a_a @ X @ Y ) ) ) ) ).

% qbs_morphism_cong
thf(fact_75_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > probab4737552677800996672pace_b,X: quasi_3431323906171122406pace_b,R: real] :
      ( ( member5892728515905534708pace_b @ Alpha @ ( qbs_Mx4221877620443553463pace_b @ X ) )
     => ( member6485455078948787817pace_b @ ( Alpha @ R ) @ ( qbs_sp9192884687904738934pace_b @ X ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_76_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > probab4737552673497767871pace_a,X: quasi_3360289866124776421pace_a,R: real] :
      ( ( member5821694475859188723pace_a @ Alpha @ ( qbs_Mx4221877616140324662pace_a @ X ) )
     => ( member6485455074645559016pace_a @ ( Alpha @ R ) @ ( qbs_sp9192884683601510133pace_a @ X ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_77_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > a > b,X: quasi_borel_a_b,R: real] :
      ( ( member_real_a_b @ Alpha @ ( qbs_Mx_a_b @ X ) )
     => ( member_a_b @ ( Alpha @ R ) @ ( qbs_space_a_b @ X ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_78_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > a > probab4737552677800996672pace_b,X: quasi_5677484998582642455pace_b,R: real] :
      ( ( member6235990094145287049pace_b @ Alpha @ ( qbs_Mx4794387083398668400pace_b @ X ) )
     => ( member7340901614391157822pace_b @ ( Alpha @ R ) @ ( qbs_sp4261357827969944817pace_b @ X ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_79_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > probab4737552673497767871pace_a > b,X: quasi_1232139159318032853ce_a_b,R: real] :
      ( ( member1790644254880677447ce_a_b @ Alpha @ ( qbs_Mx2462202012672404014ce_a_b @ X ) )
     => ( member5008716543664893436ce_a_b @ ( Alpha @ R ) @ ( qbs_sp1929172757243680431ce_a_b @ X ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_80_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > b > probab4737552677800996672pace_b,X: quasi_2250266780261042646pace_b,R: real] :
      ( ( member2808771875823687240pace_b @ Alpha @ ( qbs_Mx8245100802279453359pace_b @ X ) )
     => ( member1568243296417166973pace_b @ ( Alpha @ R ) @ ( qbs_sp7712071546850729776pace_b @ X ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_81_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > a > probab4737552673497767871pace_a,X: quasi_8198669516871678102pace_a,R: real] :
      ( ( member8757174612434322696pace_a @ Alpha @ ( qbs_Mx4723353043352322415pace_a @ X ) )
     => ( member7269867574344811837pace_a @ ( Alpha @ R ) @ ( qbs_sp4190323787923598832pace_a @ X ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_82_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > probab4737552673497767871pace_a > probab4737552677800996672pace_b,X: quasi_5025768402973351190pace_b,R: real] :
      ( ( member793202962283530632pace_b @ Alpha @ ( qbs_Mx3972598340161283567pace_b @ X ) )
     => ( member6667749562321684925pace_b @ ( Alpha @ R ) @ ( qbs_sp6092703205896766064pace_b @ X ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_83_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > a > probab8624551251471354625pace_b,X: quasi_3272867757783880152pace_b,R: real] :
      ( ( member8263674353948835402pace_b @ Alpha @ ( qbs_Mx6569390395538480049pace_b @ X ) )
     => ( member41169580844105599pace_b @ ( Alpha @ R ) @ ( qbs_sp8689495261273962546pace_b @ X ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_84_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha: real > b,X: quasi_borel_b,R: real] :
      ( ( member_real_b @ Alpha @ ( qbs_Mx_b @ X ) )
     => ( member_b @ ( Alpha @ R ) @ ( qbs_space_b @ X ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_85_qbs__morphismE_I3_J,axiom,
    ! [F: a > b,X: quasi_borel_a,Y: quasi_borel_b,Alpha: real > a] :
      ( ( member_a_b @ F @ ( qbs_morphism_a_b @ X @ Y ) )
     => ( ( member_real_a @ Alpha @ ( qbs_Mx_a @ X ) )
       => ( member_real_b @ ( comp_a_b_real @ F @ Alpha ) @ ( qbs_Mx_b @ Y ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_86_qbs__morphismE_I3_J,axiom,
    ! [F: a > probab4737552677800996672pace_b,X: quasi_borel_a,Y: quasi_3431323906171122406pace_b,Alpha: real > a] :
      ( ( member7340901614391157822pace_b @ F @ ( qbs_mo6277074943135278010pace_b @ X @ Y ) )
     => ( ( member_real_a @ Alpha @ ( qbs_Mx_a @ X ) )
       => ( member5892728515905534708pace_b @ ( comp_a6868616473110226257b_real @ F @ Alpha ) @ ( qbs_Mx4221877620443553463pace_b @ Y ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_87_qbs__morphismE_I3_J,axiom,
    ! [F: probab4737552673497767871pace_a > b,X: quasi_3360289866124776421pace_a,Y: quasi_borel_b,Alpha: real > probab4737552673497767871pace_a] :
      ( ( member5008716543664893436ce_a_b @ F @ ( qbs_mo4178970241922981112ce_a_b @ X @ Y ) )
     => ( ( member5821694475859188723pace_a @ Alpha @ ( qbs_Mx4221877616140324662pace_a @ X ) )
       => ( member_real_b @ ( comp_P3348619169354409871b_real @ F @ Alpha ) @ ( qbs_Mx_b @ Y ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_88_qbs__morphismE_I3_J,axiom,
    ! [F: b > probab4737552677800996672pace_b,X: quasi_borel_b,Y: quasi_3431323906171122406pace_b,Alpha: real > b] :
      ( ( member1568243296417166973pace_b @ F @ ( qbs_mo504416625161287161pace_b @ X @ Y ) )
     => ( ( member_real_b @ Alpha @ ( qbs_Mx_b @ X ) )
       => ( member5892728515905534708pace_b @ ( comp_b4925389053965159440b_real @ F @ Alpha ) @ ( qbs_Mx4221877620443553463pace_b @ Y ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_89_qbs__morphismE_I3_J,axiom,
    ! [F: a > probab4737552673497767871pace_a,X: quasi_borel_a,Y: quasi_3360289866124776421pace_a,Alpha: real > a] :
      ( ( member7269867574344811837pace_a @ F @ ( qbs_mo6277074938832049209pace_a @ X @ Y ) )
     => ( ( member_real_a @ Alpha @ ( qbs_Mx_a @ X ) )
       => ( member5821694475859188723pace_a @ ( comp_a423948744115472976a_real @ F @ Alpha ) @ ( qbs_Mx4221877616140324662pace_a @ Y ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_90_qbs__morphismE_I3_J,axiom,
    ! [F: probab4737552677800996672pace_b > probab4737552677800996672pace_b,X: quasi_3431323906171122406pace_b,Y: quasi_3431323906171122406pace_b,Alpha: real > probab4737552677800996672pace_b] :
      ( ( member3240531344000085116pace_b @ F @ ( qbs_mo5665329929810820088pace_b @ X @ Y ) )
     => ( ( member5892728515905534708pace_b @ Alpha @ ( qbs_Mx4221877620443553463pace_b @ X ) )
       => ( member5892728515905534708pace_b @ ( comp_P902384264663180943b_real @ F @ Alpha ) @ ( qbs_Mx4221877620443553463pace_b @ Y ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_91_qbs__morphismE_I3_J,axiom,
    ! [F: probab4737552677800996672pace_b > probab4737552673497767871pace_a,X: quasi_3431323906171122406pace_b,Y: quasi_3360289866124776421pace_a,Alpha: real > probab4737552677800996672pace_b] :
      ( ( member3169497303953739131pace_a @ F @ ( qbs_mo5665329925507591287pace_a @ X @ Y ) )
     => ( ( member5892728515905534708pace_b @ Alpha @ ( qbs_Mx4221877620443553463pace_b @ X ) )
       => ( member5821694475859188723pace_a @ ( comp_P3681088572523203470a_real @ F @ Alpha ) @ ( qbs_Mx4221877616140324662pace_a @ Y ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_92_qbs__morphismE_I3_J,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552673497767871pace_a,X: quasi_3360289866124776421pace_a,Y: quasi_3360289866124776421pace_a,Alpha: real > probab4737552673497767871pace_a] :
      ( ( member6596715522275338940pace_a @ F @ ( qbs_mo9092548143829191096pace_a @ X @ Y ) )
     => ( ( member5821694475859188723pace_a @ Alpha @ ( qbs_Mx4221877616140324662pace_a @ X ) )
       => ( member5821694475859188723pace_a @ ( comp_P2386351730793452623a_real @ F @ Alpha ) @ ( qbs_Mx4221877616140324662pace_a @ Y ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_93_qbs__morphismE_I3_J,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,X: quasi_3360289866124776421pace_a,Y: quasi_3431323906171122406pace_b,Alpha: real > probab4737552673497767871pace_a] :
      ( ( member6667749562321684925pace_b @ F @ ( qbs_mo9092548148132419897pace_b @ X @ Y ) )
     => ( ( member5821694475859188723pace_a @ Alpha @ ( qbs_Mx4221877616140324662pace_a @ X ) )
       => ( member5892728515905534708pace_b @ ( comp_P8831019459788205904b_real @ F @ Alpha ) @ ( qbs_Mx4221877620443553463pace_b @ Y ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_94_qbs__morphismE_I3_J,axiom,
    ! [F: a > probab8624551251471354625pace_b,X: quasi_borel_a,Y: quasi_5637586813637594663pace_b,Alpha: real > a] :
      ( ( member41169580844105599pace_b @ F @ ( qbs_mo7666231875222642555pace_b @ X @ Y ) )
     => ( ( member_real_a @ Alpha @ ( qbs_Mx_a @ X ) )
       => ( member4880162955186484789pace_b @ ( comp_a6393136188637473938b_real @ F @ Alpha ) @ ( qbs_Mx7464101204346440312pace_b @ Y ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_95_qbs__eqI,axiom,
    ! [X: quasi_5677484998582642455pace_b,Y: quasi_5677484998582642455pace_b] :
      ( ( ( qbs_Mx4794387083398668400pace_b @ X )
        = ( qbs_Mx4794387083398668400pace_b @ Y ) )
     => ( X = Y ) ) ).

% qbs_eqI
thf(fact_96_qbs__eqI,axiom,
    ! [X: quasi_8198669516871678102pace_a,Y: quasi_8198669516871678102pace_a] :
      ( ( ( qbs_Mx4723353043352322415pace_a @ X )
        = ( qbs_Mx4723353043352322415pace_a @ Y ) )
     => ( X = Y ) ) ).

% qbs_eqI
thf(fact_97_qbs__eqI,axiom,
    ! [X: quasi_borel_a_b,Y: quasi_borel_a_b] :
      ( ( ( qbs_Mx_a_b @ X )
        = ( qbs_Mx_a_b @ Y ) )
     => ( X = Y ) ) ).

% qbs_eqI
thf(fact_98_qbs__eqI,axiom,
    ! [X: quasi_borel_b,Y: quasi_borel_b] :
      ( ( ( qbs_Mx_b @ X )
        = ( qbs_Mx_b @ Y ) )
     => ( X = Y ) ) ).

% qbs_eqI
thf(fact_99_qbs__eqI,axiom,
    ! [X: quasi_borel_a,Y: quasi_borel_a] :
      ( ( ( qbs_Mx_a @ X )
        = ( qbs_Mx_a @ Y ) )
     => ( X = Y ) ) ).

% qbs_eqI
thf(fact_100_qbs__eqI,axiom,
    ! [X: quasi_3431323906171122406pace_b,Y: quasi_3431323906171122406pace_b] :
      ( ( ( qbs_Mx4221877620443553463pace_b @ X )
        = ( qbs_Mx4221877620443553463pace_b @ Y ) )
     => ( X = Y ) ) ).

% qbs_eqI
thf(fact_101_qbs__eqI,axiom,
    ! [X: quasi_3360289866124776421pace_a,Y: quasi_3360289866124776421pace_a] :
      ( ( ( qbs_Mx4221877616140324662pace_a @ X )
        = ( qbs_Mx4221877616140324662pace_a @ Y ) )
     => ( X = Y ) ) ).

% qbs_eqI
thf(fact_102_qbs__morphismI,axiom,
    ! [X: quasi_borel_a,F: a > b,Y: quasi_borel_b] :
      ( ! [Alpha2: real > a] :
          ( ( member_real_a @ Alpha2 @ ( qbs_Mx_a @ X ) )
         => ( member_real_b @ ( comp_a_b_real @ F @ Alpha2 ) @ ( qbs_Mx_b @ Y ) ) )
     => ( member_a_b @ F @ ( qbs_morphism_a_b @ X @ Y ) ) ) ).

% qbs_morphismI
thf(fact_103_qbs__morphismI,axiom,
    ! [X: quasi_borel_a,F: a > probab4737552677800996672pace_b,Y: quasi_3431323906171122406pace_b] :
      ( ! [Alpha2: real > a] :
          ( ( member_real_a @ Alpha2 @ ( qbs_Mx_a @ X ) )
         => ( member5892728515905534708pace_b @ ( comp_a6868616473110226257b_real @ F @ Alpha2 ) @ ( qbs_Mx4221877620443553463pace_b @ Y ) ) )
     => ( member7340901614391157822pace_b @ F @ ( qbs_mo6277074943135278010pace_b @ X @ Y ) ) ) ).

% qbs_morphismI
thf(fact_104_qbs__morphismI,axiom,
    ! [X: quasi_3360289866124776421pace_a,F: probab4737552673497767871pace_a > b,Y: quasi_borel_b] :
      ( ! [Alpha2: real > probab4737552673497767871pace_a] :
          ( ( member5821694475859188723pace_a @ Alpha2 @ ( qbs_Mx4221877616140324662pace_a @ X ) )
         => ( member_real_b @ ( comp_P3348619169354409871b_real @ F @ Alpha2 ) @ ( qbs_Mx_b @ Y ) ) )
     => ( member5008716543664893436ce_a_b @ F @ ( qbs_mo4178970241922981112ce_a_b @ X @ Y ) ) ) ).

% qbs_morphismI
thf(fact_105_qbs__morphismI,axiom,
    ! [X: quasi_borel_b,F: b > probab4737552677800996672pace_b,Y: quasi_3431323906171122406pace_b] :
      ( ! [Alpha2: real > b] :
          ( ( member_real_b @ Alpha2 @ ( qbs_Mx_b @ X ) )
         => ( member5892728515905534708pace_b @ ( comp_b4925389053965159440b_real @ F @ Alpha2 ) @ ( qbs_Mx4221877620443553463pace_b @ Y ) ) )
     => ( member1568243296417166973pace_b @ F @ ( qbs_mo504416625161287161pace_b @ X @ Y ) ) ) ).

% qbs_morphismI
thf(fact_106_qbs__morphismI,axiom,
    ! [X: quasi_borel_a,F: a > probab4737552673497767871pace_a,Y: quasi_3360289866124776421pace_a] :
      ( ! [Alpha2: real > a] :
          ( ( member_real_a @ Alpha2 @ ( qbs_Mx_a @ X ) )
         => ( member5821694475859188723pace_a @ ( comp_a423948744115472976a_real @ F @ Alpha2 ) @ ( qbs_Mx4221877616140324662pace_a @ Y ) ) )
     => ( member7269867574344811837pace_a @ F @ ( qbs_mo6277074938832049209pace_a @ X @ Y ) ) ) ).

% qbs_morphismI
thf(fact_107_qbs__morphismI,axiom,
    ! [X: quasi_3431323906171122406pace_b,F: probab4737552677800996672pace_b > probab4737552677800996672pace_b,Y: quasi_3431323906171122406pace_b] :
      ( ! [Alpha2: real > probab4737552677800996672pace_b] :
          ( ( member5892728515905534708pace_b @ Alpha2 @ ( qbs_Mx4221877620443553463pace_b @ X ) )
         => ( member5892728515905534708pace_b @ ( comp_P902384264663180943b_real @ F @ Alpha2 ) @ ( qbs_Mx4221877620443553463pace_b @ Y ) ) )
     => ( member3240531344000085116pace_b @ F @ ( qbs_mo5665329929810820088pace_b @ X @ Y ) ) ) ).

% qbs_morphismI
thf(fact_108_qbs__morphismI,axiom,
    ! [X: quasi_3431323906171122406pace_b,F: probab4737552677800996672pace_b > probab4737552673497767871pace_a,Y: quasi_3360289866124776421pace_a] :
      ( ! [Alpha2: real > probab4737552677800996672pace_b] :
          ( ( member5892728515905534708pace_b @ Alpha2 @ ( qbs_Mx4221877620443553463pace_b @ X ) )
         => ( member5821694475859188723pace_a @ ( comp_P3681088572523203470a_real @ F @ Alpha2 ) @ ( qbs_Mx4221877616140324662pace_a @ Y ) ) )
     => ( member3169497303953739131pace_a @ F @ ( qbs_mo5665329925507591287pace_a @ X @ Y ) ) ) ).

% qbs_morphismI
thf(fact_109_qbs__morphismI,axiom,
    ! [X: quasi_3360289866124776421pace_a,F: probab4737552673497767871pace_a > probab4737552673497767871pace_a,Y: quasi_3360289866124776421pace_a] :
      ( ! [Alpha2: real > probab4737552673497767871pace_a] :
          ( ( member5821694475859188723pace_a @ Alpha2 @ ( qbs_Mx4221877616140324662pace_a @ X ) )
         => ( member5821694475859188723pace_a @ ( comp_P2386351730793452623a_real @ F @ Alpha2 ) @ ( qbs_Mx4221877616140324662pace_a @ Y ) ) )
     => ( member6596715522275338940pace_a @ F @ ( qbs_mo9092548143829191096pace_a @ X @ Y ) ) ) ).

% qbs_morphismI
thf(fact_110_qbs__morphismI,axiom,
    ! [X: quasi_3360289866124776421pace_a,F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,Y: quasi_3431323906171122406pace_b] :
      ( ! [Alpha2: real > probab4737552673497767871pace_a] :
          ( ( member5821694475859188723pace_a @ Alpha2 @ ( qbs_Mx4221877616140324662pace_a @ X ) )
         => ( member5892728515905534708pace_b @ ( comp_P8831019459788205904b_real @ F @ Alpha2 ) @ ( qbs_Mx4221877620443553463pace_b @ Y ) ) )
     => ( member6667749562321684925pace_b @ F @ ( qbs_mo9092548148132419897pace_b @ X @ Y ) ) ) ).

% qbs_morphismI
thf(fact_111_qbs__morphismI,axiom,
    ! [X: quasi_borel_a,F: a > probab8624551251471354625pace_b,Y: quasi_5637586813637594663pace_b] :
      ( ! [Alpha2: real > a] :
          ( ( member_real_a @ Alpha2 @ ( qbs_Mx_a @ X ) )
         => ( member4880162955186484789pace_b @ ( comp_a6393136188637473938b_real @ F @ Alpha2 ) @ ( qbs_Mx7464101204346440312pace_b @ Y ) ) )
     => ( member41169580844105599pace_b @ F @ ( qbs_mo7666231875222642555pace_b @ X @ Y ) ) ) ).

% qbs_morphismI
thf(fact_112_qbs__space__eq__Mx,axiom,
    ! [X: quasi_5677484998582642455pace_b,Y: quasi_5677484998582642455pace_b] :
      ( ( ( qbs_Mx4794387083398668400pace_b @ X )
        = ( qbs_Mx4794387083398668400pace_b @ Y ) )
     => ( ( qbs_sp4261357827969944817pace_b @ X )
        = ( qbs_sp4261357827969944817pace_b @ Y ) ) ) ).

% qbs_space_eq_Mx
thf(fact_113_qbs__space__eq__Mx,axiom,
    ! [X: quasi_8198669516871678102pace_a,Y: quasi_8198669516871678102pace_a] :
      ( ( ( qbs_Mx4723353043352322415pace_a @ X )
        = ( qbs_Mx4723353043352322415pace_a @ Y ) )
     => ( ( qbs_sp4190323787923598832pace_a @ X )
        = ( qbs_sp4190323787923598832pace_a @ Y ) ) ) ).

% qbs_space_eq_Mx
thf(fact_114_qbs__space__eq__Mx,axiom,
    ! [X: quasi_borel_a_b,Y: quasi_borel_a_b] :
      ( ( ( qbs_Mx_a_b @ X )
        = ( qbs_Mx_a_b @ Y ) )
     => ( ( qbs_space_a_b @ X )
        = ( qbs_space_a_b @ Y ) ) ) ).

% qbs_space_eq_Mx
thf(fact_115_qbs__space__eq__Mx,axiom,
    ! [X: quasi_borel_b,Y: quasi_borel_b] :
      ( ( ( qbs_Mx_b @ X )
        = ( qbs_Mx_b @ Y ) )
     => ( ( qbs_space_b @ X )
        = ( qbs_space_b @ Y ) ) ) ).

% qbs_space_eq_Mx
thf(fact_116_qbs__space__eq__Mx,axiom,
    ! [X: quasi_borel_a,Y: quasi_borel_a] :
      ( ( ( qbs_Mx_a @ X )
        = ( qbs_Mx_a @ Y ) )
     => ( ( qbs_space_a @ X )
        = ( qbs_space_a @ Y ) ) ) ).

% qbs_space_eq_Mx
thf(fact_117_qbs__space__eq__Mx,axiom,
    ! [X: quasi_3431323906171122406pace_b,Y: quasi_3431323906171122406pace_b] :
      ( ( ( qbs_Mx4221877620443553463pace_b @ X )
        = ( qbs_Mx4221877620443553463pace_b @ Y ) )
     => ( ( qbs_sp9192884687904738934pace_b @ X )
        = ( qbs_sp9192884687904738934pace_b @ Y ) ) ) ).

% qbs_space_eq_Mx
thf(fact_118_qbs__space__eq__Mx,axiom,
    ! [X: quasi_3360289866124776421pace_a,Y: quasi_3360289866124776421pace_a] :
      ( ( ( qbs_Mx4221877616140324662pace_a @ X )
        = ( qbs_Mx4221877616140324662pace_a @ Y ) )
     => ( ( qbs_sp9192884683601510133pace_a @ X )
        = ( qbs_sp9192884683601510133pace_a @ Y ) ) ) ).

% qbs_space_eq_Mx
thf(fact_119_qbs__closed2__dest,axiom,
    ! [X3: probab4737552677800996672pace_b,X: quasi_3431323906171122406pace_b] :
      ( ( member6485455078948787817pace_b @ X3 @ ( qbs_sp9192884687904738934pace_b @ X ) )
     => ( member5892728515905534708pace_b
        @ ^ [R2: real] : X3
        @ ( qbs_Mx4221877620443553463pace_b @ X ) ) ) ).

% qbs_closed2_dest
thf(fact_120_qbs__closed2__dest,axiom,
    ! [X3: probab4737552673497767871pace_a,X: quasi_3360289866124776421pace_a] :
      ( ( member6485455074645559016pace_a @ X3 @ ( qbs_sp9192884683601510133pace_a @ X ) )
     => ( member5821694475859188723pace_a
        @ ^ [R2: real] : X3
        @ ( qbs_Mx4221877616140324662pace_a @ X ) ) ) ).

% qbs_closed2_dest
thf(fact_121_qbs__closed2__dest,axiom,
    ! [X3: a > b,X: quasi_borel_a_b] :
      ( ( member_a_b @ X3 @ ( qbs_space_a_b @ X ) )
     => ( member_real_a_b
        @ ^ [R2: real] : X3
        @ ( qbs_Mx_a_b @ X ) ) ) ).

% qbs_closed2_dest
thf(fact_122_qbs__closed2__dest,axiom,
    ! [X3: a > probab4737552677800996672pace_b,X: quasi_5677484998582642455pace_b] :
      ( ( member7340901614391157822pace_b @ X3 @ ( qbs_sp4261357827969944817pace_b @ X ) )
     => ( member6235990094145287049pace_b
        @ ^ [R2: real] : X3
        @ ( qbs_Mx4794387083398668400pace_b @ X ) ) ) ).

% qbs_closed2_dest
thf(fact_123_qbs__closed2__dest,axiom,
    ! [X3: probab4737552673497767871pace_a > b,X: quasi_1232139159318032853ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ X3 @ ( qbs_sp1929172757243680431ce_a_b @ X ) )
     => ( member1790644254880677447ce_a_b
        @ ^ [R2: real] : X3
        @ ( qbs_Mx2462202012672404014ce_a_b @ X ) ) ) ).

% qbs_closed2_dest
thf(fact_124_qbs__closed2__dest,axiom,
    ! [X3: b > probab4737552677800996672pace_b,X: quasi_2250266780261042646pace_b] :
      ( ( member1568243296417166973pace_b @ X3 @ ( qbs_sp7712071546850729776pace_b @ X ) )
     => ( member2808771875823687240pace_b
        @ ^ [R2: real] : X3
        @ ( qbs_Mx8245100802279453359pace_b @ X ) ) ) ).

% qbs_closed2_dest
thf(fact_125_qbs__closed2__dest,axiom,
    ! [X3: a > probab4737552673497767871pace_a,X: quasi_8198669516871678102pace_a] :
      ( ( member7269867574344811837pace_a @ X3 @ ( qbs_sp4190323787923598832pace_a @ X ) )
     => ( member8757174612434322696pace_a
        @ ^ [R2: real] : X3
        @ ( qbs_Mx4723353043352322415pace_a @ X ) ) ) ).

% qbs_closed2_dest
thf(fact_126_qbs__closed2__dest,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,X: quasi_5025768402973351190pace_b] :
      ( ( member6667749562321684925pace_b @ X3 @ ( qbs_sp6092703205896766064pace_b @ X ) )
     => ( member793202962283530632pace_b
        @ ^ [R2: real] : X3
        @ ( qbs_Mx3972598340161283567pace_b @ X ) ) ) ).

% qbs_closed2_dest
thf(fact_127_qbs__closed2__dest,axiom,
    ! [X3: a > probab8624551251471354625pace_b,X: quasi_3272867757783880152pace_b] :
      ( ( member41169580844105599pace_b @ X3 @ ( qbs_sp8689495261273962546pace_b @ X ) )
     => ( member8263674353948835402pace_b
        @ ^ [R2: real] : X3
        @ ( qbs_Mx6569390395538480049pace_b @ X ) ) ) ).

% qbs_closed2_dest
thf(fact_128_qbs__closed2__dest,axiom,
    ! [X3: b,X: quasi_borel_b] :
      ( ( member_b @ X3 @ ( qbs_space_b @ X ) )
     => ( member_real_b
        @ ^ [R2: real] : X3
        @ ( qbs_Mx_b @ X ) ) ) ).

% qbs_closed2_dest
thf(fact_129_comp__id,axiom,
    ! [F: a > probab4737552673497767871pace_a] :
      ( ( comp_a7340621667389922906ce_a_a @ F @ id_a )
      = F ) ).

% comp_id
thf(fact_130_comp__id,axiom,
    ! [F: a > b] :
      ( ( comp_a_b_a @ F @ id_a )
      = F ) ).

% comp_id
thf(fact_131_mem__Collect__eq,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,P: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o] :
      ( ( member6667749562321684925pace_b @ A @ ( collec7915783404360165627pace_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_132_mem__Collect__eq,axiom,
    ! [A: a > probab4737552677800996672pace_b,P: ( a > probab4737552677800996672pace_b ) > $o] :
      ( ( member7340901614391157822pace_b @ A @ ( collec5907158909762593660pace_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_133_mem__Collect__eq,axiom,
    ! [A: probab4737552673497767871pace_a > b,P: ( probab4737552673497767871pace_a > b ) > $o] :
      ( ( member5008716543664893436ce_a_b @ A @ ( collec3574973839036329274ce_a_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_134_mem__Collect__eq,axiom,
    ! [A: b > probab4737552677800996672pace_b,P: ( b > probab4737552677800996672pace_b ) > $o] :
      ( ( member1568243296417166973pace_b @ A @ ( collec134500591788602811pace_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_135_mem__Collect__eq,axiom,
    ! [A: a > probab8624551251471354625pace_b,P: ( a > probab8624551251471354625pace_b ) > $o] :
      ( ( member41169580844105599pace_b @ A @ ( collec1289203422882586301pace_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_136_mem__Collect__eq,axiom,
    ! [A: a > probab4737552673497767871pace_a,P: ( a > probab4737552673497767871pace_a ) > $o] :
      ( ( member7269867574344811837pace_a @ A @ ( collec5836124869716247675pace_a @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_137_mem__Collect__eq,axiom,
    ! [A: a > b,P: ( a > b ) > $o] :
      ( ( member_a_b @ A @ ( collect_a_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_138_Collect__mem__eq,axiom,
    ! [A2: set_Pr7742364250814120412pace_b] :
      ( ( collec7915783404360165627pace_b
        @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_139_Collect__mem__eq,axiom,
    ! [A2: set_a_3263942136899480541pace_b] :
      ( ( collec5907158909762593660pace_b
        @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_140_Collect__mem__eq,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b] :
      ( ( collec3574973839036329274ce_a_b
        @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_141_Collect__mem__eq,axiom,
    ! [A2: set_b_9060095955432656540pace_b] :
      ( ( collec134500591788602811pace_b
        @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_142_Collect__mem__eq,axiom,
    ! [A2: set_a_5989463605624649374pace_b] :
      ( ( collec1289203422882586301pace_b
        @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_143_Collect__mem__eq,axiom,
    ! [A2: set_a_5785126655188516188pace_a] :
      ( ( collec5836124869716247675pace_a
        @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_144_Collect__mem__eq,axiom,
    ! [A2: set_a_b] :
      ( ( collect_a_b
        @ ^ [X2: a > b] : ( member_a_b @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_145_monadP__qbs__closed2,axiom,
    ! [X: quasi_borel_b] : ( qbs_cl1321129224395634998pace_b @ ( monad_3932415646498543857s_Px_b @ X ) @ ( monad_4223963853064302126_MPx_b @ X ) ) ).

% monadP_qbs_closed2
thf(fact_146_monadP__qbs__closed2,axiom,
    ! [X: quasi_borel_a] : ( qbs_cl1321129220092406197pace_a @ ( monad_3932415646498543856s_Px_a @ X ) @ ( monad_4223963853064302125_MPx_a @ X ) ) ).

% monadP_qbs_closed2
thf(fact_147_max__qbs__space,axiom,
    ! [X: set_Pr8527670263787538336pace_b] :
      ( ( qbs_sp9192884687904738934pace_b @ ( max_qu2338019691940189127pace_b @ X ) )
      = X ) ).

% max_qbs_space
thf(fact_148_max__qbs__space,axiom,
    ! [X: set_Pr8456636223741192351pace_a] :
      ( ( qbs_sp9192884683601510133pace_a @ ( max_qu2338019687636960326pace_a @ X ) )
      = X ) ).

% max_qbs_space
thf(fact_149_monadP__qbs__MPx__def,axiom,
    ( monad_4223963853064302126_MPx_b
    = ( ^ [X5: quasi_borel_b] : ( collec7038231833220187958pace_b @ ( monad_in_MPx_b @ X5 ) ) ) ) ).

% monadP_qbs_MPx_def
thf(fact_150_monadP__qbs__MPx__def,axiom,
    ( monad_4223963853064302125_MPx_a
    = ( ^ [X5: quasi_borel_a] : ( collec6967197793173841973pace_a @ ( monad_in_MPx_a @ X5 ) ) ) ) ).

% monadP_qbs_MPx_def
thf(fact_151_in__Px__def,axiom,
    ( monad_in_Px_b
    = ( ^ [X5: quasi_borel_b,S: probab4737552677800996672pace_b] : ( member6485455078948787817pace_b @ S @ ( monad_3932415646498543857s_Px_b @ X5 ) ) ) ) ).

% in_Px_def
thf(fact_152_in__Px__def,axiom,
    ( monad_in_Px_a
    = ( ^ [X5: quasi_borel_a,S: probab4737552673497767871pace_a] : ( member6485455074645559016pace_a @ S @ ( monad_3932415646498543856s_Px_a @ X5 ) ) ) ) ).

% in_Px_def
thf(fact_153_in__Px_Ointro,axiom,
    ! [S2: probab4737552677800996672pace_b,X: quasi_borel_b] :
      ( ( member6485455078948787817pace_b @ S2 @ ( monad_3932415646498543857s_Px_b @ X ) )
     => ( monad_in_Px_b @ X @ S2 ) ) ).

% in_Px.intro
thf(fact_154_in__Px_Ointro,axiom,
    ! [S2: probab4737552673497767871pace_a,X: quasi_borel_a] :
      ( ( member6485455074645559016pace_a @ S2 @ ( monad_3932415646498543856s_Px_a @ X ) )
     => ( monad_in_Px_a @ X @ S2 ) ) ).

% in_Px.intro
thf(fact_155_in__Px_Oin__Px,axiom,
    ! [X: quasi_borel_b,S2: probab4737552677800996672pace_b] :
      ( ( monad_in_Px_b @ X @ S2 )
     => ( member6485455078948787817pace_b @ S2 @ ( monad_3932415646498543857s_Px_b @ X ) ) ) ).

% in_Px.in_Px
thf(fact_156_in__Px_Oin__Px,axiom,
    ! [X: quasi_borel_a,S2: probab4737552673497767871pace_a] :
      ( ( monad_in_Px_a @ X @ S2 )
     => ( member6485455074645559016pace_a @ S2 @ ( monad_3932415646498543856s_Px_a @ X ) ) ) ).

% in_Px.in_Px
thf(fact_157_qbs__closed2I,axiom,
    ! [X: set_Pr7742364250814120412pace_b,Mx: set_re9042674185653113895pace_b] :
      ( ! [X4: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
          ( ( member6667749562321684925pace_b @ X4 @ X )
         => ( member793202962283530632pace_b
            @ ^ [R2: real] : X4
            @ Mx ) )
     => ( qbs_cl3637028524066334640pace_b @ X @ Mx ) ) ).

% qbs_closed2I
thf(fact_158_qbs__closed2I,axiom,
    ! [X: set_a_3263942136899480541pace_b,Mx: set_re2719220365667798440pace_b] :
      ( ! [X4: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ X4 @ X )
         => ( member6235990094145287049pace_b
            @ ^ [R2: real] : X4
            @ Mx ) )
     => ( qbs_cl9061761898032280113pace_b @ X @ Mx ) ) ).

% qbs_closed2I
thf(fact_159_qbs__closed2I,axiom,
    ! [X: set_Pr8041968334489646747ce_a_b,Mx: set_re90006967867464038ce_a_b] :
      ( ! [X4: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ X4 @ X )
         => ( member1790644254880677447ce_a_b
            @ ^ [R2: real] : X4
            @ Mx ) )
     => ( qbs_cl6729576827306015727ce_a_b @ X @ Mx ) ) ).

% qbs_closed2I
thf(fact_160_qbs__closed2I,axiom,
    ! [X: set_b_9060095955432656540pace_b,Mx: set_re8812354042701365479pace_b] :
      ( ! [X4: b > probab4737552677800996672pace_b] :
          ( ( member1568243296417166973pace_b @ X4 @ X )
         => ( member2808771875823687240pace_b
            @ ^ [R2: real] : X4
            @ Mx ) )
     => ( qbs_cl3289103580058289264pace_b @ X @ Mx ) ) ).

% qbs_closed2I
thf(fact_161_qbs__closed2I,axiom,
    ! [X: set_a_5989463605624649374pace_b,Mx: set_re718026408605927401pace_b] :
      ( ! [X4: a > probab8624551251471354625pace_b] :
          ( ( member41169580844105599pace_b @ X4 @ X )
         => ( member8263674353948835402pace_b
            @ ^ [R2: real] : X4
            @ Mx ) )
     => ( qbs_cl6233820579443531122pace_b @ X @ Mx ) ) ).

% qbs_closed2I
thf(fact_162_qbs__closed2I,axiom,
    ! [X: set_a_5785126655188516188pace_a,Mx: set_re2878002884992651175pace_a] :
      ( ! [X4: a > probab4737552673497767871pace_a] :
          ( ( member7269867574344811837pace_a @ X4 @ X )
         => ( member8757174612434322696pace_a
            @ ^ [R2: real] : X4
            @ Mx ) )
     => ( qbs_cl8990727857985934128pace_a @ X @ Mx ) ) ).

% qbs_closed2I
thf(fact_163_qbs__closed2I,axiom,
    ! [X: set_a_b,Mx: set_real_a_b] :
      ( ! [X4: a > b] :
          ( ( member_a_b @ X4 @ X )
         => ( member_real_a_b
            @ ^ [R2: real] : X4
            @ Mx ) )
     => ( qbs_closed2_a_b @ X @ Mx ) ) ).

% qbs_closed2I
thf(fact_164_generating__Mx__Mx,axiom,
    ! [X: quasi_3431323906171122406pace_b] :
      ( ( genera2939952387339896157pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ ( qbs_Mx4221877620443553463pace_b @ X ) )
      = ( qbs_Mx4221877620443553463pace_b @ X ) ) ).

% generating_Mx_Mx
thf(fact_165_generating__Mx__Mx,axiom,
    ! [X: quasi_3360289866124776421pace_a] :
      ( ( genera2939952383036667356pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ ( qbs_Mx4221877616140324662pace_a @ X ) )
      = ( qbs_Mx4221877616140324662pace_a @ X ) ) ).

% generating_Mx_Mx
thf(fact_166_monadP__qbs__closed1,axiom,
    ! [X: quasi_borel_b] : ( qbs_cl7093787542369625847pace_b @ ( monad_4223963853064302126_MPx_b @ X ) ) ).

% monadP_qbs_closed1
thf(fact_167_monadP__qbs__closed1,axiom,
    ! [X: quasi_borel_a] : ( qbs_cl7093787538066397046pace_a @ ( monad_4223963853064302125_MPx_a @ X ) ) ).

% monadP_qbs_closed1
thf(fact_168_monadP__qbs__closed3,axiom,
    ! [X: quasi_borel_b] : ( qbs_cl4771842943276419957pace_b @ ( monad_4223963853064302126_MPx_b @ X ) ) ).

% monadP_qbs_closed3
thf(fact_169_monadP__qbs__closed3,axiom,
    ! [X: quasi_borel_a] : ( qbs_cl4771842938973191156pace_a @ ( monad_4223963853064302125_MPx_a @ X ) ) ).

% monadP_qbs_closed3
thf(fact_170_monadP__qbs__empty__iff,axiom,
    ! [X: quasi_3360289866124776421pace_a] :
      ( ( ( qbs_sp9192884683601510133pace_a @ X )
        = bot_bo2798762229408049931pace_a )
      = ( ( qbs_sp8664130063403789110pace_a @ ( monad_1549008827367920281pace_a @ X ) )
        = bot_bo7831615189048989388pace_a ) ) ).

% monadP_qbs_empty_iff
thf(fact_171_monadP__qbs__empty__iff,axiom,
    ! [X: quasi_borel_a] :
      ( ( ( qbs_space_a @ X )
        = bot_bot_set_a )
      = ( ( qbs_sp9192884683601510133pace_a @ ( monad_monadP_qbs_a @ X ) )
        = bot_bo2798762229408049931pace_a ) ) ).

% monadP_qbs_empty_iff
thf(fact_172_monadP__qbs__empty__iff,axiom,
    ! [X: quasi_borel_b] :
      ( ( ( qbs_space_b @ X )
        = bot_bot_set_b )
      = ( ( qbs_sp9192884687904738934pace_b @ ( monad_monadP_qbs_b @ X ) )
        = bot_bo2869796269454395916pace_b ) ) ).

% monadP_qbs_empty_iff
thf(fact_173_monadP__qbs__empty__iff,axiom,
    ! [X: quasi_3431323906171122406pace_b] :
      ( ( ( qbs_sp9192884687904738934pace_b @ X )
        = bot_bo2869796269454395916pace_b )
      = ( ( qbs_sp8735164103450135095pace_b @ ( monad_1549008831671149082pace_b @ X ) )
        = bot_bo5310430670759953741pace_b ) ) ).

% monadP_qbs_empty_iff
thf(fact_174_generating__Mx_OConst,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,X: set_Pr7742364250814120412pace_b,Mx: set_re9042674185653113895pace_b] :
      ( ( member6667749562321684925pace_b @ X3 @ X )
     => ( member793202962283530632pace_b
        @ ^ [R2: real] : X3
        @ ( genera3269888227925781961pace_b @ X @ Mx ) ) ) ).

% generating_Mx.Const
thf(fact_175_generating__Mx_OConst,axiom,
    ! [X3: a > probab4737552677800996672pace_b,X: set_a_3263942136899480541pace_b,Mx: set_re2719220365667798440pace_b] :
      ( ( member7340901614391157822pace_b @ X3 @ X )
     => ( member6235990094145287049pace_b
        @ ^ [R2: real] : X3
        @ ( genera5654942840741251146pace_b @ X @ Mx ) ) ) ).

% generating_Mx.Const
thf(fact_176_generating__Mx_OConst,axiom,
    ! [X3: probab4737552673497767871pace_a > b,X: set_Pr8041968334489646747ce_a_b,Mx: set_re90006967867464038ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ X3 @ X )
     => ( member1790644254880677447ce_a_b
        @ ^ [R2: real] : X3
        @ ( genera3322757770014986760ce_a_b @ X @ Mx ) ) ) ).

% generating_Mx.Const
thf(fact_177_generating__Mx_OConst,axiom,
    ! [X3: b > probab4737552677800996672pace_b,X: set_b_9060095955432656540pace_b,Mx: set_re8812354042701365479pace_b] :
      ( ( member1568243296417166973pace_b @ X3 @ X )
     => ( member2808771875823687240pace_b
        @ ^ [R2: real] : X3
        @ ( genera9105656559622036105pace_b @ X @ Mx ) ) ) ).

% generating_Mx.Const
thf(fact_178_generating__Mx_OConst,axiom,
    ! [X3: a > probab8624551251471354625pace_b,X: set_a_5989463605624649374pace_b,Mx: set_re718026408605927401pace_b] :
      ( ( member41169580844105599pace_b @ X3 @ X )
     => ( member8263674353948835402pace_b
        @ ^ [R2: real] : X3
        @ ( genera5866680283302978443pace_b @ X @ Mx ) ) ) ).

% generating_Mx.Const
thf(fact_179_generating__Mx_OConst,axiom,
    ! [X3: a > probab4737552673497767871pace_a,X: set_a_5785126655188516188pace_a,Mx: set_re2878002884992651175pace_a] :
      ( ( member7269867574344811837pace_a @ X3 @ X )
     => ( member8757174612434322696pace_a
        @ ^ [R2: real] : X3
        @ ( genera5583908800694905161pace_a @ X @ Mx ) ) ) ).

% generating_Mx.Const
thf(fact_180_generating__Mx_OConst,axiom,
    ! [X3: a > b,X: set_a_b,Mx: set_real_a_b] :
      ( ( member_a_b @ X3 @ X )
     => ( member_real_a_b
        @ ^ [R2: real] : X3
        @ ( generating_Mx_a_b @ X @ Mx ) ) ) ).

% generating_Mx.Const
thf(fact_181_qbs__empty__equiv,axiom,
    ! [X: quasi_3431323906171122406pace_b] :
      ( ( ( qbs_sp9192884687904738934pace_b @ X )
        = bot_bo2869796269454395916pace_b )
      = ( ( qbs_Mx4221877620443553463pace_b @ X )
        = bot_bo175847125064878359pace_b ) ) ).

% qbs_empty_equiv
thf(fact_182_qbs__empty__equiv,axiom,
    ! [X: quasi_3360289866124776421pace_a] :
      ( ( ( qbs_sp9192884683601510133pace_a @ X )
        = bot_bo2798762229408049931pace_a )
      = ( ( qbs_Mx4221877616140324662pace_a @ X )
        = bot_bo2697031643353914006pace_a ) ) ).

% qbs_empty_equiv
thf(fact_183_all__not__in__conv,axiom,
    ! [A2: set_Pr7742364250814120412pace_b] :
      ( ( ! [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
            ~ ( member6667749562321684925pace_b @ X2 @ A2 ) )
      = ( A2 = bot_bo5050001829711205488pace_b ) ) ).

% all_not_in_conv
thf(fact_184_all__not__in__conv,axiom,
    ! [A2: set_a_3263942136899480541pace_b] :
      ( ( ! [X2: a > probab4737552677800996672pace_b] :
            ~ ( member7340901614391157822pace_b @ X2 @ A2 ) )
      = ( A2 = bot_bo2617902995080265329pace_b ) ) ).

% all_not_in_conv
thf(fact_185_all__not__in__conv,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b] :
      ( ( ! [X2: probab4737552673497767871pace_a > b] :
            ~ ( member5008716543664893436ce_a_b @ X2 @ A2 ) )
      = ( A2 = bot_bo7395929192670431535ce_a_b ) ) ).

% all_not_in_conv
thf(fact_186_all__not__in__conv,axiom,
    ! [A2: set_b_9060095955432656540pace_b] :
      ( ( ! [X2: b > probab4737552677800996672pace_b] :
            ~ ( member1568243296417166973pace_b @ X2 @ A2 ) )
      = ( A2 = bot_bo8414056813613441328pace_b ) ) ).

% all_not_in_conv
thf(fact_187_all__not__in__conv,axiom,
    ! [A2: set_a_5989463605624649374pace_b] :
      ( ( ! [X2: a > probab8624551251471354625pace_b] :
            ~ ( member41169580844105599pace_b @ X2 @ A2 ) )
      = ( A2 = bot_bo3297101184521734450pace_b ) ) ).

% all_not_in_conv
thf(fact_188_all__not__in__conv,axiom,
    ! [A2: set_a_5785126655188516188pace_a] :
      ( ( ! [X2: a > probab4737552673497767871pace_a] :
            ~ ( member7269867574344811837pace_a @ X2 @ A2 ) )
      = ( A2 = bot_bo5139087513369300976pace_a ) ) ).

% all_not_in_conv
thf(fact_189_all__not__in__conv,axiom,
    ! [A2: set_a_b] :
      ( ( ! [X2: a > b] :
            ~ ( member_a_b @ X2 @ A2 ) )
      = ( A2 = bot_bot_set_a_b ) ) ).

% all_not_in_conv
thf(fact_190_empty__iff,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ~ ( member6667749562321684925pace_b @ C @ bot_bo5050001829711205488pace_b ) ).

% empty_iff
thf(fact_191_empty__iff,axiom,
    ! [C: a > probab4737552677800996672pace_b] :
      ~ ( member7340901614391157822pace_b @ C @ bot_bo2617902995080265329pace_b ) ).

% empty_iff
thf(fact_192_empty__iff,axiom,
    ! [C: probab4737552673497767871pace_a > b] :
      ~ ( member5008716543664893436ce_a_b @ C @ bot_bo7395929192670431535ce_a_b ) ).

% empty_iff
thf(fact_193_empty__iff,axiom,
    ! [C: b > probab4737552677800996672pace_b] :
      ~ ( member1568243296417166973pace_b @ C @ bot_bo8414056813613441328pace_b ) ).

% empty_iff
thf(fact_194_empty__iff,axiom,
    ! [C: a > probab8624551251471354625pace_b] :
      ~ ( member41169580844105599pace_b @ C @ bot_bo3297101184521734450pace_b ) ).

% empty_iff
thf(fact_195_empty__iff,axiom,
    ! [C: a > probab4737552673497767871pace_a] :
      ~ ( member7269867574344811837pace_a @ C @ bot_bo5139087513369300976pace_a ) ).

% empty_iff
thf(fact_196_empty__iff,axiom,
    ! [C: a > b] :
      ~ ( member_a_b @ C @ bot_bot_set_a_b ) ).

% empty_iff
thf(fact_197_emptyE,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ~ ( member6667749562321684925pace_b @ A @ bot_bo5050001829711205488pace_b ) ).

% emptyE
thf(fact_198_emptyE,axiom,
    ! [A: a > probab4737552677800996672pace_b] :
      ~ ( member7340901614391157822pace_b @ A @ bot_bo2617902995080265329pace_b ) ).

% emptyE
thf(fact_199_emptyE,axiom,
    ! [A: probab4737552673497767871pace_a > b] :
      ~ ( member5008716543664893436ce_a_b @ A @ bot_bo7395929192670431535ce_a_b ) ).

% emptyE
thf(fact_200_emptyE,axiom,
    ! [A: b > probab4737552677800996672pace_b] :
      ~ ( member1568243296417166973pace_b @ A @ bot_bo8414056813613441328pace_b ) ).

% emptyE
thf(fact_201_emptyE,axiom,
    ! [A: a > probab8624551251471354625pace_b] :
      ~ ( member41169580844105599pace_b @ A @ bot_bo3297101184521734450pace_b ) ).

% emptyE
thf(fact_202_emptyE,axiom,
    ! [A: a > probab4737552673497767871pace_a] :
      ~ ( member7269867574344811837pace_a @ A @ bot_bo5139087513369300976pace_a ) ).

% emptyE
thf(fact_203_emptyE,axiom,
    ! [A: a > b] :
      ~ ( member_a_b @ A @ bot_bot_set_a_b ) ).

% emptyE
thf(fact_204_equals0D,axiom,
    ! [A2: set_Pr7742364250814120412pace_b,A: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ( ( A2 = bot_bo5050001829711205488pace_b )
     => ~ ( member6667749562321684925pace_b @ A @ A2 ) ) ).

% equals0D
thf(fact_205_equals0D,axiom,
    ! [A2: set_a_3263942136899480541pace_b,A: a > probab4737552677800996672pace_b] :
      ( ( A2 = bot_bo2617902995080265329pace_b )
     => ~ ( member7340901614391157822pace_b @ A @ A2 ) ) ).

% equals0D
thf(fact_206_equals0D,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,A: probab4737552673497767871pace_a > b] :
      ( ( A2 = bot_bo7395929192670431535ce_a_b )
     => ~ ( member5008716543664893436ce_a_b @ A @ A2 ) ) ).

% equals0D
thf(fact_207_equals0D,axiom,
    ! [A2: set_b_9060095955432656540pace_b,A: b > probab4737552677800996672pace_b] :
      ( ( A2 = bot_bo8414056813613441328pace_b )
     => ~ ( member1568243296417166973pace_b @ A @ A2 ) ) ).

% equals0D
thf(fact_208_equals0D,axiom,
    ! [A2: set_a_5989463605624649374pace_b,A: a > probab8624551251471354625pace_b] :
      ( ( A2 = bot_bo3297101184521734450pace_b )
     => ~ ( member41169580844105599pace_b @ A @ A2 ) ) ).

% equals0D
thf(fact_209_equals0D,axiom,
    ! [A2: set_a_5785126655188516188pace_a,A: a > probab4737552673497767871pace_a] :
      ( ( A2 = bot_bo5139087513369300976pace_a )
     => ~ ( member7269867574344811837pace_a @ A @ A2 ) ) ).

% equals0D
thf(fact_210_equals0D,axiom,
    ! [A2: set_a_b,A: a > b] :
      ( ( A2 = bot_bot_set_a_b )
     => ~ ( member_a_b @ A @ A2 ) ) ).

% equals0D
thf(fact_211_equals0I,axiom,
    ! [A2: set_Pr7742364250814120412pace_b] :
      ( ! [Y3: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
          ~ ( member6667749562321684925pace_b @ Y3 @ A2 )
     => ( A2 = bot_bo5050001829711205488pace_b ) ) ).

% equals0I
thf(fact_212_equals0I,axiom,
    ! [A2: set_a_3263942136899480541pace_b] :
      ( ! [Y3: a > probab4737552677800996672pace_b] :
          ~ ( member7340901614391157822pace_b @ Y3 @ A2 )
     => ( A2 = bot_bo2617902995080265329pace_b ) ) ).

% equals0I
thf(fact_213_equals0I,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b] :
      ( ! [Y3: probab4737552673497767871pace_a > b] :
          ~ ( member5008716543664893436ce_a_b @ Y3 @ A2 )
     => ( A2 = bot_bo7395929192670431535ce_a_b ) ) ).

% equals0I
thf(fact_214_equals0I,axiom,
    ! [A2: set_b_9060095955432656540pace_b] :
      ( ! [Y3: b > probab4737552677800996672pace_b] :
          ~ ( member1568243296417166973pace_b @ Y3 @ A2 )
     => ( A2 = bot_bo8414056813613441328pace_b ) ) ).

% equals0I
thf(fact_215_equals0I,axiom,
    ! [A2: set_a_5989463605624649374pace_b] :
      ( ! [Y3: a > probab8624551251471354625pace_b] :
          ~ ( member41169580844105599pace_b @ Y3 @ A2 )
     => ( A2 = bot_bo3297101184521734450pace_b ) ) ).

% equals0I
thf(fact_216_equals0I,axiom,
    ! [A2: set_a_5785126655188516188pace_a] :
      ( ! [Y3: a > probab4737552673497767871pace_a] :
          ~ ( member7269867574344811837pace_a @ Y3 @ A2 )
     => ( A2 = bot_bo5139087513369300976pace_a ) ) ).

% equals0I
thf(fact_217_equals0I,axiom,
    ! [A2: set_a_b] :
      ( ! [Y3: a > b] :
          ~ ( member_a_b @ Y3 @ A2 )
     => ( A2 = bot_bot_set_a_b ) ) ).

% equals0I
thf(fact_218_ex__in__conv,axiom,
    ! [A2: set_Pr7742364250814120412pace_b] :
      ( ( ? [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ A2 ) )
      = ( A2 != bot_bo5050001829711205488pace_b ) ) ).

% ex_in_conv
thf(fact_219_ex__in__conv,axiom,
    ! [A2: set_a_3263942136899480541pace_b] :
      ( ( ? [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ A2 ) )
      = ( A2 != bot_bo2617902995080265329pace_b ) ) ).

% ex_in_conv
thf(fact_220_ex__in__conv,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b] :
      ( ( ? [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ A2 ) )
      = ( A2 != bot_bo7395929192670431535ce_a_b ) ) ).

% ex_in_conv
thf(fact_221_ex__in__conv,axiom,
    ! [A2: set_b_9060095955432656540pace_b] :
      ( ( ? [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ A2 ) )
      = ( A2 != bot_bo8414056813613441328pace_b ) ) ).

% ex_in_conv
thf(fact_222_ex__in__conv,axiom,
    ! [A2: set_a_5989463605624649374pace_b] :
      ( ( ? [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ A2 ) )
      = ( A2 != bot_bo3297101184521734450pace_b ) ) ).

% ex_in_conv
thf(fact_223_ex__in__conv,axiom,
    ! [A2: set_a_5785126655188516188pace_a] :
      ( ( ? [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ A2 ) )
      = ( A2 != bot_bo5139087513369300976pace_a ) ) ).

% ex_in_conv
thf(fact_224_ex__in__conv,axiom,
    ! [A2: set_a_b] :
      ( ( ? [X2: a > b] : ( member_a_b @ X2 @ A2 ) )
      = ( A2 != bot_bot_set_a_b ) ) ).

% ex_in_conv
thf(fact_225_eqb__Mx,axiom,
    ( ( qbs_Mx4221877620443553463pace_b @ empty_5370026449942293790pace_b )
    = bot_bo175847125064878359pace_b ) ).

% eqb_Mx
thf(fact_226_eqb__Mx,axiom,
    ( ( qbs_Mx4221877616140324662pace_a @ empty_5370026445639064989pace_a )
    = bot_bo2697031643353914006pace_a ) ).

% eqb_Mx
thf(fact_227_eqb__space,axiom,
    ( ( qbs_sp9192884687904738934pace_b @ empty_5370026449942293790pace_b )
    = bot_bo2869796269454395916pace_b ) ).

% eqb_space
thf(fact_228_eqb__space,axiom,
    ( ( qbs_sp9192884683601510133pace_a @ empty_5370026445639064989pace_a )
    = bot_bo2798762229408049931pace_a ) ).

% eqb_space
thf(fact_229_empty__quasi__borel__iff,axiom,
    ! [X: quasi_3431323906171122406pace_b] :
      ( ( ( qbs_sp9192884687904738934pace_b @ X )
        = bot_bo2869796269454395916pace_b )
      = ( X = empty_5370026449942293790pace_b ) ) ).

% empty_quasi_borel_iff
thf(fact_230_empty__quasi__borel__iff,axiom,
    ! [X: quasi_3360289866124776421pace_a] :
      ( ( ( qbs_sp9192884683601510133pace_a @ X )
        = bot_bo2798762229408049931pace_a )
      = ( X = empty_5370026445639064989pace_a ) ) ).

% empty_quasi_borel_iff
thf(fact_231_generating__Mx__def,axiom,
    ( genera3269888227925781961pace_b
    = ( ^ [X5: set_Pr7742364250814120412pace_b,Mx2: set_re9042674185653113895pace_b] :
          ( collec6445801172920120518pace_b
          @ ( genera2866437722186151605pace_b
            @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ X5 )
            @ ^ [X2: real > probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member793202962283530632pace_b @ X2 @ Mx2 ) ) ) ) ) ).

% generating_Mx_def
thf(fact_232_generating__Mx__def,axiom,
    ( genera5654942840741251146pace_b
    = ( ^ [X5: set_a_3263942136899480541pace_b,Mx2: set_re2719220365667798440pace_b] :
          ( collec1355774385663966919pace_b
          @ ( genera6889579626341601590pace_b
            @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ X5 )
            @ ^ [X2: real > a > probab4737552677800996672pace_b] : ( member6235990094145287049pace_b @ X2 @ Mx2 ) ) ) ) ) ).

% generating_Mx_def
thf(fact_233_generating__Mx__def,axiom,
    ( genera3322757770014986760ce_a_b
    = ( ^ [X5: set_Pr8041968334489646747ce_a_b,Mx2: set_re90006967867464038ce_a_b] :
          ( collec6133800583254133125ce_a_b
          @ ( genera4557394555615337204ce_a_b
            @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ X5 )
            @ ^ [X2: real > probab4737552673497767871pace_a > b] : ( member1790644254880677447ce_a_b @ X2 @ Mx2 ) ) ) ) ) ).

% generating_Mx_def
thf(fact_234_generating__Mx__def,axiom,
    ( genera9105656559622036105pace_b
    = ( ^ [X5: set_b_9060095955432656540pace_b,Mx2: set_re8812354042701365479pace_b] :
          ( collec7151928204197142918pace_b
          @ ( genera1116921308367610741pace_b
            @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ X5 )
            @ ^ [X2: real > b > probab4737552677800996672pace_b] : ( member2808771875823687240pace_b @ X2 @ Mx2 ) ) ) ) ) ).

% generating_Mx_def
thf(fact_235_generating__Mx__def,axiom,
    ( genera5866680283302978443pace_b
    = ( ^ [X5: set_a_5989463605624649374pace_b,Mx2: set_re718026408605927401pace_b] :
          ( collec4692900527730649480pace_b
          @ ( genera5463229777563348087pace_b
            @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ X5 )
            @ ^ [X2: real > a > probab8624551251471354625pace_b] : ( member8263674353948835402pace_b @ X2 @ Mx2 ) ) ) ) ) ).

% generating_Mx_def
thf(fact_236_generating__Mx__def,axiom,
    ( genera5583908800694905161pace_a
    = ( ^ [X5: set_a_5785126655188516188pace_a,Mx2: set_re2878002884992651175pace_a] :
          ( collec3876958903953002566pace_a
          @ ( genera6818545586295255605pace_a
            @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ X5 )
            @ ^ [X2: real > a > probab4737552673497767871pace_a] : ( member8757174612434322696pace_a @ X2 @ Mx2 ) ) ) ) ) ).

% generating_Mx_def
thf(fact_237_generating__Mx__def,axiom,
    ( generating_Mx_a_b
    = ( ^ [X5: set_a_b,Mx2: set_real_a_b] :
          ( collect_real_a_b
          @ ( generating_Mxp_a_b
            @ ^ [X2: a > b] : ( member_a_b @ X2 @ X5 )
            @ ^ [X2: real > a > b] : ( member_real_a_b @ X2 @ Mx2 ) ) ) ) ) ).

% generating_Mx_def
thf(fact_238_Bex__def,axiom,
    ( bex_Pr7664070296885286854pace_b
    = ( ^ [A3: set_Pr7742364250814120412pace_b,P2: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o] :
        ? [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
          ( ( member6667749562321684925pace_b @ X2 @ A3 )
          & ( P2 @ X2 ) ) ) ) ).

% Bex_def
thf(fact_239_Bex__def,axiom,
    ( bex_a_4408856295274709575pace_b
    = ( ^ [A3: set_a_3263942136899480541pace_b,P2: ( a > probab4737552677800996672pace_b ) > $o] :
        ? [X2: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ X2 @ A3 )
          & ( P2 @ X2 ) ) ) ) ).

% Bex_def
thf(fact_240_Bex__def,axiom,
    ( bex_Pr2076671224548445189ce_a_b
    = ( ^ [A3: set_Pr8041968334489646747ce_a_b,P2: ( probab4737552673497767871pace_a > b ) > $o] :
        ? [X2: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ X2 @ A3 )
          & ( P2 @ X2 ) ) ) ) ).

% Bex_def
thf(fact_241_Bex__def,axiom,
    ( bex_b_7859570014155494534pace_b
    = ( ^ [A3: set_b_9060095955432656540pace_b,P2: ( b > probab4737552677800996672pace_b ) > $o] :
        ? [X2: b > probab4737552677800996672pace_b] :
          ( ( member1568243296417166973pace_b @ X2 @ A3 )
          & ( P2 @ X2 ) ) ) ) ).

% Bex_def
thf(fact_242_Bex__def,axiom,
    ( bex_a_1037490315407707528pace_b
    = ( ^ [A3: set_a_5989463605624649374pace_b,P2: ( a > probab8624551251471354625pace_b ) > $o] :
        ? [X2: a > probab8624551251471354625pace_b] :
          ( ( member41169580844105599pace_b @ X2 @ A3 )
          & ( P2 @ X2 ) ) ) ) ).

% Bex_def
thf(fact_243_Bex__def,axiom,
    ( bex_a_4337822255228363590pace_a
    = ( ^ [A3: set_a_5785126655188516188pace_a,P2: ( a > probab4737552673497767871pace_a ) > $o] :
        ? [X2: a > probab4737552673497767871pace_a] :
          ( ( member7269867574344811837pace_a @ X2 @ A3 )
          & ( P2 @ X2 ) ) ) ) ).

% Bex_def
thf(fact_244_Bex__def,axiom,
    ( bex_a_b
    = ( ^ [A3: set_a_b,P2: ( a > b ) > $o] :
        ? [X2: a > b] :
          ( ( member_a_b @ X2 @ A3 )
          & ( P2 @ X2 ) ) ) ) ).

% Bex_def
thf(fact_245_generating__Mxp__generating__Mx__eq,axiom,
    ! [X: set_Pr7742364250814120412pace_b,Mx: set_re9042674185653113895pace_b] :
      ( ( genera2866437722186151605pace_b
        @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ X )
        @ ^ [X2: real > probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member793202962283530632pace_b @ X2 @ Mx ) )
      = ( ^ [X2: real > probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member793202962283530632pace_b @ X2 @ ( genera3269888227925781961pace_b @ X @ Mx ) ) ) ) ).

% generating_Mxp_generating_Mx_eq
thf(fact_246_generating__Mxp__generating__Mx__eq,axiom,
    ! [X: set_a_3263942136899480541pace_b,Mx: set_re2719220365667798440pace_b] :
      ( ( genera6889579626341601590pace_b
        @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ X )
        @ ^ [X2: real > a > probab4737552677800996672pace_b] : ( member6235990094145287049pace_b @ X2 @ Mx ) )
      = ( ^ [X2: real > a > probab4737552677800996672pace_b] : ( member6235990094145287049pace_b @ X2 @ ( genera5654942840741251146pace_b @ X @ Mx ) ) ) ) ).

% generating_Mxp_generating_Mx_eq
thf(fact_247_generating__Mxp__generating__Mx__eq,axiom,
    ! [X: set_Pr8041968334489646747ce_a_b,Mx: set_re90006967867464038ce_a_b] :
      ( ( genera4557394555615337204ce_a_b
        @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ X )
        @ ^ [X2: real > probab4737552673497767871pace_a > b] : ( member1790644254880677447ce_a_b @ X2 @ Mx ) )
      = ( ^ [X2: real > probab4737552673497767871pace_a > b] : ( member1790644254880677447ce_a_b @ X2 @ ( genera3322757770014986760ce_a_b @ X @ Mx ) ) ) ) ).

% generating_Mxp_generating_Mx_eq
thf(fact_248_generating__Mxp__generating__Mx__eq,axiom,
    ! [X: set_b_9060095955432656540pace_b,Mx: set_re8812354042701365479pace_b] :
      ( ( genera1116921308367610741pace_b
        @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ X )
        @ ^ [X2: real > b > probab4737552677800996672pace_b] : ( member2808771875823687240pace_b @ X2 @ Mx ) )
      = ( ^ [X2: real > b > probab4737552677800996672pace_b] : ( member2808771875823687240pace_b @ X2 @ ( genera9105656559622036105pace_b @ X @ Mx ) ) ) ) ).

% generating_Mxp_generating_Mx_eq
thf(fact_249_generating__Mxp__generating__Mx__eq,axiom,
    ! [X: set_a_5989463605624649374pace_b,Mx: set_re718026408605927401pace_b] :
      ( ( genera5463229777563348087pace_b
        @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ X )
        @ ^ [X2: real > a > probab8624551251471354625pace_b] : ( member8263674353948835402pace_b @ X2 @ Mx ) )
      = ( ^ [X2: real > a > probab8624551251471354625pace_b] : ( member8263674353948835402pace_b @ X2 @ ( genera5866680283302978443pace_b @ X @ Mx ) ) ) ) ).

% generating_Mxp_generating_Mx_eq
thf(fact_250_generating__Mxp__generating__Mx__eq,axiom,
    ! [X: set_a_5785126655188516188pace_a,Mx: set_re2878002884992651175pace_a] :
      ( ( genera6818545586295255605pace_a
        @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ X )
        @ ^ [X2: real > a > probab4737552673497767871pace_a] : ( member8757174612434322696pace_a @ X2 @ Mx ) )
      = ( ^ [X2: real > a > probab4737552673497767871pace_a] : ( member8757174612434322696pace_a @ X2 @ ( genera5583908800694905161pace_a @ X @ Mx ) ) ) ) ).

% generating_Mxp_generating_Mx_eq
thf(fact_251_generating__Mxp__generating__Mx__eq,axiom,
    ! [X: set_a_b,Mx: set_real_a_b] :
      ( ( generating_Mxp_a_b
        @ ^ [X2: a > b] : ( member_a_b @ X2 @ X )
        @ ^ [X2: real > a > b] : ( member_real_a_b @ X2 @ Mx ) )
      = ( ^ [X2: real > a > b] : ( member_real_a_b @ X2 @ ( generating_Mx_a_b @ X @ Mx ) ) ) ) ).

% generating_Mxp_generating_Mx_eq
thf(fact_252_map__qbs__Mx,axiom,
    ! [F: probab4737552677800996672pace_b > probab4737552677800996672pace_b,X: quasi_3431323906171122406pace_b] :
      ( ( qbs_Mx4221877620443553463pace_b @ ( map_qb1329406749815073291pace_b @ F @ X ) )
      = ( collec7038231833220187958pace_b
        @ ^ [Beta: real > probab4737552677800996672pace_b] :
          ? [X2: real > probab4737552677800996672pace_b] :
            ( ( member5892728515905534708pace_b @ X2 @ ( qbs_Mx4221877620443553463pace_b @ X ) )
            & ( Beta
              = ( comp_P902384264663180943b_real @ F @ X2 ) ) ) ) ) ).

% map_qbs_Mx
thf(fact_253_map__qbs__Mx,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,X: quasi_3360289866124776421pace_a] :
      ( ( qbs_Mx4221877620443553463pace_b @ ( map_qb4756624968136673100pace_b @ F @ X ) )
      = ( collec7038231833220187958pace_b
        @ ^ [Beta: real > probab4737552677800996672pace_b] :
          ? [X2: real > probab4737552673497767871pace_a] :
            ( ( member5821694475859188723pace_a @ X2 @ ( qbs_Mx4221877616140324662pace_a @ X ) )
            & ( Beta
              = ( comp_P8831019459788205904b_real @ F @ X2 ) ) ) ) ) ).

% map_qbs_Mx
thf(fact_254_map__qbs__Mx,axiom,
    ! [F: probab4737552677800996672pace_b > probab4737552673497767871pace_a,X: quasi_3431323906171122406pace_b] :
      ( ( qbs_Mx4221877616140324662pace_a @ ( map_qb1329406745511844490pace_a @ F @ X ) )
      = ( collec6967197793173841973pace_a
        @ ^ [Beta: real > probab4737552673497767871pace_a] :
          ? [X2: real > probab4737552677800996672pace_b] :
            ( ( member5892728515905534708pace_b @ X2 @ ( qbs_Mx4221877620443553463pace_b @ X ) )
            & ( Beta
              = ( comp_P3681088572523203470a_real @ F @ X2 ) ) ) ) ) ).

% map_qbs_Mx
thf(fact_255_map__qbs__Mx,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552673497767871pace_a,X: quasi_3360289866124776421pace_a] :
      ( ( qbs_Mx4221877616140324662pace_a @ ( map_qb4756624963833444299pace_a @ F @ X ) )
      = ( collec6967197793173841973pace_a
        @ ^ [Beta: real > probab4737552673497767871pace_a] :
          ? [X2: real > probab4737552673497767871pace_a] :
            ( ( member5821694475859188723pace_a @ X2 @ ( qbs_Mx4221877616140324662pace_a @ X ) )
            & ( Beta
              = ( comp_P2386351730793452623a_real @ F @ X2 ) ) ) ) ) ).

% map_qbs_Mx
thf(fact_256_bot__empty__eq,axiom,
    ( bot_bo6963241103718944789ce_b_o
    = ( ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ bot_bo5050001829711205488pace_b ) ) ) ).

% bot_empty_eq
thf(fact_257_bot__empty__eq,axiom,
    ( bot_bo5721901170993186644ce_b_o
    = ( ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ bot_bo2617902995080265329pace_b ) ) ) ).

% bot_empty_eq
thf(fact_258_bot__empty__eq,axiom,
    ( bot_bo2399283441899022870_a_b_o
    = ( ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ bot_bo7395929192670431535ce_a_b ) ) ) ).

% bot_empty_eq
thf(fact_259_bot__empty__eq,axiom,
    ( bot_bo2694108906491622229ce_b_o
    = ( ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ bot_bo8414056813613441328pace_b ) ) ) ).

% bot_empty_eq
thf(fact_260_bot__empty__eq,axiom,
    ( bot_bo2590681875679153619ce_b_o
    = ( ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ bot_bo3297101184521734450pace_b ) ) ) ).

% bot_empty_eq
thf(fact_261_bot__empty__eq,axiom,
    ( bot_bo6357550171598173333ce_a_o
    = ( ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ bot_bo5139087513369300976pace_a ) ) ) ).

% bot_empty_eq
thf(fact_262_bot__empty__eq,axiom,
    ( bot_bot_a_b_o
    = ( ^ [X2: a > b] : ( member_a_b @ X2 @ bot_bot_set_a_b ) ) ) ).

% bot_empty_eq
thf(fact_263_is__singletonI_H,axiom,
    ! [A2: set_Pr7742364250814120412pace_b] :
      ( ( A2 != bot_bo5050001829711205488pace_b )
     => ( ! [X4: probab4737552673497767871pace_a > probab4737552677800996672pace_b,Y3: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
            ( ( member6667749562321684925pace_b @ X4 @ A2 )
           => ( ( member6667749562321684925pace_b @ Y3 @ A2 )
             => ( X4 = Y3 ) ) )
       => ( is_sin6423242737633421106pace_b @ A2 ) ) ) ).

% is_singletonI'
thf(fact_264_is__singletonI_H,axiom,
    ! [A2: set_a_3263942136899480541pace_b] :
      ( ( A2 != bot_bo2617902995080265329pace_b )
     => ( ! [X4: a > probab4737552677800996672pace_b,Y3: a > probab4737552677800996672pace_b] :
            ( ( member7340901614391157822pace_b @ X4 @ A2 )
           => ( ( member7340901614391157822pace_b @ Y3 @ A2 )
             => ( X4 = Y3 ) ) )
       => ( is_sin4191138626243776947pace_b @ A2 ) ) ) ).

% is_singletonI'
thf(fact_265_is__singletonI_H,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b] :
      ( ( A2 != bot_bo7395929192670431535ce_a_b )
     => ( ! [X4: probab4737552673497767871pace_a > b,Y3: probab4737552673497767871pace_a > b] :
            ( ( member5008716543664893436ce_a_b @ X4 @ A2 )
           => ( ( member5008716543664893436ce_a_b @ Y3 @ A2 )
             => ( X4 = Y3 ) ) )
       => ( is_sin1858953555517512561ce_a_b @ A2 ) ) ) ).

% is_singletonI'
thf(fact_266_is__singletonI_H,axiom,
    ! [A2: set_b_9060095955432656540pace_b] :
      ( ( A2 != bot_bo8414056813613441328pace_b )
     => ( ! [X4: b > probab4737552677800996672pace_b,Y3: b > probab4737552677800996672pace_b] :
            ( ( member1568243296417166973pace_b @ X4 @ A2 )
           => ( ( member1568243296417166973pace_b @ Y3 @ A2 )
             => ( X4 = Y3 ) ) )
       => ( is_sin7641852345124561906pace_b @ A2 ) ) ) ).

% is_singletonI'
thf(fact_267_is__singletonI_H,axiom,
    ! [A2: set_a_5989463605624649374pace_b] :
      ( ( A2 != bot_bo3297101184521734450pace_b )
     => ( ! [X4: a > probab8624551251471354625pace_b,Y3: a > probab8624551251471354625pace_b] :
            ( ( member41169580844105599pace_b @ X4 @ A2 )
           => ( ( member41169580844105599pace_b @ Y3 @ A2 )
             => ( X4 = Y3 ) ) )
       => ( is_sin9020034793010617588pace_b @ A2 ) ) ) ).

% is_singletonI'
thf(fact_268_is__singletonI_H,axiom,
    ! [A2: set_a_5785126655188516188pace_a] :
      ( ( A2 != bot_bo5139087513369300976pace_a )
     => ( ! [X4: a > probab4737552673497767871pace_a,Y3: a > probab4737552673497767871pace_a] :
            ( ( member7269867574344811837pace_a @ X4 @ A2 )
           => ( ( member7269867574344811837pace_a @ Y3 @ A2 )
             => ( X4 = Y3 ) ) )
       => ( is_sin4120104586197430962pace_a @ A2 ) ) ) ).

% is_singletonI'
thf(fact_269_is__singletonI_H,axiom,
    ! [A2: set_a_b] :
      ( ( A2 != bot_bot_set_a_b )
     => ( ! [X4: a > b,Y3: a > b] :
            ( ( member_a_b @ X4 @ A2 )
           => ( ( member_a_b @ Y3 @ A2 )
             => ( X4 = Y3 ) ) )
       => ( is_singleton_a_b @ A2 ) ) ) ).

% is_singletonI'
thf(fact_270_image__eqI,axiom,
    ! [B: a > b,F: ( a > b ) > a > b,X3: a > b,A2: set_a_b] :
      ( ( B
        = ( F @ X3 ) )
     => ( ( member_a_b @ X3 @ A2 )
       => ( member_a_b @ B @ ( image_a_b_a_b @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_271_image__eqI,axiom,
    ! [B: a > b,F: ( a > probab4737552677800996672pace_b ) > a > b,X3: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ( B
        = ( F @ X3 ) )
     => ( ( member7340901614391157822pace_b @ X3 @ A2 )
       => ( member_a_b @ B @ ( image_5357422296895858068_b_a_b @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_272_image__eqI,axiom,
    ! [B: a > b,F: ( probab4737552673497767871pace_a > b ) > a > b,X3: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( B
        = ( F @ X3 ) )
     => ( ( member5008716543664893436ce_a_b @ X3 @ A2 )
       => ( member_a_b @ B @ ( image_2665524599124622162_b_a_b @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_273_image__eqI,axiom,
    ! [B: a > b,F: ( b > probab4737552677800996672pace_b ) > a > b,X3: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ( B
        = ( F @ X3 ) )
     => ( ( member1568243296417166973pace_b @ X3 @ A2 )
       => ( member_a_b @ B @ ( image_8215988703474630099_b_a_b @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_274_image__eqI,axiom,
    ! [B: a > b,F: ( a > probab4737552673497767871pace_a ) > a > b,X3: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ( B
        = ( F @ X3 ) )
     => ( ( member7269867574344811837pace_a @ X3 @ A2 )
       => ( member_a_b @ B @ ( image_7482003829499661459_a_a_b @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_275_image__eqI,axiom,
    ! [B: a > probab4737552677800996672pace_b,F: ( a > b ) > a > probab4737552677800996672pace_b,X3: a > b,A2: set_a_b] :
      ( ( B
        = ( F @ X3 ) )
     => ( ( member_a_b @ X3 @ A2 )
       => ( member7340901614391157822pace_b @ B @ ( image_6394579700060191636pace_b @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_276_image__eqI,axiom,
    ! [B: probab4737552673497767871pace_a > b,F: ( a > b ) > probab4737552673497767871pace_a > b,X3: a > b,A2: set_a_b] :
      ( ( B
        = ( F @ X3 ) )
     => ( ( member_a_b @ X3 @ A2 )
       => ( member5008716543664893436ce_a_b @ B @ ( image_4062394629333927250ce_a_b @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_277_image__eqI,axiom,
    ! [B: b > probab4737552677800996672pace_b,F: ( a > b ) > b > probab4737552677800996672pace_b,X3: a > b,A2: set_a_b] :
      ( ( B
        = ( F @ X3 ) )
     => ( ( member_a_b @ X3 @ A2 )
       => ( member1568243296417166973pace_b @ B @ ( image_621921382086200787pace_b @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_278_image__eqI,axiom,
    ! [B: a > probab4737552673497767871pace_a,F: ( a > b ) > a > probab4737552673497767871pace_a,X3: a > b,A2: set_a_b] :
      ( ( B
        = ( F @ X3 ) )
     => ( ( member_a_b @ X3 @ A2 )
       => ( member7269867574344811837pace_a @ B @ ( image_6323545660013845651pace_a @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_279_image__eqI,axiom,
    ! [B: a > b,F: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > a > b,X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b] :
      ( ( B
        = ( F @ X3 ) )
     => ( ( member6667749562321684925pace_b @ X3 @ A2 )
       => ( member_a_b @ B @ ( image_750332364051833107_b_a_b @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_280_Pi__I,axiom,
    ! [A2: set_a,F: a > b,B2: a > set_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member_a_b @ F @ ( pi_a_b @ A2 @ B2 ) ) ) ).

% Pi_I
thf(fact_281_Pi__I,axiom,
    ! [A2: set_a,F: a > probab4737552677800996672pace_b,B2: a > set_Pr8527670263787538336pace_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member6485455078948787817pace_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member7340901614391157822pace_b @ F @ ( pi_a_P1132609506902963085pace_b @ A2 @ B2 ) ) ) ).

% Pi_I
thf(fact_282_Pi__I,axiom,
    ! [A2: set_Pr8456636223741192351pace_a,F: probab4737552673497767871pace_a > b,B2: probab4737552673497767871pace_a > set_b] :
      ( ! [X4: probab4737552673497767871pace_a] :
          ( ( member6485455074645559016pace_a @ X4 @ A2 )
         => ( member_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member5008716543664893436ce_a_b @ F @ ( pi_Pro8257876842545441995ce_a_b @ A2 @ B2 ) ) ) ).

% Pi_I
thf(fact_283_Pi__I,axiom,
    ! [A2: set_b,F: b > probab4737552677800996672pace_b,B2: b > set_Pr8527670263787538336pace_b] :
      ( ! [X4: b] :
          ( ( member_b @ X4 @ A2 )
         => ( member6485455078948787817pace_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member1568243296417166973pace_b @ F @ ( pi_b_P4583323225783748044pace_b @ A2 @ B2 ) ) ) ).

% Pi_I
thf(fact_284_Pi__I,axiom,
    ! [A2: set_a,F: a > probab4737552673497767871pace_a,B2: a > set_Pr8456636223741192351pace_a] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member6485455074645559016pace_a @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member7269867574344811837pace_a @ F @ ( pi_a_P1132609502599734284pace_a @ A2 @ B2 ) ) ) ).

% Pi_I
thf(fact_285_Pi__I,axiom,
    ! [A2: set_Pr8456636223741192351pace_a,F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ! [X4: probab4737552673497767871pace_a] :
          ( ( member6485455074645559016pace_a @ X4 @ A2 )
         => ( member6485455078948787817pace_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member6667749562321684925pace_b @ F @ ( pi_Pro4287250843231025420pace_b @ A2 @ B2 ) ) ) ).

% Pi_I
thf(fact_286_Pi__I,axiom,
    ! [A2: set_a,F: a > probab8624551251471354625pace_b,B2: a > set_Pr2974436765678502625pace_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member7462078926031725098pace_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member41169580844105599pace_b @ F @ ( pi_a_P2860934570321248078pace_b @ A2 @ B2 ) ) ) ).

% Pi_I
thf(fact_287_Pi__I,axiom,
    ! [A2: set_a_b,F: ( a > b ) > a > b,B2: ( a > b ) > set_a_b] :
      ( ! [X4: a > b] :
          ( ( member_a_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member_a_b_a_b @ F @ ( pi_a_b_a_b @ A2 @ B2 ) ) ) ).

% Pi_I
thf(fact_288_Pi__I,axiom,
    ! [A2: set_a_3263942136899480541pace_b,F: ( a > probab4737552677800996672pace_b ) > a > b,B2: ( a > probab4737552677800996672pace_b ) > set_a_b] :
      ( ! [X4: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member4717814410477825091_b_a_b @ F @ ( pi_a_P7357289706263199834_b_a_b @ A2 @ B2 ) ) ) ).

% Pi_I
thf(fact_289_Pi__I,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,F: ( probab4737552673497767871pace_a > b ) > a > b,B2: ( probab4737552673497767871pace_a > b ) > set_a_b] :
      ( ! [X4: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member2025916712706589185_b_a_b @ F @ ( pi_Pro4665392008491963928_b_a_b @ A2 @ B2 ) ) ) ).

% Pi_I
thf(fact_290_map__qbs__space,axiom,
    ! [F: probab4737552677800996672pace_b > probab4737552677800996672pace_b,X: quasi_3431323906171122406pace_b] :
      ( ( qbs_sp9192884687904738934pace_b @ ( map_qb1329406749815073291pace_b @ F @ X ) )
      = ( image_8482562952832070661pace_b @ F @ ( qbs_sp9192884687904738934pace_b @ X ) ) ) ).

% map_qbs_space
thf(fact_291_map__qbs__space,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,X: quasi_3360289866124776421pace_a] :
      ( ( qbs_sp9192884687904738934pace_b @ ( map_qb4756624968136673100pace_b @ F @ X ) )
      = ( image_2686409134298894662pace_b @ F @ ( qbs_sp9192884683601510133pace_a @ X ) ) ) ).

% map_qbs_space
thf(fact_292_map__qbs__space,axiom,
    ! [F: probab4737552677800996672pace_b > probab4737552673497767871pace_a,X: quasi_3431323906171122406pace_b] :
      ( ( qbs_sp9192884683601510133pace_a @ ( map_qb1329406745511844490pace_a @ F @ X ) )
      = ( image_8482562948528841860pace_a @ F @ ( qbs_sp9192884687904738934pace_b @ X ) ) ) ).

% map_qbs_space
thf(fact_293_map__qbs__space,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552673497767871pace_a,X: quasi_3360289866124776421pace_a] :
      ( ( qbs_sp9192884683601510133pace_a @ ( map_qb4756624963833444299pace_a @ F @ X ) )
      = ( image_2686409129995665861pace_a @ F @ ( qbs_sp9192884683601510133pace_a @ X ) ) ) ).

% map_qbs_space
thf(fact_294_imageE,axiom,
    ! [B: a > b,F: ( a > b ) > a > b,A2: set_a_b] :
      ( ( member_a_b @ B @ ( image_a_b_a_b @ F @ A2 ) )
     => ~ ! [X4: a > b] :
            ( ( B
              = ( F @ X4 ) )
           => ~ ( member_a_b @ X4 @ A2 ) ) ) ).

% imageE
thf(fact_295_imageE,axiom,
    ! [B: a > probab4737552677800996672pace_b,F: ( a > b ) > a > probab4737552677800996672pace_b,A2: set_a_b] :
      ( ( member7340901614391157822pace_b @ B @ ( image_6394579700060191636pace_b @ F @ A2 ) )
     => ~ ! [X4: a > b] :
            ( ( B
              = ( F @ X4 ) )
           => ~ ( member_a_b @ X4 @ A2 ) ) ) ).

% imageE
thf(fact_296_imageE,axiom,
    ! [B: probab4737552673497767871pace_a > b,F: ( a > b ) > probab4737552673497767871pace_a > b,A2: set_a_b] :
      ( ( member5008716543664893436ce_a_b @ B @ ( image_4062394629333927250ce_a_b @ F @ A2 ) )
     => ~ ! [X4: a > b] :
            ( ( B
              = ( F @ X4 ) )
           => ~ ( member_a_b @ X4 @ A2 ) ) ) ).

% imageE
thf(fact_297_imageE,axiom,
    ! [B: b > probab4737552677800996672pace_b,F: ( a > b ) > b > probab4737552677800996672pace_b,A2: set_a_b] :
      ( ( member1568243296417166973pace_b @ B @ ( image_621921382086200787pace_b @ F @ A2 ) )
     => ~ ! [X4: a > b] :
            ( ( B
              = ( F @ X4 ) )
           => ~ ( member_a_b @ X4 @ A2 ) ) ) ).

% imageE
thf(fact_298_imageE,axiom,
    ! [B: a > probab4737552673497767871pace_a,F: ( a > b ) > a > probab4737552673497767871pace_a,A2: set_a_b] :
      ( ( member7269867574344811837pace_a @ B @ ( image_6323545660013845651pace_a @ F @ A2 ) )
     => ~ ! [X4: a > b] :
            ( ( B
              = ( F @ X4 ) )
           => ~ ( member_a_b @ X4 @ A2 ) ) ) ).

% imageE
thf(fact_299_imageE,axiom,
    ! [B: a > b,F: ( a > probab4737552677800996672pace_b ) > a > b,A2: set_a_3263942136899480541pace_b] :
      ( ( member_a_b @ B @ ( image_5357422296895858068_b_a_b @ F @ A2 ) )
     => ~ ! [X4: a > probab4737552677800996672pace_b] :
            ( ( B
              = ( F @ X4 ) )
           => ~ ( member7340901614391157822pace_b @ X4 @ A2 ) ) ) ).

% imageE
thf(fact_300_imageE,axiom,
    ! [B: a > b,F: ( probab4737552673497767871pace_a > b ) > a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( member_a_b @ B @ ( image_2665524599124622162_b_a_b @ F @ A2 ) )
     => ~ ! [X4: probab4737552673497767871pace_a > b] :
            ( ( B
              = ( F @ X4 ) )
           => ~ ( member5008716543664893436ce_a_b @ X4 @ A2 ) ) ) ).

% imageE
thf(fact_301_imageE,axiom,
    ! [B: a > b,F: ( b > probab4737552677800996672pace_b ) > a > b,A2: set_b_9060095955432656540pace_b] :
      ( ( member_a_b @ B @ ( image_8215988703474630099_b_a_b @ F @ A2 ) )
     => ~ ! [X4: b > probab4737552677800996672pace_b] :
            ( ( B
              = ( F @ X4 ) )
           => ~ ( member1568243296417166973pace_b @ X4 @ A2 ) ) ) ).

% imageE
thf(fact_302_imageE,axiom,
    ! [B: a > b,F: ( a > probab4737552673497767871pace_a ) > a > b,A2: set_a_5785126655188516188pace_a] :
      ( ( member_a_b @ B @ ( image_7482003829499661459_a_a_b @ F @ A2 ) )
     => ~ ! [X4: a > probab4737552673497767871pace_a] :
            ( ( B
              = ( F @ X4 ) )
           => ~ ( member7269867574344811837pace_a @ X4 @ A2 ) ) ) ).

% imageE
thf(fact_303_imageE,axiom,
    ! [B: probab4737552673497767871pace_a > probab4737552677800996672pace_b,F: ( a > b ) > probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_a_b] :
      ( ( member6667749562321684925pace_b @ B @ ( image_8327537902732214547pace_b @ F @ A2 ) )
     => ~ ! [X4: a > b] :
            ( ( B
              = ( F @ X4 ) )
           => ~ ( member_a_b @ X4 @ A2 ) ) ) ).

% imageE
thf(fact_304_Compr__image__eq,axiom,
    ! [F: ( a > b ) > a > b,A2: set_a_b,P: ( a > b ) > $o] :
      ( ( collect_a_b
        @ ^ [X2: a > b] :
            ( ( member_a_b @ X2 @ ( image_a_b_a_b @ F @ A2 ) )
            & ( P @ X2 ) ) )
      = ( image_a_b_a_b @ F
        @ ( collect_a_b
          @ ^ [X2: a > b] :
              ( ( member_a_b @ X2 @ A2 )
              & ( P @ ( F @ X2 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_305_Compr__image__eq,axiom,
    ! [F: ( a > b ) > a > probab4737552677800996672pace_b,A2: set_a_b,P: ( a > probab4737552677800996672pace_b ) > $o] :
      ( ( collec5907158909762593660pace_b
        @ ^ [X2: a > probab4737552677800996672pace_b] :
            ( ( member7340901614391157822pace_b @ X2 @ ( image_6394579700060191636pace_b @ F @ A2 ) )
            & ( P @ X2 ) ) )
      = ( image_6394579700060191636pace_b @ F
        @ ( collect_a_b
          @ ^ [X2: a > b] :
              ( ( member_a_b @ X2 @ A2 )
              & ( P @ ( F @ X2 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_306_Compr__image__eq,axiom,
    ! [F: ( a > b ) > probab4737552673497767871pace_a > b,A2: set_a_b,P: ( probab4737552673497767871pace_a > b ) > $o] :
      ( ( collec3574973839036329274ce_a_b
        @ ^ [X2: probab4737552673497767871pace_a > b] :
            ( ( member5008716543664893436ce_a_b @ X2 @ ( image_4062394629333927250ce_a_b @ F @ A2 ) )
            & ( P @ X2 ) ) )
      = ( image_4062394629333927250ce_a_b @ F
        @ ( collect_a_b
          @ ^ [X2: a > b] :
              ( ( member_a_b @ X2 @ A2 )
              & ( P @ ( F @ X2 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_307_Compr__image__eq,axiom,
    ! [F: ( a > b ) > b > probab4737552677800996672pace_b,A2: set_a_b,P: ( b > probab4737552677800996672pace_b ) > $o] :
      ( ( collec134500591788602811pace_b
        @ ^ [X2: b > probab4737552677800996672pace_b] :
            ( ( member1568243296417166973pace_b @ X2 @ ( image_621921382086200787pace_b @ F @ A2 ) )
            & ( P @ X2 ) ) )
      = ( image_621921382086200787pace_b @ F
        @ ( collect_a_b
          @ ^ [X2: a > b] :
              ( ( member_a_b @ X2 @ A2 )
              & ( P @ ( F @ X2 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_308_Compr__image__eq,axiom,
    ! [F: ( a > b ) > a > probab4737552673497767871pace_a,A2: set_a_b,P: ( a > probab4737552673497767871pace_a ) > $o] :
      ( ( collec5836124869716247675pace_a
        @ ^ [X2: a > probab4737552673497767871pace_a] :
            ( ( member7269867574344811837pace_a @ X2 @ ( image_6323545660013845651pace_a @ F @ A2 ) )
            & ( P @ X2 ) ) )
      = ( image_6323545660013845651pace_a @ F
        @ ( collect_a_b
          @ ^ [X2: a > b] :
              ( ( member_a_b @ X2 @ A2 )
              & ( P @ ( F @ X2 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_309_Compr__image__eq,axiom,
    ! [F: ( a > probab4737552677800996672pace_b ) > a > b,A2: set_a_3263942136899480541pace_b,P: ( a > b ) > $o] :
      ( ( collect_a_b
        @ ^ [X2: a > b] :
            ( ( member_a_b @ X2 @ ( image_5357422296895858068_b_a_b @ F @ A2 ) )
            & ( P @ X2 ) ) )
      = ( image_5357422296895858068_b_a_b @ F
        @ ( collec5907158909762593660pace_b
          @ ^ [X2: a > probab4737552677800996672pace_b] :
              ( ( member7340901614391157822pace_b @ X2 @ A2 )
              & ( P @ ( F @ X2 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_310_Compr__image__eq,axiom,
    ! [F: ( probab4737552673497767871pace_a > b ) > a > b,A2: set_Pr8041968334489646747ce_a_b,P: ( a > b ) > $o] :
      ( ( collect_a_b
        @ ^ [X2: a > b] :
            ( ( member_a_b @ X2 @ ( image_2665524599124622162_b_a_b @ F @ A2 ) )
            & ( P @ X2 ) ) )
      = ( image_2665524599124622162_b_a_b @ F
        @ ( collec3574973839036329274ce_a_b
          @ ^ [X2: probab4737552673497767871pace_a > b] :
              ( ( member5008716543664893436ce_a_b @ X2 @ A2 )
              & ( P @ ( F @ X2 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_311_Compr__image__eq,axiom,
    ! [F: ( b > probab4737552677800996672pace_b ) > a > b,A2: set_b_9060095955432656540pace_b,P: ( a > b ) > $o] :
      ( ( collect_a_b
        @ ^ [X2: a > b] :
            ( ( member_a_b @ X2 @ ( image_8215988703474630099_b_a_b @ F @ A2 ) )
            & ( P @ X2 ) ) )
      = ( image_8215988703474630099_b_a_b @ F
        @ ( collec134500591788602811pace_b
          @ ^ [X2: b > probab4737552677800996672pace_b] :
              ( ( member1568243296417166973pace_b @ X2 @ A2 )
              & ( P @ ( F @ X2 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_312_Compr__image__eq,axiom,
    ! [F: ( a > probab4737552673497767871pace_a ) > a > b,A2: set_a_5785126655188516188pace_a,P: ( a > b ) > $o] :
      ( ( collect_a_b
        @ ^ [X2: a > b] :
            ( ( member_a_b @ X2 @ ( image_7482003829499661459_a_a_b @ F @ A2 ) )
            & ( P @ X2 ) ) )
      = ( image_7482003829499661459_a_a_b @ F
        @ ( collec5836124869716247675pace_a
          @ ^ [X2: a > probab4737552673497767871pace_a] :
              ( ( member7269867574344811837pace_a @ X2 @ A2 )
              & ( P @ ( F @ X2 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_313_Compr__image__eq,axiom,
    ! [F: ( a > b ) > probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_a_b,P: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o] :
      ( ( collec7915783404360165627pace_b
        @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
            ( ( member6667749562321684925pace_b @ X2 @ ( image_8327537902732214547pace_b @ F @ A2 ) )
            & ( P @ X2 ) ) )
      = ( image_8327537902732214547pace_b @ F
        @ ( collect_a_b
          @ ^ [X2: a > b] :
              ( ( member_a_b @ X2 @ A2 )
              & ( P @ ( F @ X2 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_314_funcset__mem,axiom,
    ! [F: a > b,A2: set_a,B2: set_b,X3: a] :
      ( ( member_a_b @ F
        @ ( pi_a_b @ A2
          @ ^ [Uu: a] : B2 ) )
     => ( ( member_a @ X3 @ A2 )
       => ( member_b @ ( F @ X3 ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_315_funcset__mem,axiom,
    ! [F: a > probab4737552677800996672pace_b,A2: set_a,B2: set_Pr8527670263787538336pace_b,X3: a] :
      ( ( member7340901614391157822pace_b @ F
        @ ( pi_a_P1132609506902963085pace_b @ A2
          @ ^ [Uu: a] : B2 ) )
     => ( ( member_a @ X3 @ A2 )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_316_funcset__mem,axiom,
    ! [F: probab4737552673497767871pace_a > b,A2: set_Pr8456636223741192351pace_a,B2: set_b,X3: probab4737552673497767871pace_a] :
      ( ( member5008716543664893436ce_a_b @ F
        @ ( pi_Pro8257876842545441995ce_a_b @ A2
          @ ^ [Uu: probab4737552673497767871pace_a] : B2 ) )
     => ( ( member6485455074645559016pace_a @ X3 @ A2 )
       => ( member_b @ ( F @ X3 ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_317_funcset__mem,axiom,
    ! [F: b > probab4737552677800996672pace_b,A2: set_b,B2: set_Pr8527670263787538336pace_b,X3: b] :
      ( ( member1568243296417166973pace_b @ F
        @ ( pi_b_P4583323225783748044pace_b @ A2
          @ ^ [Uu: b] : B2 ) )
     => ( ( member_b @ X3 @ A2 )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_318_funcset__mem,axiom,
    ! [F: a > probab4737552673497767871pace_a,A2: set_a,B2: set_Pr8456636223741192351pace_a,X3: a] :
      ( ( member7269867574344811837pace_a @ F
        @ ( pi_a_P1132609502599734284pace_a @ A2
          @ ^ [Uu: a] : B2 ) )
     => ( ( member_a @ X3 @ A2 )
       => ( member6485455074645559016pace_a @ ( F @ X3 ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_319_funcset__mem,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr8456636223741192351pace_a,B2: set_Pr8527670263787538336pace_b,X3: probab4737552673497767871pace_a] :
      ( ( member6667749562321684925pace_b @ F
        @ ( pi_Pro4287250843231025420pace_b @ A2
          @ ^ [Uu: probab4737552673497767871pace_a] : B2 ) )
     => ( ( member6485455074645559016pace_a @ X3 @ A2 )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_320_funcset__mem,axiom,
    ! [F: a > probab8624551251471354625pace_b,A2: set_a,B2: set_Pr2974436765678502625pace_b,X3: a] :
      ( ( member41169580844105599pace_b @ F
        @ ( pi_a_P2860934570321248078pace_b @ A2
          @ ^ [Uu: a] : B2 ) )
     => ( ( member_a @ X3 @ A2 )
       => ( member7462078926031725098pace_b @ ( F @ X3 ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_321_funcset__mem,axiom,
    ! [F: ( a > b ) > a > b,A2: set_a_b,B2: set_a_b,X3: a > b] :
      ( ( member_a_b_a_b @ F
        @ ( pi_a_b_a_b @ A2
          @ ^ [Uu: a > b] : B2 ) )
     => ( ( member_a_b @ X3 @ A2 )
       => ( member_a_b @ ( F @ X3 ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_322_funcset__mem,axiom,
    ! [F: ( a > probab4737552677800996672pace_b ) > a > b,A2: set_a_3263942136899480541pace_b,B2: set_a_b,X3: a > probab4737552677800996672pace_b] :
      ( ( member4717814410477825091_b_a_b @ F
        @ ( pi_a_P7357289706263199834_b_a_b @ A2
          @ ^ [Uu: a > probab4737552677800996672pace_b] : B2 ) )
     => ( ( member7340901614391157822pace_b @ X3 @ A2 )
       => ( member_a_b @ ( F @ X3 ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_323_funcset__mem,axiom,
    ! [F: ( probab4737552673497767871pace_a > b ) > a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_a_b,X3: probab4737552673497767871pace_a > b] :
      ( ( member2025916712706589185_b_a_b @ F
        @ ( pi_Pro4665392008491963928_b_a_b @ A2
          @ ^ [Uu: probab4737552673497767871pace_a > b] : B2 ) )
     => ( ( member5008716543664893436ce_a_b @ X3 @ A2 )
       => ( member_a_b @ ( F @ X3 ) @ B2 ) ) ) ).

% funcset_mem
thf(fact_324_funcsetI,axiom,
    ! [A2: set_a,F: a > b,B2: set_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member_b @ ( F @ X4 ) @ B2 ) )
     => ( member_a_b @ F
        @ ( pi_a_b @ A2
          @ ^ [Uu: a] : B2 ) ) ) ).

% funcsetI
thf(fact_325_funcsetI,axiom,
    ! [A2: set_a,F: a > probab4737552677800996672pace_b,B2: set_Pr8527670263787538336pace_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member6485455078948787817pace_b @ ( F @ X4 ) @ B2 ) )
     => ( member7340901614391157822pace_b @ F
        @ ( pi_a_P1132609506902963085pace_b @ A2
          @ ^ [Uu: a] : B2 ) ) ) ).

% funcsetI
thf(fact_326_funcsetI,axiom,
    ! [A2: set_Pr8456636223741192351pace_a,F: probab4737552673497767871pace_a > b,B2: set_b] :
      ( ! [X4: probab4737552673497767871pace_a] :
          ( ( member6485455074645559016pace_a @ X4 @ A2 )
         => ( member_b @ ( F @ X4 ) @ B2 ) )
     => ( member5008716543664893436ce_a_b @ F
        @ ( pi_Pro8257876842545441995ce_a_b @ A2
          @ ^ [Uu: probab4737552673497767871pace_a] : B2 ) ) ) ).

% funcsetI
thf(fact_327_funcsetI,axiom,
    ! [A2: set_b,F: b > probab4737552677800996672pace_b,B2: set_Pr8527670263787538336pace_b] :
      ( ! [X4: b] :
          ( ( member_b @ X4 @ A2 )
         => ( member6485455078948787817pace_b @ ( F @ X4 ) @ B2 ) )
     => ( member1568243296417166973pace_b @ F
        @ ( pi_b_P4583323225783748044pace_b @ A2
          @ ^ [Uu: b] : B2 ) ) ) ).

% funcsetI
thf(fact_328_funcsetI,axiom,
    ! [A2: set_a,F: a > probab4737552673497767871pace_a,B2: set_Pr8456636223741192351pace_a] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member6485455074645559016pace_a @ ( F @ X4 ) @ B2 ) )
     => ( member7269867574344811837pace_a @ F
        @ ( pi_a_P1132609502599734284pace_a @ A2
          @ ^ [Uu: a] : B2 ) ) ) ).

% funcsetI
thf(fact_329_funcsetI,axiom,
    ! [A2: set_Pr8456636223741192351pace_a,F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: set_Pr8527670263787538336pace_b] :
      ( ! [X4: probab4737552673497767871pace_a] :
          ( ( member6485455074645559016pace_a @ X4 @ A2 )
         => ( member6485455078948787817pace_b @ ( F @ X4 ) @ B2 ) )
     => ( member6667749562321684925pace_b @ F
        @ ( pi_Pro4287250843231025420pace_b @ A2
          @ ^ [Uu: probab4737552673497767871pace_a] : B2 ) ) ) ).

% funcsetI
thf(fact_330_funcsetI,axiom,
    ! [A2: set_a,F: a > probab8624551251471354625pace_b,B2: set_Pr2974436765678502625pace_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member7462078926031725098pace_b @ ( F @ X4 ) @ B2 ) )
     => ( member41169580844105599pace_b @ F
        @ ( pi_a_P2860934570321248078pace_b @ A2
          @ ^ [Uu: a] : B2 ) ) ) ).

% funcsetI
thf(fact_331_funcsetI,axiom,
    ! [A2: set_a_b,F: ( a > b ) > a > b,B2: set_a_b] :
      ( ! [X4: a > b] :
          ( ( member_a_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ B2 ) )
     => ( member_a_b_a_b @ F
        @ ( pi_a_b_a_b @ A2
          @ ^ [Uu: a > b] : B2 ) ) ) ).

% funcsetI
thf(fact_332_funcsetI,axiom,
    ! [A2: set_a_3263942136899480541pace_b,F: ( a > probab4737552677800996672pace_b ) > a > b,B2: set_a_b] :
      ( ! [X4: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ B2 ) )
     => ( member4717814410477825091_b_a_b @ F
        @ ( pi_a_P7357289706263199834_b_a_b @ A2
          @ ^ [Uu: a > probab4737552677800996672pace_b] : B2 ) ) ) ).

% funcsetI
thf(fact_333_funcsetI,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,F: ( probab4737552673497767871pace_a > b ) > a > b,B2: set_a_b] :
      ( ! [X4: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ B2 ) )
     => ( member2025916712706589185_b_a_b @ F
        @ ( pi_Pro4665392008491963928_b_a_b @ A2
          @ ^ [Uu: probab4737552673497767871pace_a > b] : B2 ) ) ) ).

% funcsetI
thf(fact_334_Pi__cong,axiom,
    ! [A2: set_Pr8456636223741192351pace_a,F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,G: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ! [W: probab4737552673497767871pace_a] :
          ( ( member6485455074645559016pace_a @ W @ A2 )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member6667749562321684925pace_b @ F @ ( pi_Pro4287250843231025420pace_b @ A2 @ B2 ) )
        = ( member6667749562321684925pace_b @ G @ ( pi_Pro4287250843231025420pace_b @ A2 @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_335_Pi__cong,axiom,
    ! [A2: set_a,F: a > probab4737552677800996672pace_b,G: a > probab4737552677800996672pace_b,B2: a > set_Pr8527670263787538336pace_b] :
      ( ! [W: a] :
          ( ( member_a @ W @ A2 )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member7340901614391157822pace_b @ F @ ( pi_a_P1132609506902963085pace_b @ A2 @ B2 ) )
        = ( member7340901614391157822pace_b @ G @ ( pi_a_P1132609506902963085pace_b @ A2 @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_336_Pi__cong,axiom,
    ! [A2: set_Pr8456636223741192351pace_a,F: probab4737552673497767871pace_a > b,G: probab4737552673497767871pace_a > b,B2: probab4737552673497767871pace_a > set_b] :
      ( ! [W: probab4737552673497767871pace_a] :
          ( ( member6485455074645559016pace_a @ W @ A2 )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member5008716543664893436ce_a_b @ F @ ( pi_Pro8257876842545441995ce_a_b @ A2 @ B2 ) )
        = ( member5008716543664893436ce_a_b @ G @ ( pi_Pro8257876842545441995ce_a_b @ A2 @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_337_Pi__cong,axiom,
    ! [A2: set_b,F: b > probab4737552677800996672pace_b,G: b > probab4737552677800996672pace_b,B2: b > set_Pr8527670263787538336pace_b] :
      ( ! [W: b] :
          ( ( member_b @ W @ A2 )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member1568243296417166973pace_b @ F @ ( pi_b_P4583323225783748044pace_b @ A2 @ B2 ) )
        = ( member1568243296417166973pace_b @ G @ ( pi_b_P4583323225783748044pace_b @ A2 @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_338_Pi__cong,axiom,
    ! [A2: set_a,F: a > probab8624551251471354625pace_b,G: a > probab8624551251471354625pace_b,B2: a > set_Pr2974436765678502625pace_b] :
      ( ! [W: a] :
          ( ( member_a @ W @ A2 )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member41169580844105599pace_b @ F @ ( pi_a_P2860934570321248078pace_b @ A2 @ B2 ) )
        = ( member41169580844105599pace_b @ G @ ( pi_a_P2860934570321248078pace_b @ A2 @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_339_Pi__cong,axiom,
    ! [A2: set_a,F: a > probab4737552673497767871pace_a,G: a > probab4737552673497767871pace_a,B2: a > set_Pr8456636223741192351pace_a] :
      ( ! [W: a] :
          ( ( member_a @ W @ A2 )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member7269867574344811837pace_a @ F @ ( pi_a_P1132609502599734284pace_a @ A2 @ B2 ) )
        = ( member7269867574344811837pace_a @ G @ ( pi_a_P1132609502599734284pace_a @ A2 @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_340_Pi__cong,axiom,
    ! [A2: set_a,F: a > b,G: a > b,B2: a > set_b] :
      ( ! [W: a] :
          ( ( member_a @ W @ A2 )
         => ( ( F @ W )
            = ( G @ W ) ) )
     => ( ( member_a_b @ F @ ( pi_a_b @ A2 @ B2 ) )
        = ( member_a_b @ G @ ( pi_a_b @ A2 @ B2 ) ) ) ) ).

% Pi_cong
thf(fact_341_PiE__mem,axiom,
    ! [F: a > b,S3: set_a,T: a > set_b,X3: a] :
      ( ( member_a_b @ F @ ( piE_a_b @ S3 @ T ) )
     => ( ( member_a @ X3 @ S3 )
       => ( member_b @ ( F @ X3 ) @ ( T @ X3 ) ) ) ) ).

% PiE_mem
thf(fact_342_PiE__mem,axiom,
    ! [F: a > probab4737552677800996672pace_b,S3: set_a,T: a > set_Pr8527670263787538336pace_b,X3: a] :
      ( ( member7340901614391157822pace_b @ F @ ( piE_a_4194508618861114364pace_b @ S3 @ T ) )
     => ( ( member_a @ X3 @ S3 )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( T @ X3 ) ) ) ) ).

% PiE_mem
thf(fact_343_PiE__mem,axiom,
    ! [F: probab4737552673497767871pace_a > b,S3: set_Pr8456636223741192351pace_a,T: probab4737552673497767871pace_a > set_b,X3: probab4737552673497767871pace_a] :
      ( ( member5008716543664893436ce_a_b @ F @ ( piE_Pr2096403917648817466ce_a_b @ S3 @ T ) )
     => ( ( member6485455074645559016pace_a @ X3 @ S3 )
       => ( member_b @ ( F @ X3 ) @ ( T @ X3 ) ) ) ) ).

% PiE_mem
thf(fact_344_PiE__mem,axiom,
    ! [F: b > probab4737552677800996672pace_b,S3: set_b,T: b > set_Pr8527670263787538336pace_b,X3: b] :
      ( ( member1568243296417166973pace_b @ F @ ( piE_b_7645222337741899323pace_b @ S3 @ T ) )
     => ( ( member_b @ X3 @ S3 )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( T @ X3 ) ) ) ) ).

% PiE_mem
thf(fact_345_PiE__mem,axiom,
    ! [F: a > probab4737552673497767871pace_a,S3: set_a,T: a > set_Pr8456636223741192351pace_a,X3: a] :
      ( ( member7269867574344811837pace_a @ F @ ( piE_a_4194508614557885563pace_a @ S3 @ T ) )
     => ( ( member_a @ X3 @ S3 )
       => ( member6485455074645559016pace_a @ ( F @ X3 ) @ ( T @ X3 ) ) ) ) ).

% PiE_mem
thf(fact_346_PiE__mem,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,S3: set_Pr8456636223741192351pace_a,T: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b,X3: probab4737552673497767871pace_a] :
      ( ( member6667749562321684925pace_b @ F @ ( piE_Pr1548282726383880571pace_b @ S3 @ T ) )
     => ( ( member6485455074645559016pace_a @ X3 @ S3 )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( T @ X3 ) ) ) ) ).

% PiE_mem
thf(fact_347_PiE__mem,axiom,
    ! [F: a > probab8624551251471354625pace_b,S3: set_a,T: a > set_Pr2974436765678502625pace_b,X3: a] :
      ( ( member41169580844105599pace_b @ F @ ( piE_a_121966453474103229pace_b @ S3 @ T ) )
     => ( ( member_a @ X3 @ S3 )
       => ( member7462078926031725098pace_b @ ( F @ X3 ) @ ( T @ X3 ) ) ) ) ).

% PiE_mem
thf(fact_348_PiE__mem,axiom,
    ! [F: ( a > b ) > a > b,S3: set_a_b,T: ( a > b ) > set_a_b,X3: a > b] :
      ( ( member_a_b_a_b @ F @ ( piE_a_b_a_b @ S3 @ T ) )
     => ( ( member_a_b @ X3 @ S3 )
       => ( member_a_b @ ( F @ X3 ) @ ( T @ X3 ) ) ) ) ).

% PiE_mem
thf(fact_349_PiE__mem,axiom,
    ! [F: ( a > probab4737552677800996672pace_b ) > a > b,S3: set_a_3263942136899480541pace_b,T: ( a > probab4737552677800996672pace_b ) > set_a_b,X3: a > probab4737552677800996672pace_b] :
      ( ( member4717814410477825091_b_a_b @ F @ ( piE_a_2307012063832232009_b_a_b @ S3 @ T ) )
     => ( ( member7340901614391157822pace_b @ X3 @ S3 )
       => ( member_a_b @ ( F @ X3 ) @ ( T @ X3 ) ) ) ) ).

% PiE_mem
thf(fact_350_PiE__mem,axiom,
    ! [F: ( probab4737552673497767871pace_a > b ) > a > b,S3: set_Pr8041968334489646747ce_a_b,T: ( probab4737552673497767871pace_a > b ) > set_a_b,X3: probab4737552673497767871pace_a > b] :
      ( ( member2025916712706589185_b_a_b @ F @ ( piE_Pr8838486402915771911_b_a_b @ S3 @ T ) )
     => ( ( member5008716543664893436ce_a_b @ X3 @ S3 )
       => ( member_a_b @ ( F @ X3 ) @ ( T @ X3 ) ) ) ) ).

% PiE_mem
thf(fact_351_PiE__ext,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,K: set_Pr8456636223741192351pace_a,S2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b,Y2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ( ( member6667749562321684925pace_b @ X3 @ ( piE_Pr1548282726383880571pace_b @ K @ S2 ) )
     => ( ( member6667749562321684925pace_b @ Y2 @ ( piE_Pr1548282726383880571pace_b @ K @ S2 ) )
       => ( ! [I: probab4737552673497767871pace_a] :
              ( ( member6485455074645559016pace_a @ I @ K )
             => ( ( X3 @ I )
                = ( Y2 @ I ) ) )
         => ( X3 = Y2 ) ) ) ) ).

% PiE_ext
thf(fact_352_PiE__ext,axiom,
    ! [X3: a > probab4737552677800996672pace_b,K: set_a,S2: a > set_Pr8527670263787538336pace_b,Y2: a > probab4737552677800996672pace_b] :
      ( ( member7340901614391157822pace_b @ X3 @ ( piE_a_4194508618861114364pace_b @ K @ S2 ) )
     => ( ( member7340901614391157822pace_b @ Y2 @ ( piE_a_4194508618861114364pace_b @ K @ S2 ) )
       => ( ! [I: a] :
              ( ( member_a @ I @ K )
             => ( ( X3 @ I )
                = ( Y2 @ I ) ) )
         => ( X3 = Y2 ) ) ) ) ).

% PiE_ext
thf(fact_353_PiE__ext,axiom,
    ! [X3: probab4737552673497767871pace_a > b,K: set_Pr8456636223741192351pace_a,S2: probab4737552673497767871pace_a > set_b,Y2: probab4737552673497767871pace_a > b] :
      ( ( member5008716543664893436ce_a_b @ X3 @ ( piE_Pr2096403917648817466ce_a_b @ K @ S2 ) )
     => ( ( member5008716543664893436ce_a_b @ Y2 @ ( piE_Pr2096403917648817466ce_a_b @ K @ S2 ) )
       => ( ! [I: probab4737552673497767871pace_a] :
              ( ( member6485455074645559016pace_a @ I @ K )
             => ( ( X3 @ I )
                = ( Y2 @ I ) ) )
         => ( X3 = Y2 ) ) ) ) ).

% PiE_ext
thf(fact_354_PiE__ext,axiom,
    ! [X3: b > probab4737552677800996672pace_b,K: set_b,S2: b > set_Pr8527670263787538336pace_b,Y2: b > probab4737552677800996672pace_b] :
      ( ( member1568243296417166973pace_b @ X3 @ ( piE_b_7645222337741899323pace_b @ K @ S2 ) )
     => ( ( member1568243296417166973pace_b @ Y2 @ ( piE_b_7645222337741899323pace_b @ K @ S2 ) )
       => ( ! [I: b] :
              ( ( member_b @ I @ K )
             => ( ( X3 @ I )
                = ( Y2 @ I ) ) )
         => ( X3 = Y2 ) ) ) ) ).

% PiE_ext
thf(fact_355_PiE__ext,axiom,
    ! [X3: a > probab8624551251471354625pace_b,K: set_a,S2: a > set_Pr2974436765678502625pace_b,Y2: a > probab8624551251471354625pace_b] :
      ( ( member41169580844105599pace_b @ X3 @ ( piE_a_121966453474103229pace_b @ K @ S2 ) )
     => ( ( member41169580844105599pace_b @ Y2 @ ( piE_a_121966453474103229pace_b @ K @ S2 ) )
       => ( ! [I: a] :
              ( ( member_a @ I @ K )
             => ( ( X3 @ I )
                = ( Y2 @ I ) ) )
         => ( X3 = Y2 ) ) ) ) ).

% PiE_ext
thf(fact_356_PiE__ext,axiom,
    ! [X3: a > probab4737552673497767871pace_a,K: set_a,S2: a > set_Pr8456636223741192351pace_a,Y2: a > probab4737552673497767871pace_a] :
      ( ( member7269867574344811837pace_a @ X3 @ ( piE_a_4194508614557885563pace_a @ K @ S2 ) )
     => ( ( member7269867574344811837pace_a @ Y2 @ ( piE_a_4194508614557885563pace_a @ K @ S2 ) )
       => ( ! [I: a] :
              ( ( member_a @ I @ K )
             => ( ( X3 @ I )
                = ( Y2 @ I ) ) )
         => ( X3 = Y2 ) ) ) ) ).

% PiE_ext
thf(fact_357_PiE__ext,axiom,
    ! [X3: a > b,K: set_a,S2: a > set_b,Y2: a > b] :
      ( ( member_a_b @ X3 @ ( piE_a_b @ K @ S2 ) )
     => ( ( member_a_b @ Y2 @ ( piE_a_b @ K @ S2 ) )
       => ( ! [I: a] :
              ( ( member_a @ I @ K )
             => ( ( X3 @ I )
                = ( Y2 @ I ) ) )
         => ( X3 = Y2 ) ) ) ) ).

% PiE_ext
thf(fact_358_Pi__mem,axiom,
    ! [F: a > b,A2: set_a,B2: a > set_b,X3: a] :
      ( ( member_a_b @ F @ ( pi_a_b @ A2 @ B2 ) )
     => ( ( member_a @ X3 @ A2 )
       => ( member_b @ ( F @ X3 ) @ ( B2 @ X3 ) ) ) ) ).

% Pi_mem
thf(fact_359_Pi__mem,axiom,
    ! [F: a > probab4737552677800996672pace_b,A2: set_a,B2: a > set_Pr8527670263787538336pace_b,X3: a] :
      ( ( member7340901614391157822pace_b @ F @ ( pi_a_P1132609506902963085pace_b @ A2 @ B2 ) )
     => ( ( member_a @ X3 @ A2 )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( B2 @ X3 ) ) ) ) ).

% Pi_mem
thf(fact_360_Pi__mem,axiom,
    ! [F: probab4737552673497767871pace_a > b,A2: set_Pr8456636223741192351pace_a,B2: probab4737552673497767871pace_a > set_b,X3: probab4737552673497767871pace_a] :
      ( ( member5008716543664893436ce_a_b @ F @ ( pi_Pro8257876842545441995ce_a_b @ A2 @ B2 ) )
     => ( ( member6485455074645559016pace_a @ X3 @ A2 )
       => ( member_b @ ( F @ X3 ) @ ( B2 @ X3 ) ) ) ) ).

% Pi_mem
thf(fact_361_Pi__mem,axiom,
    ! [F: b > probab4737552677800996672pace_b,A2: set_b,B2: b > set_Pr8527670263787538336pace_b,X3: b] :
      ( ( member1568243296417166973pace_b @ F @ ( pi_b_P4583323225783748044pace_b @ A2 @ B2 ) )
     => ( ( member_b @ X3 @ A2 )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( B2 @ X3 ) ) ) ) ).

% Pi_mem
thf(fact_362_Pi__mem,axiom,
    ! [F: a > probab4737552673497767871pace_a,A2: set_a,B2: a > set_Pr8456636223741192351pace_a,X3: a] :
      ( ( member7269867574344811837pace_a @ F @ ( pi_a_P1132609502599734284pace_a @ A2 @ B2 ) )
     => ( ( member_a @ X3 @ A2 )
       => ( member6485455074645559016pace_a @ ( F @ X3 ) @ ( B2 @ X3 ) ) ) ) ).

% Pi_mem
thf(fact_363_Pi__mem,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr8456636223741192351pace_a,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b,X3: probab4737552673497767871pace_a] :
      ( ( member6667749562321684925pace_b @ F @ ( pi_Pro4287250843231025420pace_b @ A2 @ B2 ) )
     => ( ( member6485455074645559016pace_a @ X3 @ A2 )
       => ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( B2 @ X3 ) ) ) ) ).

% Pi_mem
thf(fact_364_Pi__mem,axiom,
    ! [F: a > probab8624551251471354625pace_b,A2: set_a,B2: a > set_Pr2974436765678502625pace_b,X3: a] :
      ( ( member41169580844105599pace_b @ F @ ( pi_a_P2860934570321248078pace_b @ A2 @ B2 ) )
     => ( ( member_a @ X3 @ A2 )
       => ( member7462078926031725098pace_b @ ( F @ X3 ) @ ( B2 @ X3 ) ) ) ) ).

% Pi_mem
thf(fact_365_Pi__mem,axiom,
    ! [F: ( a > b ) > a > b,A2: set_a_b,B2: ( a > b ) > set_a_b,X3: a > b] :
      ( ( member_a_b_a_b @ F @ ( pi_a_b_a_b @ A2 @ B2 ) )
     => ( ( member_a_b @ X3 @ A2 )
       => ( member_a_b @ ( F @ X3 ) @ ( B2 @ X3 ) ) ) ) ).

% Pi_mem
thf(fact_366_Pi__mem,axiom,
    ! [F: ( a > probab4737552677800996672pace_b ) > a > b,A2: set_a_3263942136899480541pace_b,B2: ( a > probab4737552677800996672pace_b ) > set_a_b,X3: a > probab4737552677800996672pace_b] :
      ( ( member4717814410477825091_b_a_b @ F @ ( pi_a_P7357289706263199834_b_a_b @ A2 @ B2 ) )
     => ( ( member7340901614391157822pace_b @ X3 @ A2 )
       => ( member_a_b @ ( F @ X3 ) @ ( B2 @ X3 ) ) ) ) ).

% Pi_mem
thf(fact_367_Pi__mem,axiom,
    ! [F: ( probab4737552673497767871pace_a > b ) > a > b,A2: set_Pr8041968334489646747ce_a_b,B2: ( probab4737552673497767871pace_a > b ) > set_a_b,X3: probab4737552673497767871pace_a > b] :
      ( ( member2025916712706589185_b_a_b @ F @ ( pi_Pro4665392008491963928_b_a_b @ A2 @ B2 ) )
     => ( ( member5008716543664893436ce_a_b @ X3 @ A2 )
       => ( member_a_b @ ( F @ X3 ) @ ( B2 @ X3 ) ) ) ) ).

% Pi_mem
thf(fact_368_Pi__iff,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,I2: set_Pr8456636223741192351pace_a,X: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( member6667749562321684925pace_b @ F @ ( pi_Pro4287250843231025420pace_b @ I2 @ X ) )
      = ( ! [X2: probab4737552673497767871pace_a] :
            ( ( member6485455074645559016pace_a @ X2 @ I2 )
           => ( member6485455078948787817pace_b @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% Pi_iff
thf(fact_369_Pi__iff,axiom,
    ! [F: a > probab4737552677800996672pace_b,I2: set_a,X: a > set_Pr8527670263787538336pace_b] :
      ( ( member7340901614391157822pace_b @ F @ ( pi_a_P1132609506902963085pace_b @ I2 @ X ) )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ I2 )
           => ( member6485455078948787817pace_b @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% Pi_iff
thf(fact_370_Pi__iff,axiom,
    ! [F: probab4737552673497767871pace_a > b,I2: set_Pr8456636223741192351pace_a,X: probab4737552673497767871pace_a > set_b] :
      ( ( member5008716543664893436ce_a_b @ F @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ X ) )
      = ( ! [X2: probab4737552673497767871pace_a] :
            ( ( member6485455074645559016pace_a @ X2 @ I2 )
           => ( member_b @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% Pi_iff
thf(fact_371_Pi__iff,axiom,
    ! [F: b > probab4737552677800996672pace_b,I2: set_b,X: b > set_Pr8527670263787538336pace_b] :
      ( ( member1568243296417166973pace_b @ F @ ( pi_b_P4583323225783748044pace_b @ I2 @ X ) )
      = ( ! [X2: b] :
            ( ( member_b @ X2 @ I2 )
           => ( member6485455078948787817pace_b @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% Pi_iff
thf(fact_372_Pi__iff,axiom,
    ! [F: a > probab8624551251471354625pace_b,I2: set_a,X: a > set_Pr2974436765678502625pace_b] :
      ( ( member41169580844105599pace_b @ F @ ( pi_a_P2860934570321248078pace_b @ I2 @ X ) )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ I2 )
           => ( member7462078926031725098pace_b @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% Pi_iff
thf(fact_373_Pi__iff,axiom,
    ! [F: a > probab4737552673497767871pace_a,I2: set_a,X: a > set_Pr8456636223741192351pace_a] :
      ( ( member7269867574344811837pace_a @ F @ ( pi_a_P1132609502599734284pace_a @ I2 @ X ) )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ I2 )
           => ( member6485455074645559016pace_a @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% Pi_iff
thf(fact_374_Pi__iff,axiom,
    ! [F: a > b,I2: set_a,X: a > set_b] :
      ( ( member_a_b @ F @ ( pi_a_b @ I2 @ X ) )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ I2 )
           => ( member_b @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% Pi_iff
thf(fact_375_Pi__I_H,axiom,
    ! [A2: set_a,F: a > b,B2: a > set_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member_a_b @ F @ ( pi_a_b @ A2 @ B2 ) ) ) ).

% Pi_I'
thf(fact_376_Pi__I_H,axiom,
    ! [A2: set_a,F: a > probab4737552677800996672pace_b,B2: a > set_Pr8527670263787538336pace_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member6485455078948787817pace_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member7340901614391157822pace_b @ F @ ( pi_a_P1132609506902963085pace_b @ A2 @ B2 ) ) ) ).

% Pi_I'
thf(fact_377_Pi__I_H,axiom,
    ! [A2: set_Pr8456636223741192351pace_a,F: probab4737552673497767871pace_a > b,B2: probab4737552673497767871pace_a > set_b] :
      ( ! [X4: probab4737552673497767871pace_a] :
          ( ( member6485455074645559016pace_a @ X4 @ A2 )
         => ( member_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member5008716543664893436ce_a_b @ F @ ( pi_Pro8257876842545441995ce_a_b @ A2 @ B2 ) ) ) ).

% Pi_I'
thf(fact_378_Pi__I_H,axiom,
    ! [A2: set_b,F: b > probab4737552677800996672pace_b,B2: b > set_Pr8527670263787538336pace_b] :
      ( ! [X4: b] :
          ( ( member_b @ X4 @ A2 )
         => ( member6485455078948787817pace_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member1568243296417166973pace_b @ F @ ( pi_b_P4583323225783748044pace_b @ A2 @ B2 ) ) ) ).

% Pi_I'
thf(fact_379_Pi__I_H,axiom,
    ! [A2: set_a,F: a > probab4737552673497767871pace_a,B2: a > set_Pr8456636223741192351pace_a] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member6485455074645559016pace_a @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member7269867574344811837pace_a @ F @ ( pi_a_P1132609502599734284pace_a @ A2 @ B2 ) ) ) ).

% Pi_I'
thf(fact_380_Pi__I_H,axiom,
    ! [A2: set_Pr8456636223741192351pace_a,F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ! [X4: probab4737552673497767871pace_a] :
          ( ( member6485455074645559016pace_a @ X4 @ A2 )
         => ( member6485455078948787817pace_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member6667749562321684925pace_b @ F @ ( pi_Pro4287250843231025420pace_b @ A2 @ B2 ) ) ) ).

% Pi_I'
thf(fact_381_Pi__I_H,axiom,
    ! [A2: set_a,F: a > probab8624551251471354625pace_b,B2: a > set_Pr2974436765678502625pace_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member7462078926031725098pace_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member41169580844105599pace_b @ F @ ( pi_a_P2860934570321248078pace_b @ A2 @ B2 ) ) ) ).

% Pi_I'
thf(fact_382_Pi__I_H,axiom,
    ! [A2: set_a_b,F: ( a > b ) > a > b,B2: ( a > b ) > set_a_b] :
      ( ! [X4: a > b] :
          ( ( member_a_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member_a_b_a_b @ F @ ( pi_a_b_a_b @ A2 @ B2 ) ) ) ).

% Pi_I'
thf(fact_383_Pi__I_H,axiom,
    ! [A2: set_a_3263942136899480541pace_b,F: ( a > probab4737552677800996672pace_b ) > a > b,B2: ( a > probab4737552677800996672pace_b ) > set_a_b] :
      ( ! [X4: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member4717814410477825091_b_a_b @ F @ ( pi_a_P7357289706263199834_b_a_b @ A2 @ B2 ) ) ) ).

% Pi_I'
thf(fact_384_Pi__I_H,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,F: ( probab4737552673497767871pace_a > b ) > a > b,B2: ( probab4737552673497767871pace_a > b ) > set_a_b] :
      ( ! [X4: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member2025916712706589185_b_a_b @ F @ ( pi_Pro4665392008491963928_b_a_b @ A2 @ B2 ) ) ) ).

% Pi_I'
thf(fact_385_PiE,axiom,
    ! [F: a > b,A2: set_a,B2: a > set_b,X3: a] :
      ( ( member_a_b @ F @ ( pi_a_b @ A2 @ B2 ) )
     => ( ~ ( member_b @ ( F @ X3 ) @ ( B2 @ X3 ) )
       => ~ ( member_a @ X3 @ A2 ) ) ) ).

% PiE
thf(fact_386_PiE,axiom,
    ! [F: a > probab4737552677800996672pace_b,A2: set_a,B2: a > set_Pr8527670263787538336pace_b,X3: a] :
      ( ( member7340901614391157822pace_b @ F @ ( pi_a_P1132609506902963085pace_b @ A2 @ B2 ) )
     => ( ~ ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( B2 @ X3 ) )
       => ~ ( member_a @ X3 @ A2 ) ) ) ).

% PiE
thf(fact_387_PiE,axiom,
    ! [F: probab4737552673497767871pace_a > b,A2: set_Pr8456636223741192351pace_a,B2: probab4737552673497767871pace_a > set_b,X3: probab4737552673497767871pace_a] :
      ( ( member5008716543664893436ce_a_b @ F @ ( pi_Pro8257876842545441995ce_a_b @ A2 @ B2 ) )
     => ( ~ ( member_b @ ( F @ X3 ) @ ( B2 @ X3 ) )
       => ~ ( member6485455074645559016pace_a @ X3 @ A2 ) ) ) ).

% PiE
thf(fact_388_PiE,axiom,
    ! [F: b > probab4737552677800996672pace_b,A2: set_b,B2: b > set_Pr8527670263787538336pace_b,X3: b] :
      ( ( member1568243296417166973pace_b @ F @ ( pi_b_P4583323225783748044pace_b @ A2 @ B2 ) )
     => ( ~ ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( B2 @ X3 ) )
       => ~ ( member_b @ X3 @ A2 ) ) ) ).

% PiE
thf(fact_389_PiE,axiom,
    ! [F: a > probab4737552673497767871pace_a,A2: set_a,B2: a > set_Pr8456636223741192351pace_a,X3: a] :
      ( ( member7269867574344811837pace_a @ F @ ( pi_a_P1132609502599734284pace_a @ A2 @ B2 ) )
     => ( ~ ( member6485455074645559016pace_a @ ( F @ X3 ) @ ( B2 @ X3 ) )
       => ~ ( member_a @ X3 @ A2 ) ) ) ).

% PiE
thf(fact_390_PiE,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr8456636223741192351pace_a,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b,X3: probab4737552673497767871pace_a] :
      ( ( member6667749562321684925pace_b @ F @ ( pi_Pro4287250843231025420pace_b @ A2 @ B2 ) )
     => ( ~ ( member6485455078948787817pace_b @ ( F @ X3 ) @ ( B2 @ X3 ) )
       => ~ ( member6485455074645559016pace_a @ X3 @ A2 ) ) ) ).

% PiE
thf(fact_391_PiE,axiom,
    ! [F: a > probab8624551251471354625pace_b,A2: set_a,B2: a > set_Pr2974436765678502625pace_b,X3: a] :
      ( ( member41169580844105599pace_b @ F @ ( pi_a_P2860934570321248078pace_b @ A2 @ B2 ) )
     => ( ~ ( member7462078926031725098pace_b @ ( F @ X3 ) @ ( B2 @ X3 ) )
       => ~ ( member_a @ X3 @ A2 ) ) ) ).

% PiE
thf(fact_392_PiE,axiom,
    ! [F: ( a > b ) > a > b,A2: set_a_b,B2: ( a > b ) > set_a_b,X3: a > b] :
      ( ( member_a_b_a_b @ F @ ( pi_a_b_a_b @ A2 @ B2 ) )
     => ( ~ ( member_a_b @ ( F @ X3 ) @ ( B2 @ X3 ) )
       => ~ ( member_a_b @ X3 @ A2 ) ) ) ).

% PiE
thf(fact_393_PiE,axiom,
    ! [F: ( a > b ) > a > probab4737552677800996672pace_b,A2: set_a_b,B2: ( a > b ) > set_a_3263942136899480541pace_b,X3: a > b] :
      ( ( member1663858255587783107pace_b @ F @ ( pi_a_b8394447109427533402pace_b @ A2 @ B2 ) )
     => ( ~ ( member7340901614391157822pace_b @ ( F @ X3 ) @ ( B2 @ X3 ) )
       => ~ ( member_a_b @ X3 @ A2 ) ) ) ).

% PiE
thf(fact_394_PiE,axiom,
    ! [F: ( a > b ) > probab4737552673497767871pace_a > b,A2: set_a_b,B2: ( a > b ) > set_Pr8041968334489646747ce_a_b,X3: a > b] :
      ( ( member6441884453177949313ce_a_b @ F @ ( pi_a_b6062262038701269016ce_a_b @ A2 @ B2 ) )
     => ( ~ ( member5008716543664893436ce_a_b @ ( F @ X3 ) @ ( B2 @ X3 ) )
       => ~ ( member_a_b @ X3 @ A2 ) ) ) ).

% PiE
thf(fact_395_rev__image__eqI,axiom,
    ! [X3: a > b,A2: set_a_b,B: a > b,F: ( a > b ) > a > b] :
      ( ( member_a_b @ X3 @ A2 )
     => ( ( B
          = ( F @ X3 ) )
       => ( member_a_b @ B @ ( image_a_b_a_b @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_396_rev__image__eqI,axiom,
    ! [X3: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B: a > b,F: ( a > probab4737552677800996672pace_b ) > a > b] :
      ( ( member7340901614391157822pace_b @ X3 @ A2 )
     => ( ( B
          = ( F @ X3 ) )
       => ( member_a_b @ B @ ( image_5357422296895858068_b_a_b @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_397_rev__image__eqI,axiom,
    ! [X3: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B: a > b,F: ( probab4737552673497767871pace_a > b ) > a > b] :
      ( ( member5008716543664893436ce_a_b @ X3 @ A2 )
     => ( ( B
          = ( F @ X3 ) )
       => ( member_a_b @ B @ ( image_2665524599124622162_b_a_b @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_398_rev__image__eqI,axiom,
    ! [X3: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B: a > b,F: ( b > probab4737552677800996672pace_b ) > a > b] :
      ( ( member1568243296417166973pace_b @ X3 @ A2 )
     => ( ( B
          = ( F @ X3 ) )
       => ( member_a_b @ B @ ( image_8215988703474630099_b_a_b @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_399_rev__image__eqI,axiom,
    ! [X3: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B: a > b,F: ( a > probab4737552673497767871pace_a ) > a > b] :
      ( ( member7269867574344811837pace_a @ X3 @ A2 )
     => ( ( B
          = ( F @ X3 ) )
       => ( member_a_b @ B @ ( image_7482003829499661459_a_a_b @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_400_rev__image__eqI,axiom,
    ! [X3: a > b,A2: set_a_b,B: a > probab4737552677800996672pace_b,F: ( a > b ) > a > probab4737552677800996672pace_b] :
      ( ( member_a_b @ X3 @ A2 )
     => ( ( B
          = ( F @ X3 ) )
       => ( member7340901614391157822pace_b @ B @ ( image_6394579700060191636pace_b @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_401_rev__image__eqI,axiom,
    ! [X3: a > b,A2: set_a_b,B: probab4737552673497767871pace_a > b,F: ( a > b ) > probab4737552673497767871pace_a > b] :
      ( ( member_a_b @ X3 @ A2 )
     => ( ( B
          = ( F @ X3 ) )
       => ( member5008716543664893436ce_a_b @ B @ ( image_4062394629333927250ce_a_b @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_402_rev__image__eqI,axiom,
    ! [X3: a > b,A2: set_a_b,B: b > probab4737552677800996672pace_b,F: ( a > b ) > b > probab4737552677800996672pace_b] :
      ( ( member_a_b @ X3 @ A2 )
     => ( ( B
          = ( F @ X3 ) )
       => ( member1568243296417166973pace_b @ B @ ( image_621921382086200787pace_b @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_403_rev__image__eqI,axiom,
    ! [X3: a > b,A2: set_a_b,B: a > probab4737552673497767871pace_a,F: ( a > b ) > a > probab4737552673497767871pace_a] :
      ( ( member_a_b @ X3 @ A2 )
     => ( ( B
          = ( F @ X3 ) )
       => ( member7269867574344811837pace_a @ B @ ( image_6323545660013845651pace_a @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_404_rev__image__eqI,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B: a > b,F: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > a > b] :
      ( ( member6667749562321684925pace_b @ X3 @ A2 )
     => ( ( B
          = ( F @ X3 ) )
       => ( member_a_b @ B @ ( image_750332364051833107_b_a_b @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_405_imageI,axiom,
    ! [X3: a > b,A2: set_a_b,F: ( a > b ) > a > b] :
      ( ( member_a_b @ X3 @ A2 )
     => ( member_a_b @ ( F @ X3 ) @ ( image_a_b_a_b @ F @ A2 ) ) ) ).

% imageI
thf(fact_406_imageI,axiom,
    ! [X3: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,F: ( a > probab4737552677800996672pace_b ) > a > b] :
      ( ( member7340901614391157822pace_b @ X3 @ A2 )
     => ( member_a_b @ ( F @ X3 ) @ ( image_5357422296895858068_b_a_b @ F @ A2 ) ) ) ).

% imageI
thf(fact_407_imageI,axiom,
    ! [X3: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,F: ( probab4737552673497767871pace_a > b ) > a > b] :
      ( ( member5008716543664893436ce_a_b @ X3 @ A2 )
     => ( member_a_b @ ( F @ X3 ) @ ( image_2665524599124622162_b_a_b @ F @ A2 ) ) ) ).

% imageI
thf(fact_408_imageI,axiom,
    ! [X3: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,F: ( b > probab4737552677800996672pace_b ) > a > b] :
      ( ( member1568243296417166973pace_b @ X3 @ A2 )
     => ( member_a_b @ ( F @ X3 ) @ ( image_8215988703474630099_b_a_b @ F @ A2 ) ) ) ).

% imageI
thf(fact_409_imageI,axiom,
    ! [X3: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,F: ( a > probab4737552673497767871pace_a ) > a > b] :
      ( ( member7269867574344811837pace_a @ X3 @ A2 )
     => ( member_a_b @ ( F @ X3 ) @ ( image_7482003829499661459_a_a_b @ F @ A2 ) ) ) ).

% imageI
thf(fact_410_imageI,axiom,
    ! [X3: a > b,A2: set_a_b,F: ( a > b ) > a > probab4737552677800996672pace_b] :
      ( ( member_a_b @ X3 @ A2 )
     => ( member7340901614391157822pace_b @ ( F @ X3 ) @ ( image_6394579700060191636pace_b @ F @ A2 ) ) ) ).

% imageI
thf(fact_411_imageI,axiom,
    ! [X3: a > b,A2: set_a_b,F: ( a > b ) > probab4737552673497767871pace_a > b] :
      ( ( member_a_b @ X3 @ A2 )
     => ( member5008716543664893436ce_a_b @ ( F @ X3 ) @ ( image_4062394629333927250ce_a_b @ F @ A2 ) ) ) ).

% imageI
thf(fact_412_imageI,axiom,
    ! [X3: a > b,A2: set_a_b,F: ( a > b ) > b > probab4737552677800996672pace_b] :
      ( ( member_a_b @ X3 @ A2 )
     => ( member1568243296417166973pace_b @ ( F @ X3 ) @ ( image_621921382086200787pace_b @ F @ A2 ) ) ) ).

% imageI
thf(fact_413_imageI,axiom,
    ! [X3: a > b,A2: set_a_b,F: ( a > b ) > a > probab4737552673497767871pace_a] :
      ( ( member_a_b @ X3 @ A2 )
     => ( member7269867574344811837pace_a @ ( F @ X3 ) @ ( image_6323545660013845651pace_a @ F @ A2 ) ) ) ).

% imageI
thf(fact_414_imageI,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,F: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > a > b] :
      ( ( member6667749562321684925pace_b @ X3 @ A2 )
     => ( member_a_b @ ( F @ X3 ) @ ( image_750332364051833107_b_a_b @ F @ A2 ) ) ) ).

% imageI
thf(fact_415_qbs__morphismE_I1_J,axiom,
    ! [F: probab4737552677800996672pace_b > probab4737552677800996672pace_b,X: quasi_3431323906171122406pace_b,Y: quasi_3431323906171122406pace_b] :
      ( ( member3240531344000085116pace_b @ F @ ( qbs_mo5665329929810820088pace_b @ X @ Y ) )
     => ( member3240531344000085116pace_b @ F
        @ ( pi_Pro860032624909425611pace_b @ ( qbs_sp9192884687904738934pace_b @ X )
          @ ^ [Uu: probab4737552677800996672pace_b] : ( qbs_sp9192884687904738934pace_b @ Y ) ) ) ) ).

% qbs_morphismE(1)
thf(fact_416_qbs__morphismE_I1_J,axiom,
    ! [F: probab4737552677800996672pace_b > probab4737552673497767871pace_a,X: quasi_3431323906171122406pace_b,Y: quasi_3360289866124776421pace_a] :
      ( ( member3169497303953739131pace_a @ F @ ( qbs_mo5665329925507591287pace_a @ X @ Y ) )
     => ( member3169497303953739131pace_a @ F
        @ ( pi_Pro860032620606196810pace_a @ ( qbs_sp9192884687904738934pace_b @ X )
          @ ^ [Uu: probab4737552677800996672pace_b] : ( qbs_sp9192884683601510133pace_a @ Y ) ) ) ) ).

% qbs_morphismE(1)
thf(fact_417_qbs__morphismE_I1_J,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552673497767871pace_a,X: quasi_3360289866124776421pace_a,Y: quasi_3360289866124776421pace_a] :
      ( ( member6596715522275338940pace_a @ F @ ( qbs_mo9092548143829191096pace_a @ X @ Y ) )
     => ( member6596715522275338940pace_a @ F
        @ ( pi_Pro4287250838927796619pace_a @ ( qbs_sp9192884683601510133pace_a @ X )
          @ ^ [Uu: probab4737552673497767871pace_a] : ( qbs_sp9192884683601510133pace_a @ Y ) ) ) ) ).

% qbs_morphismE(1)
thf(fact_418_qbs__morphismE_I1_J,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,X: quasi_3360289866124776421pace_a,Y: quasi_3431323906171122406pace_b] :
      ( ( member6667749562321684925pace_b @ F @ ( qbs_mo9092548148132419897pace_b @ X @ Y ) )
     => ( member6667749562321684925pace_b @ F
        @ ( pi_Pro4287250843231025420pace_b @ ( qbs_sp9192884683601510133pace_a @ X )
          @ ^ [Uu: probab4737552673497767871pace_a] : ( qbs_sp9192884687904738934pace_b @ Y ) ) ) ) ).

% qbs_morphismE(1)
thf(fact_419_qbs__morphismE_I1_J,axiom,
    ! [F: a > probab4737552677800996672pace_b,X: quasi_borel_a,Y: quasi_3431323906171122406pace_b] :
      ( ( member7340901614391157822pace_b @ F @ ( qbs_mo6277074943135278010pace_b @ X @ Y ) )
     => ( member7340901614391157822pace_b @ F
        @ ( pi_a_P1132609506902963085pace_b @ ( qbs_space_a @ X )
          @ ^ [Uu: a] : ( qbs_sp9192884687904738934pace_b @ Y ) ) ) ) ).

% qbs_morphismE(1)
thf(fact_420_qbs__morphismE_I1_J,axiom,
    ! [F: probab4737552673497767871pace_a > b,X: quasi_3360289866124776421pace_a,Y: quasi_borel_b] :
      ( ( member5008716543664893436ce_a_b @ F @ ( qbs_mo4178970241922981112ce_a_b @ X @ Y ) )
     => ( member5008716543664893436ce_a_b @ F
        @ ( pi_Pro8257876842545441995ce_a_b @ ( qbs_sp9192884683601510133pace_a @ X )
          @ ^ [Uu: probab4737552673497767871pace_a] : ( qbs_space_b @ Y ) ) ) ) ).

% qbs_morphismE(1)
thf(fact_421_qbs__morphismE_I1_J,axiom,
    ! [F: b > probab4737552677800996672pace_b,X: quasi_borel_b,Y: quasi_3431323906171122406pace_b] :
      ( ( member1568243296417166973pace_b @ F @ ( qbs_mo504416625161287161pace_b @ X @ Y ) )
     => ( member1568243296417166973pace_b @ F
        @ ( pi_b_P4583323225783748044pace_b @ ( qbs_space_b @ X )
          @ ^ [Uu: b] : ( qbs_sp9192884687904738934pace_b @ Y ) ) ) ) ).

% qbs_morphismE(1)
thf(fact_422_qbs__morphismE_I1_J,axiom,
    ! [F: a > probab8624551251471354625pace_b,X: quasi_borel_a,Y: quasi_5637586813637594663pace_b] :
      ( ( member41169580844105599pace_b @ F @ ( qbs_mo7666231875222642555pace_b @ X @ Y ) )
     => ( member41169580844105599pace_b @ F
        @ ( pi_a_P2860934570321248078pace_b @ ( qbs_space_a @ X )
          @ ^ [Uu: a] : ( qbs_sp8735164103450135095pace_b @ Y ) ) ) ) ).

% qbs_morphismE(1)
thf(fact_423_qbs__morphismE_I1_J,axiom,
    ! [F: a > probab4737552673497767871pace_a,X: quasi_borel_a,Y: quasi_3360289866124776421pace_a] :
      ( ( member7269867574344811837pace_a @ F @ ( qbs_mo6277074938832049209pace_a @ X @ Y ) )
     => ( member7269867574344811837pace_a @ F
        @ ( pi_a_P1132609502599734284pace_a @ ( qbs_space_a @ X )
          @ ^ [Uu: a] : ( qbs_sp9192884683601510133pace_a @ Y ) ) ) ) ).

% qbs_morphismE(1)
thf(fact_424_qbs__morphismE_I1_J,axiom,
    ! [F: a > b,X: quasi_borel_a,Y: quasi_borel_b] :
      ( ( member_a_b @ F @ ( qbs_morphism_a_b @ X @ Y ) )
     => ( member_a_b @ F
        @ ( pi_a_b @ ( qbs_space_a @ X )
          @ ^ [Uu: a] : ( qbs_space_b @ Y ) ) ) ) ).

% qbs_morphismE(1)
thf(fact_425_qbs__morphism__def,axiom,
    ( qbs_mo5665329929810820088pace_b
    = ( ^ [X5: quasi_3431323906171122406pace_b,Y4: quasi_3431323906171122406pace_b] :
          ( collec4488565186038565818pace_b
          @ ^ [F2: probab4737552677800996672pace_b > probab4737552677800996672pace_b] :
              ( ( member3240531344000085116pace_b @ F2
                @ ( pi_Pro860032624909425611pace_b @ ( qbs_sp9192884687904738934pace_b @ X5 )
                  @ ^ [Uu: probab4737552677800996672pace_b] : ( qbs_sp9192884687904738934pace_b @ Y4 ) ) )
              & ! [X2: real > probab4737552677800996672pace_b] :
                  ( ( member5892728515905534708pace_b @ X2 @ ( qbs_Mx4221877620443553463pace_b @ X5 ) )
                 => ( member5892728515905534708pace_b @ ( comp_P902384264663180943b_real @ F2 @ X2 ) @ ( qbs_Mx4221877620443553463pace_b @ Y4 ) ) ) ) ) ) ) ).

% qbs_morphism_def
thf(fact_426_qbs__morphism__def,axiom,
    ( qbs_mo5665329925507591287pace_a
    = ( ^ [X5: quasi_3431323906171122406pace_b,Y4: quasi_3360289866124776421pace_a] :
          ( collec4417531145992219833pace_a
          @ ^ [F2: probab4737552677800996672pace_b > probab4737552673497767871pace_a] :
              ( ( member3169497303953739131pace_a @ F2
                @ ( pi_Pro860032620606196810pace_a @ ( qbs_sp9192884687904738934pace_b @ X5 )
                  @ ^ [Uu: probab4737552677800996672pace_b] : ( qbs_sp9192884683601510133pace_a @ Y4 ) ) )
              & ! [X2: real > probab4737552677800996672pace_b] :
                  ( ( member5892728515905534708pace_b @ X2 @ ( qbs_Mx4221877620443553463pace_b @ X5 ) )
                 => ( member5821694475859188723pace_a @ ( comp_P3681088572523203470a_real @ F2 @ X2 ) @ ( qbs_Mx4221877616140324662pace_a @ Y4 ) ) ) ) ) ) ) ).

% qbs_morphism_def
thf(fact_427_qbs__morphism__def,axiom,
    ( qbs_mo9092548143829191096pace_a
    = ( ^ [X5: quasi_3360289866124776421pace_a,Y4: quasi_3360289866124776421pace_a] :
          ( collec7844749364313819642pace_a
          @ ^ [F2: probab4737552673497767871pace_a > probab4737552673497767871pace_a] :
              ( ( member6596715522275338940pace_a @ F2
                @ ( pi_Pro4287250838927796619pace_a @ ( qbs_sp9192884683601510133pace_a @ X5 )
                  @ ^ [Uu: probab4737552673497767871pace_a] : ( qbs_sp9192884683601510133pace_a @ Y4 ) ) )
              & ! [X2: real > probab4737552673497767871pace_a] :
                  ( ( member5821694475859188723pace_a @ X2 @ ( qbs_Mx4221877616140324662pace_a @ X5 ) )
                 => ( member5821694475859188723pace_a @ ( comp_P2386351730793452623a_real @ F2 @ X2 ) @ ( qbs_Mx4221877616140324662pace_a @ Y4 ) ) ) ) ) ) ) ).

% qbs_morphism_def
thf(fact_428_qbs__morphism__def,axiom,
    ( qbs_mo9092548148132419897pace_b
    = ( ^ [X5: quasi_3360289866124776421pace_a,Y4: quasi_3431323906171122406pace_b] :
          ( collec7915783404360165627pace_b
          @ ^ [F2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
              ( ( member6667749562321684925pace_b @ F2
                @ ( pi_Pro4287250843231025420pace_b @ ( qbs_sp9192884683601510133pace_a @ X5 )
                  @ ^ [Uu: probab4737552673497767871pace_a] : ( qbs_sp9192884687904738934pace_b @ Y4 ) ) )
              & ! [X2: real > probab4737552673497767871pace_a] :
                  ( ( member5821694475859188723pace_a @ X2 @ ( qbs_Mx4221877616140324662pace_a @ X5 ) )
                 => ( member5892728515905534708pace_b @ ( comp_P8831019459788205904b_real @ F2 @ X2 ) @ ( qbs_Mx4221877620443553463pace_b @ Y4 ) ) ) ) ) ) ) ).

% qbs_morphism_def
thf(fact_429_qbs__morphism__def,axiom,
    ( qbs_mo6277074943135278010pace_b
    = ( ^ [X5: quasi_borel_a,Y4: quasi_3431323906171122406pace_b] :
          ( collec5907158909762593660pace_b
          @ ^ [F2: a > probab4737552677800996672pace_b] :
              ( ( member7340901614391157822pace_b @ F2
                @ ( pi_a_P1132609506902963085pace_b @ ( qbs_space_a @ X5 )
                  @ ^ [Uu: a] : ( qbs_sp9192884687904738934pace_b @ Y4 ) ) )
              & ! [X2: real > a] :
                  ( ( member_real_a @ X2 @ ( qbs_Mx_a @ X5 ) )
                 => ( member5892728515905534708pace_b @ ( comp_a6868616473110226257b_real @ F2 @ X2 ) @ ( qbs_Mx4221877620443553463pace_b @ Y4 ) ) ) ) ) ) ) ).

% qbs_morphism_def
thf(fact_430_qbs__morphism__def,axiom,
    ( qbs_mo4178970241922981112ce_a_b
    = ( ^ [X5: quasi_3360289866124776421pace_a,Y4: quasi_borel_b] :
          ( collec3574973839036329274ce_a_b
          @ ^ [F2: probab4737552673497767871pace_a > b] :
              ( ( member5008716543664893436ce_a_b @ F2
                @ ( pi_Pro8257876842545441995ce_a_b @ ( qbs_sp9192884683601510133pace_a @ X5 )
                  @ ^ [Uu: probab4737552673497767871pace_a] : ( qbs_space_b @ Y4 ) ) )
              & ! [X2: real > probab4737552673497767871pace_a] :
                  ( ( member5821694475859188723pace_a @ X2 @ ( qbs_Mx4221877616140324662pace_a @ X5 ) )
                 => ( member_real_b @ ( comp_P3348619169354409871b_real @ F2 @ X2 ) @ ( qbs_Mx_b @ Y4 ) ) ) ) ) ) ) ).

% qbs_morphism_def
thf(fact_431_qbs__morphism__def,axiom,
    ( qbs_mo504416625161287161pace_b
    = ( ^ [X5: quasi_borel_b,Y4: quasi_3431323906171122406pace_b] :
          ( collec134500591788602811pace_b
          @ ^ [F2: b > probab4737552677800996672pace_b] :
              ( ( member1568243296417166973pace_b @ F2
                @ ( pi_b_P4583323225783748044pace_b @ ( qbs_space_b @ X5 )
                  @ ^ [Uu: b] : ( qbs_sp9192884687904738934pace_b @ Y4 ) ) )
              & ! [X2: real > b] :
                  ( ( member_real_b @ X2 @ ( qbs_Mx_b @ X5 ) )
                 => ( member5892728515905534708pace_b @ ( comp_b4925389053965159440b_real @ F2 @ X2 ) @ ( qbs_Mx4221877620443553463pace_b @ Y4 ) ) ) ) ) ) ) ).

% qbs_morphism_def
thf(fact_432_qbs__morphism__def,axiom,
    ( qbs_mo7666231875222642555pace_b
    = ( ^ [X5: quasi_borel_a,Y4: quasi_5637586813637594663pace_b] :
          ( collec1289203422882586301pace_b
          @ ^ [F2: a > probab8624551251471354625pace_b] :
              ( ( member41169580844105599pace_b @ F2
                @ ( pi_a_P2860934570321248078pace_b @ ( qbs_space_a @ X5 )
                  @ ^ [Uu: a] : ( qbs_sp8735164103450135095pace_b @ Y4 ) ) )
              & ! [X2: real > a] :
                  ( ( member_real_a @ X2 @ ( qbs_Mx_a @ X5 ) )
                 => ( member4880162955186484789pace_b @ ( comp_a6393136188637473938b_real @ F2 @ X2 ) @ ( qbs_Mx7464101204346440312pace_b @ Y4 ) ) ) ) ) ) ) ).

% qbs_morphism_def
thf(fact_433_qbs__morphism__def,axiom,
    ( qbs_mo6277074938832049209pace_a
    = ( ^ [X5: quasi_borel_a,Y4: quasi_3360289866124776421pace_a] :
          ( collec5836124869716247675pace_a
          @ ^ [F2: a > probab4737552673497767871pace_a] :
              ( ( member7269867574344811837pace_a @ F2
                @ ( pi_a_P1132609502599734284pace_a @ ( qbs_space_a @ X5 )
                  @ ^ [Uu: a] : ( qbs_sp9192884683601510133pace_a @ Y4 ) ) )
              & ! [X2: real > a] :
                  ( ( member_real_a @ X2 @ ( qbs_Mx_a @ X5 ) )
                 => ( member5821694475859188723pace_a @ ( comp_a423948744115472976a_real @ F2 @ X2 ) @ ( qbs_Mx4221877616140324662pace_a @ Y4 ) ) ) ) ) ) ) ).

% qbs_morphism_def
thf(fact_434_qbs__morphism__def,axiom,
    ( qbs_morphism_a_b
    = ( ^ [X5: quasi_borel_a,Y4: quasi_borel_b] :
          ( collect_a_b
          @ ^ [F2: a > b] :
              ( ( member_a_b @ F2
                @ ( pi_a_b @ ( qbs_space_a @ X5 )
                  @ ^ [Uu: a] : ( qbs_space_b @ Y4 ) ) )
              & ! [X2: real > a] :
                  ( ( member_real_a @ X2 @ ( qbs_Mx_a @ X5 ) )
                 => ( member_real_b @ ( comp_a_b_real @ F2 @ X2 ) @ ( qbs_Mx_b @ Y4 ) ) ) ) ) ) ) ).

% qbs_morphism_def
thf(fact_435_max__qbs__Mx,axiom,
    ! [X: set_Pr8527670263787538336pace_b] :
      ( ( qbs_Mx4221877620443553463pace_b @ ( max_qu2338019691940189127pace_b @ X ) )
      = ( pi_rea6523506394092168711pace_b @ top_top_set_real
        @ ^ [Uu: real] : X ) ) ).

% max_qbs_Mx
thf(fact_436_max__qbs__Mx,axiom,
    ! [X: set_Pr8456636223741192351pace_a] :
      ( ( qbs_Mx4221877616140324662pace_a @ ( max_qu2338019687636960326pace_a @ X ) )
      = ( pi_rea6523506389788939910pace_a @ top_top_set_real
        @ ^ [Uu: real] : X ) ) ).

% max_qbs_Mx
thf(fact_437_UNIV__I,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X3 @ top_to5580905317348245644pace_b ) ).

% UNIV_I
thf(fact_438_UNIV__I,axiom,
    ! [X3: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X3 @ top_to1927542458104261261pace_b ) ).

% UNIV_I
thf(fact_439_UNIV__I,axiom,
    ! [X3: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X3 @ top_to6705568655694427467ce_a_b ) ).

% UNIV_I
thf(fact_440_UNIV__I,axiom,
    ! [X3: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X3 @ top_to7723696276637437260pace_b ) ).

% UNIV_I
thf(fact_441_UNIV__I,axiom,
    ! [X3: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X3 @ top_to3828004672158774606pace_b ) ).

% UNIV_I
thf(fact_442_UNIV__I,axiom,
    ! [X3: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X3 @ top_to4448726976393296908pace_a ) ).

% UNIV_I
thf(fact_443_UNIV__I,axiom,
    ! [X3: a > b] : ( member_a_b @ X3 @ top_top_set_a_b ) ).

% UNIV_I
thf(fact_444_iso__tuple__UNIV__I,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X3 @ top_to5580905317348245644pace_b ) ).

% iso_tuple_UNIV_I
thf(fact_445_iso__tuple__UNIV__I,axiom,
    ! [X3: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X3 @ top_to1927542458104261261pace_b ) ).

% iso_tuple_UNIV_I
thf(fact_446_iso__tuple__UNIV__I,axiom,
    ! [X3: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X3 @ top_to6705568655694427467ce_a_b ) ).

% iso_tuple_UNIV_I
thf(fact_447_iso__tuple__UNIV__I,axiom,
    ! [X3: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X3 @ top_to7723696276637437260pace_b ) ).

% iso_tuple_UNIV_I
thf(fact_448_iso__tuple__UNIV__I,axiom,
    ! [X3: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X3 @ top_to3828004672158774606pace_b ) ).

% iso_tuple_UNIV_I
thf(fact_449_iso__tuple__UNIV__I,axiom,
    ! [X3: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X3 @ top_to4448726976393296908pace_a ) ).

% iso_tuple_UNIV_I
thf(fact_450_iso__tuple__UNIV__I,axiom,
    ! [X3: a > b] : ( member_a_b @ X3 @ top_top_set_a_b ) ).

% iso_tuple_UNIV_I
thf(fact_451_Ball__def,axiom,
    ( ball_P5473461039576396540pace_b
    = ( ^ [A3: set_Pr7742364250814120412pace_b,P2: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o] :
        ! [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
          ( ( member6667749562321684925pace_b @ X2 @ A3 )
         => ( P2 @ X2 ) ) ) ) ).

% Ball_def
thf(fact_452_Ball__def,axiom,
    ( ball_a4774122588079340925pace_b
    = ( ^ [A3: set_a_3263942136899480541pace_b,P2: ( a > probab4737552677800996672pace_b ) > $o] :
        ! [X2: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ X2 @ A3 )
         => ( P2 @ X2 ) ) ) ) ).

% Ball_def
thf(fact_453_Ball__def,axiom,
    ( ball_P2441937517353076539ce_a_b
    = ( ^ [A3: set_Pr8041968334489646747ce_a_b,P2: ( probab4737552673497767871pace_a > b ) > $o] :
        ! [X2: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ X2 @ A3 )
         => ( P2 @ X2 ) ) ) ) ).

% Ball_def
thf(fact_454_Ball__def,axiom,
    ( ball_b8224836306960125884pace_b
    = ( ^ [A3: set_b_9060095955432656540pace_b,P2: ( b > probab4737552677800996672pace_b ) > $o] :
        ! [X2: b > probab4737552677800996672pace_b] :
          ( ( member1568243296417166973pace_b @ X2 @ A3 )
         => ( P2 @ X2 ) ) ) ) ).

% Ball_def
thf(fact_455_Ball__def,axiom,
    ( ball_a8070253094953593022pace_b
    = ( ^ [A3: set_a_5989463605624649374pace_b,P2: ( a > probab8624551251471354625pace_b ) > $o] :
        ! [X2: a > probab8624551251471354625pace_b] :
          ( ( member41169580844105599pace_b @ X2 @ A3 )
         => ( P2 @ X2 ) ) ) ) ).

% Ball_def
thf(fact_456_Ball__def,axiom,
    ( ball_a4703088548032994940pace_a
    = ( ^ [A3: set_a_5785126655188516188pace_a,P2: ( a > probab4737552673497767871pace_a ) > $o] :
        ! [X2: a > probab4737552673497767871pace_a] :
          ( ( member7269867574344811837pace_a @ X2 @ A3 )
         => ( P2 @ X2 ) ) ) ) ).

% Ball_def
thf(fact_457_Ball__def,axiom,
    ( ball_a_b
    = ( ^ [A3: set_a_b,P2: ( a > b ) > $o] :
        ! [X2: a > b] :
          ( ( member_a_b @ X2 @ A3 )
         => ( P2 @ X2 ) ) ) ) ).

% Ball_def
thf(fact_458_UNIV__eq__I,axiom,
    ! [A2: set_Pr7742364250814120412pace_b] :
      ( ! [X4: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X4 @ A2 )
     => ( top_to5580905317348245644pace_b = A2 ) ) ).

% UNIV_eq_I
thf(fact_459_UNIV__eq__I,axiom,
    ! [A2: set_a_3263942136899480541pace_b] :
      ( ! [X4: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X4 @ A2 )
     => ( top_to1927542458104261261pace_b = A2 ) ) ).

% UNIV_eq_I
thf(fact_460_UNIV__eq__I,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b] :
      ( ! [X4: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X4 @ A2 )
     => ( top_to6705568655694427467ce_a_b = A2 ) ) ).

% UNIV_eq_I
thf(fact_461_UNIV__eq__I,axiom,
    ! [A2: set_b_9060095955432656540pace_b] :
      ( ! [X4: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X4 @ A2 )
     => ( top_to7723696276637437260pace_b = A2 ) ) ).

% UNIV_eq_I
thf(fact_462_UNIV__eq__I,axiom,
    ! [A2: set_a_5989463605624649374pace_b] :
      ( ! [X4: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X4 @ A2 )
     => ( top_to3828004672158774606pace_b = A2 ) ) ).

% UNIV_eq_I
thf(fact_463_UNIV__eq__I,axiom,
    ! [A2: set_a_5785126655188516188pace_a] :
      ( ! [X4: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X4 @ A2 )
     => ( top_to4448726976393296908pace_a = A2 ) ) ).

% UNIV_eq_I
thf(fact_464_UNIV__eq__I,axiom,
    ! [A2: set_a_b] :
      ( ! [X4: a > b] : ( member_a_b @ X4 @ A2 )
     => ( top_top_set_a_b = A2 ) ) ).

% UNIV_eq_I
thf(fact_465_UNIV__witness,axiom,
    ? [X4: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X4 @ top_to5580905317348245644pace_b ) ).

% UNIV_witness
thf(fact_466_UNIV__witness,axiom,
    ? [X4: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X4 @ top_to1927542458104261261pace_b ) ).

% UNIV_witness
thf(fact_467_UNIV__witness,axiom,
    ? [X4: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X4 @ top_to6705568655694427467ce_a_b ) ).

% UNIV_witness
thf(fact_468_UNIV__witness,axiom,
    ? [X4: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X4 @ top_to7723696276637437260pace_b ) ).

% UNIV_witness
thf(fact_469_UNIV__witness,axiom,
    ? [X4: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X4 @ top_to3828004672158774606pace_b ) ).

% UNIV_witness
thf(fact_470_UNIV__witness,axiom,
    ? [X4: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X4 @ top_to4448726976393296908pace_a ) ).

% UNIV_witness
thf(fact_471_UNIV__witness,axiom,
    ? [X4: a > b] : ( member_a_b @ X4 @ top_top_set_a_b ) ).

% UNIV_witness
thf(fact_472_DEADID_Oin__rel,axiom,
    ( ( ^ [Y5: probab4737552673497767871pace_a > probab4737552677800996672pace_b,Z2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( Y5 = Z2 ) )
    = ( ^ [A4: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B3: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
        ? [Z3: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
          ( ( member6667749562321684925pace_b @ Z3 @ top_to5580905317348245644pace_b )
          & ( ( id_Pro8631783166541050741pace_b @ Z3 )
            = A4 )
          & ( ( id_Pro8631783166541050741pace_b @ Z3 )
            = B3 ) ) ) ) ).

% DEADID.in_rel
thf(fact_473_DEADID_Oin__rel,axiom,
    ( ( ^ [Y5: a > probab4737552677800996672pace_b,Z2: a > probab4737552677800996672pace_b] : ( Y5 = Z2 ) )
    = ( ^ [A4: a > probab4737552677800996672pace_b,B3: a > probab4737552677800996672pace_b] :
        ? [Z3: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ Z3 @ top_to1927542458104261261pace_b )
          & ( ( id_a_P7518677818618203638pace_b @ Z3 )
            = A4 )
          & ( ( id_a_P7518677818618203638pace_b @ Z3 )
            = B3 ) ) ) ) ).

% DEADID.in_rel
thf(fact_474_DEADID_Oin__rel,axiom,
    ( ( ^ [Y5: probab4737552673497767871pace_a > b,Z2: probab4737552673497767871pace_a > b] : ( Y5 = Z2 ) )
    = ( ^ [A4: probab4737552673497767871pace_a > b,B3: probab4737552673497767871pace_a > b] :
        ? [Z3: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ Z3 @ top_to6705568655694427467ce_a_b )
          & ( ( id_Pro5186492747891939252ce_a_b @ Z3 )
            = A4 )
          & ( ( id_Pro5186492747891939252ce_a_b @ Z3 )
            = B3 ) ) ) ) ).

% DEADID.in_rel
thf(fact_475_DEADID_Oin__rel,axiom,
    ( ( ^ [Y5: b > probab4737552677800996672pace_b,Z2: b > probab4737552677800996672pace_b] : ( Y5 = Z2 ) )
    = ( ^ [A4: b > probab4737552677800996672pace_b,B3: b > probab4737552677800996672pace_b] :
        ? [Z3: b > probab4737552677800996672pace_b] :
          ( ( member1568243296417166973pace_b @ Z3 @ top_to7723696276637437260pace_b )
          & ( ( id_b_P1746019500644212789pace_b @ Z3 )
            = A4 )
          & ( ( id_b_P1746019500644212789pace_b @ Z3 )
            = B3 ) ) ) ) ).

% DEADID.in_rel
thf(fact_476_DEADID_Oin__rel,axiom,
    ( ( ^ [Y5: a > probab8624551251471354625pace_b,Z2: a > probab8624551251471354625pace_b] : ( Y5 = Z2 ) )
    = ( ^ [A4: a > probab8624551251471354625pace_b,B3: a > probab8624551251471354625pace_b] :
        ? [Z3: a > probab8624551251471354625pace_b] :
          ( ( member41169580844105599pace_b @ Z3 @ top_to3828004672158774606pace_b )
          & ( ( id_a_P2005203185063471415pace_b @ Z3 )
            = A4 )
          & ( ( id_a_P2005203185063471415pace_b @ Z3 )
            = B3 ) ) ) ) ).

% DEADID.in_rel
thf(fact_477_DEADID_Oin__rel,axiom,
    ( ( ^ [Y5: a > probab4737552673497767871pace_a,Z2: a > probab4737552673497767871pace_a] : ( Y5 = Z2 ) )
    = ( ^ [A4: a > probab4737552673497767871pace_a,B3: a > probab4737552673497767871pace_a] :
        ? [Z3: a > probab4737552673497767871pace_a] :
          ( ( member7269867574344811837pace_a @ Z3 @ top_to4448726976393296908pace_a )
          & ( ( id_a_P7447643778571857653pace_a @ Z3 )
            = A4 )
          & ( ( id_a_P7447643778571857653pace_a @ Z3 )
            = B3 ) ) ) ) ).

% DEADID.in_rel
thf(fact_478_DEADID_Oin__rel,axiom,
    ( ( ^ [Y5: a > b,Z2: a > b] : ( Y5 = Z2 ) )
    = ( ^ [A4: a > b,B3: a > b] :
        ? [Z3: a > b] :
          ( ( member_a_b @ Z3 @ top_top_set_a_b )
          & ( ( id_a_b @ Z3 )
            = A4 )
          & ( ( id_a_b @ Z3 )
            = B3 ) ) ) ) ).

% DEADID.in_rel
thf(fact_479_monadP__qbs__correct,axiom,
    ! [X: quasi_3431323906171122406pace_b] :
      ( ( quasi_3034280610782357560pace_b @ ( monad_1549008831671149082pace_b @ X ) )
      = ( produc7684423503814015074pace_b @ ( monad_8082909354289562930pace_b @ X ) @ ( monad_2041073082211224175pace_b @ X ) ) ) ).

% monadP_qbs_correct
thf(fact_480_monadP__qbs__correct,axiom,
    ! [X: quasi_borel_b] :
      ( ( quasi_159326149610617975pace_b @ ( monad_monadP_qbs_b @ X ) )
      = ( produc5532427567629089954pace_b @ ( monad_3932415646498543857s_Px_b @ X ) @ ( monad_4223963853064302126_MPx_b @ X ) ) ) ).

% monadP_qbs_correct
thf(fact_481_monadP__qbs__correct,axiom,
    ! [X: quasi_borel_a] :
      ( ( quasi_159326145307389174pace_a @ ( monad_monadP_qbs_a @ X ) )
      = ( produc6037706855006621922pace_a @ ( monad_3932415646498543856s_Px_a @ X ) @ ( monad_4223963853064302125_MPx_a @ X ) ) ) ).

% monadP_qbs_correct
thf(fact_482_qbs__Mx__to__X_I1_J,axiom,
    ! [Alpha: real > probab4737552677800996672pace_b,X: quasi_3431323906171122406pace_b] :
      ( ( member5892728515905534708pace_b @ Alpha @ ( qbs_Mx4221877620443553463pace_b @ X ) )
     => ( member5892728515905534708pace_b @ Alpha
        @ ( pi_rea6523506394092168711pace_b @ top_top_set_real
          @ ^ [Uu: real] : ( qbs_sp9192884687904738934pace_b @ X ) ) ) ) ).

% qbs_Mx_to_X(1)
thf(fact_483_qbs__Mx__to__X_I1_J,axiom,
    ! [Alpha: real > probab4737552673497767871pace_a,X: quasi_3360289866124776421pace_a] :
      ( ( member5821694475859188723pace_a @ Alpha @ ( qbs_Mx4221877616140324662pace_a @ X ) )
     => ( member5821694475859188723pace_a @ Alpha
        @ ( pi_rea6523506389788939910pace_a @ top_top_set_real
          @ ^ [Uu: real] : ( qbs_sp9192884683601510133pace_a @ X ) ) ) ) ).

% qbs_Mx_to_X(1)
thf(fact_484_sub__qbs__closed_I1_J,axiom,
    ! [X: quasi_3431323906171122406pace_b,U: set_Pr8527670263787538336pace_b] :
      ( qbs_cl7093787542369625847pace_b
      @ ( collec7038231833220187958pace_b
        @ ^ [F2: real > probab4737552677800996672pace_b] :
            ( ( member5892728515905534708pace_b @ F2
              @ ( pi_rea6523506394092168711pace_b @ top_top_set_real
                @ ^ [Uu: real] : ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ U ) ) )
            & ( member5892728515905534708pace_b @ F2 @ ( qbs_Mx4221877620443553463pace_b @ X ) ) ) ) ) ).

% sub_qbs_closed(1)
thf(fact_485_sub__qbs__closed_I1_J,axiom,
    ! [X: quasi_3360289866124776421pace_a,U: set_Pr8456636223741192351pace_a] :
      ( qbs_cl7093787538066397046pace_a
      @ ( collec6967197793173841973pace_a
        @ ^ [F2: real > probab4737552673497767871pace_a] :
            ( ( member5821694475859188723pace_a @ F2
              @ ( pi_rea6523506389788939910pace_a @ top_top_set_real
                @ ^ [Uu: real] : ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ U ) ) )
            & ( member5821694475859188723pace_a @ F2 @ ( qbs_Mx4221877616140324662pace_a @ X ) ) ) ) ) ).

% sub_qbs_closed(1)
thf(fact_486_sub__qbs__closed_I2_J,axiom,
    ! [X: quasi_3431323906171122406pace_b,U: set_Pr8527670263787538336pace_b] :
      ( qbs_cl1321129224395634998pace_b @ ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ U )
      @ ( collec7038231833220187958pace_b
        @ ^ [F2: real > probab4737552677800996672pace_b] :
            ( ( member5892728515905534708pace_b @ F2
              @ ( pi_rea6523506394092168711pace_b @ top_top_set_real
                @ ^ [Uu: real] : ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ U ) ) )
            & ( member5892728515905534708pace_b @ F2 @ ( qbs_Mx4221877620443553463pace_b @ X ) ) ) ) ) ).

% sub_qbs_closed(2)
thf(fact_487_sub__qbs__closed_I2_J,axiom,
    ! [X: quasi_3360289866124776421pace_a,U: set_Pr8456636223741192351pace_a] :
      ( qbs_cl1321129220092406197pace_a @ ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ U )
      @ ( collec6967197793173841973pace_a
        @ ^ [F2: real > probab4737552673497767871pace_a] :
            ( ( member5821694475859188723pace_a @ F2
              @ ( pi_rea6523506389788939910pace_a @ top_top_set_real
                @ ^ [Uu: real] : ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ U ) ) )
            & ( member5821694475859188723pace_a @ F2 @ ( qbs_Mx4221877616140324662pace_a @ X ) ) ) ) ) ).

% sub_qbs_closed(2)
thf(fact_488_subsetI,axiom,
    ! [A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ! [X4: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
          ( ( member6667749562321684925pace_b @ X4 @ A2 )
         => ( member6667749562321684925pace_b @ X4 @ B2 ) )
     => ( ord_le1280929228223758908pace_b @ A2 @ B2 ) ) ).

% subsetI
thf(fact_489_subsetI,axiom,
    ! [A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ! [X4: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ X4 @ A2 )
         => ( member7340901614391157822pace_b @ X4 @ B2 ) )
     => ( ord_le130150003083865149pace_b @ A2 @ B2 ) ) ).

% subsetI
thf(fact_490_subsetI,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ! [X4: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ X4 @ A2 )
         => ( member5008716543664893436ce_a_b @ X4 @ B2 ) )
     => ( ord_le4908176200674031355ce_a_b @ A2 @ B2 ) ) ).

% subsetI
thf(fact_491_subsetI,axiom,
    ! [A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ! [X4: b > probab4737552677800996672pace_b] :
          ( ( member1568243296417166973pace_b @ X4 @ A2 )
         => ( member1568243296417166973pace_b @ X4 @ B2 ) )
     => ( ord_le5926303821617041148pace_b @ A2 @ B2 ) ) ).

% subsetI
thf(fact_492_subsetI,axiom,
    ! [A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ! [X4: a > probab8624551251471354625pace_b] :
          ( ( member41169580844105599pace_b @ X4 @ A2 )
         => ( member41169580844105599pace_b @ X4 @ B2 ) )
     => ( ord_le8751400619889063678pace_b @ A2 @ B2 ) ) ).

% subsetI
thf(fact_493_subsetI,axiom,
    ! [A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ! [X4: a > probab4737552673497767871pace_a] :
          ( ( member7269867574344811837pace_a @ X4 @ A2 )
         => ( member7269867574344811837pace_a @ X4 @ B2 ) )
     => ( ord_le2651334521372900796pace_a @ A2 @ B2 ) ) ).

% subsetI
thf(fact_494_subsetI,axiom,
    ! [A2: set_a_b,B2: set_a_b] :
      ( ! [X4: a > b] :
          ( ( member_a_b @ X4 @ A2 )
         => ( member_a_b @ X4 @ B2 ) )
     => ( ord_less_eq_set_a_b @ A2 @ B2 ) ) ).

% subsetI
thf(fact_495_Int__iff,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ C @ ( inf_in8598470101551243374pace_b @ A2 @ B2 ) )
      = ( ( member6667749562321684925pace_b @ C @ A2 )
        & ( member6667749562321684925pace_b @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_496_Int__iff,axiom,
    ! [C: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ C @ ( inf_in3860511187648227951pace_b @ A2 @ B2 ) )
      = ( ( member7340901614391157822pace_b @ C @ A2 )
        & ( member7340901614391157822pace_b @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_497_Int__iff,axiom,
    ! [C: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ C @ ( inf_in8638537385238394157ce_a_b @ A2 @ B2 ) )
      = ( ( member5008716543664893436ce_a_b @ C @ A2 )
        & ( member5008716543664893436ce_a_b @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_498_Int__iff,axiom,
    ! [C: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ C @ ( inf_in433292969326628142pace_b @ A2 @ B2 ) )
      = ( ( member1568243296417166973pace_b @ C @ A2 )
        & ( member1568243296417166973pace_b @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_499_Int__iff,axiom,
    ! [C: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ C @ ( inf_in6845569456361772336pace_b @ A2 @ B2 ) )
      = ( ( member41169580844105599pace_b @ C @ A2 )
        & ( member41169580844105599pace_b @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_500_Int__iff,axiom,
    ! [C: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ C @ ( inf_in6381695705937263598pace_a @ A2 @ B2 ) )
      = ( ( member7269867574344811837pace_a @ C @ A2 )
        & ( member7269867574344811837pace_a @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_501_Int__iff,axiom,
    ! [C: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( member_a_b @ C @ ( inf_inf_set_a_b @ A2 @ B2 ) )
      = ( ( member_a_b @ C @ A2 )
        & ( member_a_b @ C @ B2 ) ) ) ).

% Int_iff
thf(fact_502_IntI,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ C @ A2 )
     => ( ( member6667749562321684925pace_b @ C @ B2 )
       => ( member6667749562321684925pace_b @ C @ ( inf_in8598470101551243374pace_b @ A2 @ B2 ) ) ) ) ).

% IntI
thf(fact_503_IntI,axiom,
    ! [C: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ C @ A2 )
     => ( ( member7340901614391157822pace_b @ C @ B2 )
       => ( member7340901614391157822pace_b @ C @ ( inf_in3860511187648227951pace_b @ A2 @ B2 ) ) ) ) ).

% IntI
thf(fact_504_IntI,axiom,
    ! [C: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ C @ A2 )
     => ( ( member5008716543664893436ce_a_b @ C @ B2 )
       => ( member5008716543664893436ce_a_b @ C @ ( inf_in8638537385238394157ce_a_b @ A2 @ B2 ) ) ) ) ).

% IntI
thf(fact_505_IntI,axiom,
    ! [C: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ C @ A2 )
     => ( ( member1568243296417166973pace_b @ C @ B2 )
       => ( member1568243296417166973pace_b @ C @ ( inf_in433292969326628142pace_b @ A2 @ B2 ) ) ) ) ).

% IntI
thf(fact_506_IntI,axiom,
    ! [C: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ C @ A2 )
     => ( ( member41169580844105599pace_b @ C @ B2 )
       => ( member41169580844105599pace_b @ C @ ( inf_in6845569456361772336pace_b @ A2 @ B2 ) ) ) ) ).

% IntI
thf(fact_507_IntI,axiom,
    ! [C: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ C @ A2 )
     => ( ( member7269867574344811837pace_a @ C @ B2 )
       => ( member7269867574344811837pace_a @ C @ ( inf_in6381695705937263598pace_a @ A2 @ B2 ) ) ) ) ).

% IntI
thf(fact_508_IntI,axiom,
    ! [C: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( member_a_b @ C @ A2 )
     => ( ( member_a_b @ C @ B2 )
       => ( member_a_b @ C @ ( inf_inf_set_a_b @ A2 @ B2 ) ) ) ) ).

% IntI
thf(fact_509_ComplI,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b] :
      ( ~ ( member6667749562321684925pace_b @ C @ A2 )
     => ( member6667749562321684925pace_b @ C @ ( uminus2224264783410452005pace_b @ A2 ) ) ) ).

% ComplI
thf(fact_510_ComplI,axiom,
    ! [C: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ~ ( member7340901614391157822pace_b @ C @ A2 )
     => ( member7340901614391157822pace_b @ C @ ( uminus9143991737638391846pace_b @ A2 ) ) ) ).

% ComplI
thf(fact_511_ComplI,axiom,
    ! [C: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ~ ( member5008716543664893436ce_a_b @ C @ A2 )
     => ( member5008716543664893436ce_a_b @ C @ ( uminus4698645898373782244ce_a_b @ A2 ) ) ) ).

% ComplI
thf(fact_512_ComplI,axiom,
    ! [C: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ~ ( member1568243296417166973pace_b @ C @ A2 )
     => ( member1568243296417166973pace_b @ C @ ( uminus5716773519316792037pace_b @ A2 ) ) ) ).

% ComplI
thf(fact_513_ComplI,axiom,
    ! [C: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b] :
      ( ~ ( member41169580844105599pace_b @ C @ A2 )
     => ( member41169580844105599pace_b @ C @ ( uminus471364138220980967pace_b @ A2 ) ) ) ).

% ComplI
thf(fact_514_ComplI,axiom,
    ! [C: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ~ ( member7269867574344811837pace_a @ C @ A2 )
     => ( member7269867574344811837pace_a @ C @ ( uminus2441804219072651685pace_a @ A2 ) ) ) ).

% ComplI
thf(fact_515_ComplI,axiom,
    ! [C: a > b,A2: set_a_b] :
      ( ~ ( member_a_b @ C @ A2 )
     => ( member_a_b @ C @ ( uminus6731694806113723621et_a_b @ A2 ) ) ) ).

% ComplI
thf(fact_516_Compl__iff,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ C @ ( uminus2224264783410452005pace_b @ A2 ) )
      = ( ~ ( member6667749562321684925pace_b @ C @ A2 ) ) ) ).

% Compl_iff
thf(fact_517_Compl__iff,axiom,
    ! [C: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ C @ ( uminus9143991737638391846pace_b @ A2 ) )
      = ( ~ ( member7340901614391157822pace_b @ C @ A2 ) ) ) ).

% Compl_iff
thf(fact_518_Compl__iff,axiom,
    ! [C: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ C @ ( uminus4698645898373782244ce_a_b @ A2 ) )
      = ( ~ ( member5008716543664893436ce_a_b @ C @ A2 ) ) ) ).

% Compl_iff
thf(fact_519_Compl__iff,axiom,
    ! [C: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ C @ ( uminus5716773519316792037pace_b @ A2 ) )
      = ( ~ ( member1568243296417166973pace_b @ C @ A2 ) ) ) ).

% Compl_iff
thf(fact_520_Compl__iff,axiom,
    ! [C: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ C @ ( uminus471364138220980967pace_b @ A2 ) )
      = ( ~ ( member41169580844105599pace_b @ C @ A2 ) ) ) ).

% Compl_iff
thf(fact_521_Compl__iff,axiom,
    ! [C: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ C @ ( uminus2441804219072651685pace_a @ A2 ) )
      = ( ~ ( member7269867574344811837pace_a @ C @ A2 ) ) ) ).

% Compl_iff
thf(fact_522_Compl__iff,axiom,
    ! [C: a > b,A2: set_a_b] :
      ( ( member_a_b @ C @ ( uminus6731694806113723621et_a_b @ A2 ) )
      = ( ~ ( member_a_b @ C @ A2 ) ) ) ).

% Compl_iff
thf(fact_523_Collect__restrict,axiom,
    ! [X: set_Pr7742364250814120412pace_b,P: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o] :
      ( ord_le1280929228223758908pace_b
      @ ( collec7915783404360165627pace_b
        @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
            ( ( member6667749562321684925pace_b @ X2 @ X )
            & ( P @ X2 ) ) )
      @ X ) ).

% Collect_restrict
thf(fact_524_Collect__restrict,axiom,
    ! [X: set_a_3263942136899480541pace_b,P: ( a > probab4737552677800996672pace_b ) > $o] :
      ( ord_le130150003083865149pace_b
      @ ( collec5907158909762593660pace_b
        @ ^ [X2: a > probab4737552677800996672pace_b] :
            ( ( member7340901614391157822pace_b @ X2 @ X )
            & ( P @ X2 ) ) )
      @ X ) ).

% Collect_restrict
thf(fact_525_Collect__restrict,axiom,
    ! [X: set_Pr8041968334489646747ce_a_b,P: ( probab4737552673497767871pace_a > b ) > $o] :
      ( ord_le4908176200674031355ce_a_b
      @ ( collec3574973839036329274ce_a_b
        @ ^ [X2: probab4737552673497767871pace_a > b] :
            ( ( member5008716543664893436ce_a_b @ X2 @ X )
            & ( P @ X2 ) ) )
      @ X ) ).

% Collect_restrict
thf(fact_526_Collect__restrict,axiom,
    ! [X: set_b_9060095955432656540pace_b,P: ( b > probab4737552677800996672pace_b ) > $o] :
      ( ord_le5926303821617041148pace_b
      @ ( collec134500591788602811pace_b
        @ ^ [X2: b > probab4737552677800996672pace_b] :
            ( ( member1568243296417166973pace_b @ X2 @ X )
            & ( P @ X2 ) ) )
      @ X ) ).

% Collect_restrict
thf(fact_527_Collect__restrict,axiom,
    ! [X: set_a_5989463605624649374pace_b,P: ( a > probab8624551251471354625pace_b ) > $o] :
      ( ord_le8751400619889063678pace_b
      @ ( collec1289203422882586301pace_b
        @ ^ [X2: a > probab8624551251471354625pace_b] :
            ( ( member41169580844105599pace_b @ X2 @ X )
            & ( P @ X2 ) ) )
      @ X ) ).

% Collect_restrict
thf(fact_528_Collect__restrict,axiom,
    ! [X: set_a_5785126655188516188pace_a,P: ( a > probab4737552673497767871pace_a ) > $o] :
      ( ord_le2651334521372900796pace_a
      @ ( collec5836124869716247675pace_a
        @ ^ [X2: a > probab4737552673497767871pace_a] :
            ( ( member7269867574344811837pace_a @ X2 @ X )
            & ( P @ X2 ) ) )
      @ X ) ).

% Collect_restrict
thf(fact_529_Collect__restrict,axiom,
    ! [X: set_a_b,P: ( a > b ) > $o] :
      ( ord_less_eq_set_a_b
      @ ( collect_a_b
        @ ^ [X2: a > b] :
            ( ( member_a_b @ X2 @ X )
            & ( P @ X2 ) ) )
      @ X ) ).

% Collect_restrict
thf(fact_530_prop__restrict,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,Z: set_Pr7742364250814120412pace_b,X: set_Pr7742364250814120412pace_b,P: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o] :
      ( ( member6667749562321684925pace_b @ X3 @ Z )
     => ( ( ord_le1280929228223758908pace_b @ Z
          @ ( collec7915783404360165627pace_b
            @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
                ( ( member6667749562321684925pace_b @ X2 @ X )
                & ( P @ X2 ) ) ) )
       => ( P @ X3 ) ) ) ).

% prop_restrict
thf(fact_531_prop__restrict,axiom,
    ! [X3: a > probab4737552677800996672pace_b,Z: set_a_3263942136899480541pace_b,X: set_a_3263942136899480541pace_b,P: ( a > probab4737552677800996672pace_b ) > $o] :
      ( ( member7340901614391157822pace_b @ X3 @ Z )
     => ( ( ord_le130150003083865149pace_b @ Z
          @ ( collec5907158909762593660pace_b
            @ ^ [X2: a > probab4737552677800996672pace_b] :
                ( ( member7340901614391157822pace_b @ X2 @ X )
                & ( P @ X2 ) ) ) )
       => ( P @ X3 ) ) ) ).

% prop_restrict
thf(fact_532_prop__restrict,axiom,
    ! [X3: probab4737552673497767871pace_a > b,Z: set_Pr8041968334489646747ce_a_b,X: set_Pr8041968334489646747ce_a_b,P: ( probab4737552673497767871pace_a > b ) > $o] :
      ( ( member5008716543664893436ce_a_b @ X3 @ Z )
     => ( ( ord_le4908176200674031355ce_a_b @ Z
          @ ( collec3574973839036329274ce_a_b
            @ ^ [X2: probab4737552673497767871pace_a > b] :
                ( ( member5008716543664893436ce_a_b @ X2 @ X )
                & ( P @ X2 ) ) ) )
       => ( P @ X3 ) ) ) ).

% prop_restrict
thf(fact_533_prop__restrict,axiom,
    ! [X3: b > probab4737552677800996672pace_b,Z: set_b_9060095955432656540pace_b,X: set_b_9060095955432656540pace_b,P: ( b > probab4737552677800996672pace_b ) > $o] :
      ( ( member1568243296417166973pace_b @ X3 @ Z )
     => ( ( ord_le5926303821617041148pace_b @ Z
          @ ( collec134500591788602811pace_b
            @ ^ [X2: b > probab4737552677800996672pace_b] :
                ( ( member1568243296417166973pace_b @ X2 @ X )
                & ( P @ X2 ) ) ) )
       => ( P @ X3 ) ) ) ).

% prop_restrict
thf(fact_534_prop__restrict,axiom,
    ! [X3: a > probab8624551251471354625pace_b,Z: set_a_5989463605624649374pace_b,X: set_a_5989463605624649374pace_b,P: ( a > probab8624551251471354625pace_b ) > $o] :
      ( ( member41169580844105599pace_b @ X3 @ Z )
     => ( ( ord_le8751400619889063678pace_b @ Z
          @ ( collec1289203422882586301pace_b
            @ ^ [X2: a > probab8624551251471354625pace_b] :
                ( ( member41169580844105599pace_b @ X2 @ X )
                & ( P @ X2 ) ) ) )
       => ( P @ X3 ) ) ) ).

% prop_restrict
thf(fact_535_prop__restrict,axiom,
    ! [X3: a > probab4737552673497767871pace_a,Z: set_a_5785126655188516188pace_a,X: set_a_5785126655188516188pace_a,P: ( a > probab4737552673497767871pace_a ) > $o] :
      ( ( member7269867574344811837pace_a @ X3 @ Z )
     => ( ( ord_le2651334521372900796pace_a @ Z
          @ ( collec5836124869716247675pace_a
            @ ^ [X2: a > probab4737552673497767871pace_a] :
                ( ( member7269867574344811837pace_a @ X2 @ X )
                & ( P @ X2 ) ) ) )
       => ( P @ X3 ) ) ) ).

% prop_restrict
thf(fact_536_prop__restrict,axiom,
    ! [X3: a > b,Z: set_a_b,X: set_a_b,P: ( a > b ) > $o] :
      ( ( member_a_b @ X3 @ Z )
     => ( ( ord_less_eq_set_a_b @ Z
          @ ( collect_a_b
            @ ^ [X2: a > b] :
                ( ( member_a_b @ X2 @ X )
                & ( P @ X2 ) ) ) )
       => ( P @ X3 ) ) ) ).

% prop_restrict
thf(fact_537_Int__Collect__mono,axiom,
    ! [A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b,P: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o,Q: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o] :
      ( ( ord_le1280929228223758908pace_b @ A2 @ B2 )
     => ( ! [X4: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
            ( ( member6667749562321684925pace_b @ X4 @ A2 )
           => ( ( P @ X4 )
             => ( Q @ X4 ) ) )
       => ( ord_le1280929228223758908pace_b @ ( inf_in8598470101551243374pace_b @ A2 @ ( collec7915783404360165627pace_b @ P ) ) @ ( inf_in8598470101551243374pace_b @ B2 @ ( collec7915783404360165627pace_b @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_538_Int__Collect__mono,axiom,
    ! [A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b,P: ( a > probab4737552677800996672pace_b ) > $o,Q: ( a > probab4737552677800996672pace_b ) > $o] :
      ( ( ord_le130150003083865149pace_b @ A2 @ B2 )
     => ( ! [X4: a > probab4737552677800996672pace_b] :
            ( ( member7340901614391157822pace_b @ X4 @ A2 )
           => ( ( P @ X4 )
             => ( Q @ X4 ) ) )
       => ( ord_le130150003083865149pace_b @ ( inf_in3860511187648227951pace_b @ A2 @ ( collec5907158909762593660pace_b @ P ) ) @ ( inf_in3860511187648227951pace_b @ B2 @ ( collec5907158909762593660pace_b @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_539_Int__Collect__mono,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b,P: ( probab4737552673497767871pace_a > b ) > $o,Q: ( probab4737552673497767871pace_a > b ) > $o] :
      ( ( ord_le4908176200674031355ce_a_b @ A2 @ B2 )
     => ( ! [X4: probab4737552673497767871pace_a > b] :
            ( ( member5008716543664893436ce_a_b @ X4 @ A2 )
           => ( ( P @ X4 )
             => ( Q @ X4 ) ) )
       => ( ord_le4908176200674031355ce_a_b @ ( inf_in8638537385238394157ce_a_b @ A2 @ ( collec3574973839036329274ce_a_b @ P ) ) @ ( inf_in8638537385238394157ce_a_b @ B2 @ ( collec3574973839036329274ce_a_b @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_540_Int__Collect__mono,axiom,
    ! [A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b,P: ( b > probab4737552677800996672pace_b ) > $o,Q: ( b > probab4737552677800996672pace_b ) > $o] :
      ( ( ord_le5926303821617041148pace_b @ A2 @ B2 )
     => ( ! [X4: b > probab4737552677800996672pace_b] :
            ( ( member1568243296417166973pace_b @ X4 @ A2 )
           => ( ( P @ X4 )
             => ( Q @ X4 ) ) )
       => ( ord_le5926303821617041148pace_b @ ( inf_in433292969326628142pace_b @ A2 @ ( collec134500591788602811pace_b @ P ) ) @ ( inf_in433292969326628142pace_b @ B2 @ ( collec134500591788602811pace_b @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_541_Int__Collect__mono,axiom,
    ! [A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b,P: ( a > probab8624551251471354625pace_b ) > $o,Q: ( a > probab8624551251471354625pace_b ) > $o] :
      ( ( ord_le8751400619889063678pace_b @ A2 @ B2 )
     => ( ! [X4: a > probab8624551251471354625pace_b] :
            ( ( member41169580844105599pace_b @ X4 @ A2 )
           => ( ( P @ X4 )
             => ( Q @ X4 ) ) )
       => ( ord_le8751400619889063678pace_b @ ( inf_in6845569456361772336pace_b @ A2 @ ( collec1289203422882586301pace_b @ P ) ) @ ( inf_in6845569456361772336pace_b @ B2 @ ( collec1289203422882586301pace_b @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_542_Int__Collect__mono,axiom,
    ! [A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a,P: ( a > probab4737552673497767871pace_a ) > $o,Q: ( a > probab4737552673497767871pace_a ) > $o] :
      ( ( ord_le2651334521372900796pace_a @ A2 @ B2 )
     => ( ! [X4: a > probab4737552673497767871pace_a] :
            ( ( member7269867574344811837pace_a @ X4 @ A2 )
           => ( ( P @ X4 )
             => ( Q @ X4 ) ) )
       => ( ord_le2651334521372900796pace_a @ ( inf_in6381695705937263598pace_a @ A2 @ ( collec5836124869716247675pace_a @ P ) ) @ ( inf_in6381695705937263598pace_a @ B2 @ ( collec5836124869716247675pace_a @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_543_Int__Collect__mono,axiom,
    ! [A2: set_a_b,B2: set_a_b,P: ( a > b ) > $o,Q: ( a > b ) > $o] :
      ( ( ord_less_eq_set_a_b @ A2 @ B2 )
     => ( ! [X4: a > b] :
            ( ( member_a_b @ X4 @ A2 )
           => ( ( P @ X4 )
             => ( Q @ X4 ) ) )
       => ( ord_less_eq_set_a_b @ ( inf_inf_set_a_b @ A2 @ ( collect_a_b @ P ) ) @ ( inf_inf_set_a_b @ B2 @ ( collect_a_b @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_544_subset__iff,axiom,
    ( ord_le1280929228223758908pace_b
    = ( ^ [A3: set_Pr7742364250814120412pace_b,B4: set_Pr7742364250814120412pace_b] :
        ! [T2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
          ( ( member6667749562321684925pace_b @ T2 @ A3 )
         => ( member6667749562321684925pace_b @ T2 @ B4 ) ) ) ) ).

% subset_iff
thf(fact_545_subset__iff,axiom,
    ( ord_le130150003083865149pace_b
    = ( ^ [A3: set_a_3263942136899480541pace_b,B4: set_a_3263942136899480541pace_b] :
        ! [T2: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ T2 @ A3 )
         => ( member7340901614391157822pace_b @ T2 @ B4 ) ) ) ) ).

% subset_iff
thf(fact_546_subset__iff,axiom,
    ( ord_le4908176200674031355ce_a_b
    = ( ^ [A3: set_Pr8041968334489646747ce_a_b,B4: set_Pr8041968334489646747ce_a_b] :
        ! [T2: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ T2 @ A3 )
         => ( member5008716543664893436ce_a_b @ T2 @ B4 ) ) ) ) ).

% subset_iff
thf(fact_547_subset__iff,axiom,
    ( ord_le5926303821617041148pace_b
    = ( ^ [A3: set_b_9060095955432656540pace_b,B4: set_b_9060095955432656540pace_b] :
        ! [T2: b > probab4737552677800996672pace_b] :
          ( ( member1568243296417166973pace_b @ T2 @ A3 )
         => ( member1568243296417166973pace_b @ T2 @ B4 ) ) ) ) ).

% subset_iff
thf(fact_548_subset__iff,axiom,
    ( ord_le8751400619889063678pace_b
    = ( ^ [A3: set_a_5989463605624649374pace_b,B4: set_a_5989463605624649374pace_b] :
        ! [T2: a > probab8624551251471354625pace_b] :
          ( ( member41169580844105599pace_b @ T2 @ A3 )
         => ( member41169580844105599pace_b @ T2 @ B4 ) ) ) ) ).

% subset_iff
thf(fact_549_subset__iff,axiom,
    ( ord_le2651334521372900796pace_a
    = ( ^ [A3: set_a_5785126655188516188pace_a,B4: set_a_5785126655188516188pace_a] :
        ! [T2: a > probab4737552673497767871pace_a] :
          ( ( member7269867574344811837pace_a @ T2 @ A3 )
         => ( member7269867574344811837pace_a @ T2 @ B4 ) ) ) ) ).

% subset_iff
thf(fact_550_subset__iff,axiom,
    ( ord_less_eq_set_a_b
    = ( ^ [A3: set_a_b,B4: set_a_b] :
        ! [T2: a > b] :
          ( ( member_a_b @ T2 @ A3 )
         => ( member_a_b @ T2 @ B4 ) ) ) ) ).

% subset_iff
thf(fact_551_subset__eq,axiom,
    ( ord_le1280929228223758908pace_b
    = ( ^ [A3: set_Pr7742364250814120412pace_b,B4: set_Pr7742364250814120412pace_b] :
        ! [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
          ( ( member6667749562321684925pace_b @ X2 @ A3 )
         => ( member6667749562321684925pace_b @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_552_subset__eq,axiom,
    ( ord_le130150003083865149pace_b
    = ( ^ [A3: set_a_3263942136899480541pace_b,B4: set_a_3263942136899480541pace_b] :
        ! [X2: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ X2 @ A3 )
         => ( member7340901614391157822pace_b @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_553_subset__eq,axiom,
    ( ord_le4908176200674031355ce_a_b
    = ( ^ [A3: set_Pr8041968334489646747ce_a_b,B4: set_Pr8041968334489646747ce_a_b] :
        ! [X2: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ X2 @ A3 )
         => ( member5008716543664893436ce_a_b @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_554_subset__eq,axiom,
    ( ord_le5926303821617041148pace_b
    = ( ^ [A3: set_b_9060095955432656540pace_b,B4: set_b_9060095955432656540pace_b] :
        ! [X2: b > probab4737552677800996672pace_b] :
          ( ( member1568243296417166973pace_b @ X2 @ A3 )
         => ( member1568243296417166973pace_b @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_555_subset__eq,axiom,
    ( ord_le8751400619889063678pace_b
    = ( ^ [A3: set_a_5989463605624649374pace_b,B4: set_a_5989463605624649374pace_b] :
        ! [X2: a > probab8624551251471354625pace_b] :
          ( ( member41169580844105599pace_b @ X2 @ A3 )
         => ( member41169580844105599pace_b @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_556_subset__eq,axiom,
    ( ord_le2651334521372900796pace_a
    = ( ^ [A3: set_a_5785126655188516188pace_a,B4: set_a_5785126655188516188pace_a] :
        ! [X2: a > probab4737552673497767871pace_a] :
          ( ( member7269867574344811837pace_a @ X2 @ A3 )
         => ( member7269867574344811837pace_a @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_557_subset__eq,axiom,
    ( ord_less_eq_set_a_b
    = ( ^ [A3: set_a_b,B4: set_a_b] :
        ! [X2: a > b] :
          ( ( member_a_b @ X2 @ A3 )
         => ( member_a_b @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_558_subsetD,axiom,
    ! [A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b,C: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ( ( ord_le1280929228223758908pace_b @ A2 @ B2 )
     => ( ( member6667749562321684925pace_b @ C @ A2 )
       => ( member6667749562321684925pace_b @ C @ B2 ) ) ) ).

% subsetD
thf(fact_559_subsetD,axiom,
    ! [A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b,C: a > probab4737552677800996672pace_b] :
      ( ( ord_le130150003083865149pace_b @ A2 @ B2 )
     => ( ( member7340901614391157822pace_b @ C @ A2 )
       => ( member7340901614391157822pace_b @ C @ B2 ) ) ) ).

% subsetD
thf(fact_560_subsetD,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b,C: probab4737552673497767871pace_a > b] :
      ( ( ord_le4908176200674031355ce_a_b @ A2 @ B2 )
     => ( ( member5008716543664893436ce_a_b @ C @ A2 )
       => ( member5008716543664893436ce_a_b @ C @ B2 ) ) ) ).

% subsetD
thf(fact_561_subsetD,axiom,
    ! [A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b,C: b > probab4737552677800996672pace_b] :
      ( ( ord_le5926303821617041148pace_b @ A2 @ B2 )
     => ( ( member1568243296417166973pace_b @ C @ A2 )
       => ( member1568243296417166973pace_b @ C @ B2 ) ) ) ).

% subsetD
thf(fact_562_subsetD,axiom,
    ! [A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b,C: a > probab8624551251471354625pace_b] :
      ( ( ord_le8751400619889063678pace_b @ A2 @ B2 )
     => ( ( member41169580844105599pace_b @ C @ A2 )
       => ( member41169580844105599pace_b @ C @ B2 ) ) ) ).

% subsetD
thf(fact_563_subsetD,axiom,
    ! [A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a,C: a > probab4737552673497767871pace_a] :
      ( ( ord_le2651334521372900796pace_a @ A2 @ B2 )
     => ( ( member7269867574344811837pace_a @ C @ A2 )
       => ( member7269867574344811837pace_a @ C @ B2 ) ) ) ).

% subsetD
thf(fact_564_subsetD,axiom,
    ! [A2: set_a_b,B2: set_a_b,C: a > b] :
      ( ( ord_less_eq_set_a_b @ A2 @ B2 )
     => ( ( member_a_b @ C @ A2 )
       => ( member_a_b @ C @ B2 ) ) ) ).

% subsetD
thf(fact_565_in__mono,axiom,
    ! [A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b,X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ( ( ord_le1280929228223758908pace_b @ A2 @ B2 )
     => ( ( member6667749562321684925pace_b @ X3 @ A2 )
       => ( member6667749562321684925pace_b @ X3 @ B2 ) ) ) ).

% in_mono
thf(fact_566_in__mono,axiom,
    ! [A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b,X3: a > probab4737552677800996672pace_b] :
      ( ( ord_le130150003083865149pace_b @ A2 @ B2 )
     => ( ( member7340901614391157822pace_b @ X3 @ A2 )
       => ( member7340901614391157822pace_b @ X3 @ B2 ) ) ) ).

% in_mono
thf(fact_567_in__mono,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b,X3: probab4737552673497767871pace_a > b] :
      ( ( ord_le4908176200674031355ce_a_b @ A2 @ B2 )
     => ( ( member5008716543664893436ce_a_b @ X3 @ A2 )
       => ( member5008716543664893436ce_a_b @ X3 @ B2 ) ) ) ).

% in_mono
thf(fact_568_in__mono,axiom,
    ! [A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b,X3: b > probab4737552677800996672pace_b] :
      ( ( ord_le5926303821617041148pace_b @ A2 @ B2 )
     => ( ( member1568243296417166973pace_b @ X3 @ A2 )
       => ( member1568243296417166973pace_b @ X3 @ B2 ) ) ) ).

% in_mono
thf(fact_569_in__mono,axiom,
    ! [A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b,X3: a > probab8624551251471354625pace_b] :
      ( ( ord_le8751400619889063678pace_b @ A2 @ B2 )
     => ( ( member41169580844105599pace_b @ X3 @ A2 )
       => ( member41169580844105599pace_b @ X3 @ B2 ) ) ) ).

% in_mono
thf(fact_570_in__mono,axiom,
    ! [A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a,X3: a > probab4737552673497767871pace_a] :
      ( ( ord_le2651334521372900796pace_a @ A2 @ B2 )
     => ( ( member7269867574344811837pace_a @ X3 @ A2 )
       => ( member7269867574344811837pace_a @ X3 @ B2 ) ) ) ).

% in_mono
thf(fact_571_in__mono,axiom,
    ! [A2: set_a_b,B2: set_a_b,X3: a > b] :
      ( ( ord_less_eq_set_a_b @ A2 @ B2 )
     => ( ( member_a_b @ X3 @ A2 )
       => ( member_a_b @ X3 @ B2 ) ) ) ).

% in_mono
thf(fact_572_IntD2,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ C @ ( inf_in8598470101551243374pace_b @ A2 @ B2 ) )
     => ( member6667749562321684925pace_b @ C @ B2 ) ) ).

% IntD2
thf(fact_573_IntD2,axiom,
    ! [C: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ C @ ( inf_in3860511187648227951pace_b @ A2 @ B2 ) )
     => ( member7340901614391157822pace_b @ C @ B2 ) ) ).

% IntD2
thf(fact_574_IntD2,axiom,
    ! [C: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ C @ ( inf_in8638537385238394157ce_a_b @ A2 @ B2 ) )
     => ( member5008716543664893436ce_a_b @ C @ B2 ) ) ).

% IntD2
thf(fact_575_IntD2,axiom,
    ! [C: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ C @ ( inf_in433292969326628142pace_b @ A2 @ B2 ) )
     => ( member1568243296417166973pace_b @ C @ B2 ) ) ).

% IntD2
thf(fact_576_IntD2,axiom,
    ! [C: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ C @ ( inf_in6845569456361772336pace_b @ A2 @ B2 ) )
     => ( member41169580844105599pace_b @ C @ B2 ) ) ).

% IntD2
thf(fact_577_IntD2,axiom,
    ! [C: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ C @ ( inf_in6381695705937263598pace_a @ A2 @ B2 ) )
     => ( member7269867574344811837pace_a @ C @ B2 ) ) ).

% IntD2
thf(fact_578_IntD2,axiom,
    ! [C: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( member_a_b @ C @ ( inf_inf_set_a_b @ A2 @ B2 ) )
     => ( member_a_b @ C @ B2 ) ) ).

% IntD2
thf(fact_579_IntD1,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ C @ ( inf_in8598470101551243374pace_b @ A2 @ B2 ) )
     => ( member6667749562321684925pace_b @ C @ A2 ) ) ).

% IntD1
thf(fact_580_IntD1,axiom,
    ! [C: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ C @ ( inf_in3860511187648227951pace_b @ A2 @ B2 ) )
     => ( member7340901614391157822pace_b @ C @ A2 ) ) ).

% IntD1
thf(fact_581_IntD1,axiom,
    ! [C: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ C @ ( inf_in8638537385238394157ce_a_b @ A2 @ B2 ) )
     => ( member5008716543664893436ce_a_b @ C @ A2 ) ) ).

% IntD1
thf(fact_582_IntD1,axiom,
    ! [C: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ C @ ( inf_in433292969326628142pace_b @ A2 @ B2 ) )
     => ( member1568243296417166973pace_b @ C @ A2 ) ) ).

% IntD1
thf(fact_583_IntD1,axiom,
    ! [C: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ C @ ( inf_in6845569456361772336pace_b @ A2 @ B2 ) )
     => ( member41169580844105599pace_b @ C @ A2 ) ) ).

% IntD1
thf(fact_584_IntD1,axiom,
    ! [C: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ C @ ( inf_in6381695705937263598pace_a @ A2 @ B2 ) )
     => ( member7269867574344811837pace_a @ C @ A2 ) ) ).

% IntD1
thf(fact_585_IntD1,axiom,
    ! [C: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( member_a_b @ C @ ( inf_inf_set_a_b @ A2 @ B2 ) )
     => ( member_a_b @ C @ A2 ) ) ).

% IntD1
thf(fact_586_IntE,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ C @ ( inf_in8598470101551243374pace_b @ A2 @ B2 ) )
     => ~ ( ( member6667749562321684925pace_b @ C @ A2 )
         => ~ ( member6667749562321684925pace_b @ C @ B2 ) ) ) ).

% IntE
thf(fact_587_IntE,axiom,
    ! [C: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ C @ ( inf_in3860511187648227951pace_b @ A2 @ B2 ) )
     => ~ ( ( member7340901614391157822pace_b @ C @ A2 )
         => ~ ( member7340901614391157822pace_b @ C @ B2 ) ) ) ).

% IntE
thf(fact_588_IntE,axiom,
    ! [C: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ C @ ( inf_in8638537385238394157ce_a_b @ A2 @ B2 ) )
     => ~ ( ( member5008716543664893436ce_a_b @ C @ A2 )
         => ~ ( member5008716543664893436ce_a_b @ C @ B2 ) ) ) ).

% IntE
thf(fact_589_IntE,axiom,
    ! [C: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ C @ ( inf_in433292969326628142pace_b @ A2 @ B2 ) )
     => ~ ( ( member1568243296417166973pace_b @ C @ A2 )
         => ~ ( member1568243296417166973pace_b @ C @ B2 ) ) ) ).

% IntE
thf(fact_590_IntE,axiom,
    ! [C: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ C @ ( inf_in6845569456361772336pace_b @ A2 @ B2 ) )
     => ~ ( ( member41169580844105599pace_b @ C @ A2 )
         => ~ ( member41169580844105599pace_b @ C @ B2 ) ) ) ).

% IntE
thf(fact_591_IntE,axiom,
    ! [C: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ C @ ( inf_in6381695705937263598pace_a @ A2 @ B2 ) )
     => ~ ( ( member7269867574344811837pace_a @ C @ A2 )
         => ~ ( member7269867574344811837pace_a @ C @ B2 ) ) ) ).

% IntE
thf(fact_592_IntE,axiom,
    ! [C: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( member_a_b @ C @ ( inf_inf_set_a_b @ A2 @ B2 ) )
     => ~ ( ( member_a_b @ C @ A2 )
         => ~ ( member_a_b @ C @ B2 ) ) ) ).

% IntE
thf(fact_593_ComplD,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ C @ ( uminus2224264783410452005pace_b @ A2 ) )
     => ~ ( member6667749562321684925pace_b @ C @ A2 ) ) ).

% ComplD
thf(fact_594_ComplD,axiom,
    ! [C: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ C @ ( uminus9143991737638391846pace_b @ A2 ) )
     => ~ ( member7340901614391157822pace_b @ C @ A2 ) ) ).

% ComplD
thf(fact_595_ComplD,axiom,
    ! [C: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ C @ ( uminus4698645898373782244ce_a_b @ A2 ) )
     => ~ ( member5008716543664893436ce_a_b @ C @ A2 ) ) ).

% ComplD
thf(fact_596_ComplD,axiom,
    ! [C: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ C @ ( uminus5716773519316792037pace_b @ A2 ) )
     => ~ ( member1568243296417166973pace_b @ C @ A2 ) ) ).

% ComplD
thf(fact_597_ComplD,axiom,
    ! [C: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ C @ ( uminus471364138220980967pace_b @ A2 ) )
     => ~ ( member41169580844105599pace_b @ C @ A2 ) ) ).

% ComplD
thf(fact_598_ComplD,axiom,
    ! [C: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ C @ ( uminus2441804219072651685pace_a @ A2 ) )
     => ~ ( member7269867574344811837pace_a @ C @ A2 ) ) ).

% ComplD
thf(fact_599_ComplD,axiom,
    ! [C: a > b,A2: set_a_b] :
      ( ( member_a_b @ C @ ( uminus6731694806113723621et_a_b @ A2 ) )
     => ~ ( member_a_b @ C @ A2 ) ) ).

% ComplD
thf(fact_600_uminus__set__def,axiom,
    ( uminus2224264783410452005pace_b
    = ( ^ [A3: set_Pr7742364250814120412pace_b] :
          ( collec7915783404360165627pace_b
          @ ( uminus4069396184545879712ce_b_o
            @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ A3 ) ) ) ) ) ).

% uminus_set_def
thf(fact_601_uminus__set__def,axiom,
    ( uminus9143991737638391846pace_b
    = ( ^ [A3: set_a_3263942136899480541pace_b] :
          ( collec5907158909762593660pace_b
          @ ( uminus4899921597970664927ce_b_o
            @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ A3 ) ) ) ) ) ).

% uminus_set_def
thf(fact_602_uminus__set__def,axiom,
    ( uminus4698645898373782244ce_a_b
    = ( ^ [A3: set_Pr8041968334489646747ce_a_b] :
          ( collec3574973839036329274ce_a_b
          @ ( uminus1577303868876501153_a_b_o
            @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ A3 ) ) ) ) ) ).

% uminus_set_def
thf(fact_603_uminus__set__def,axiom,
    ( uminus5716773519316792037pace_b
    = ( ^ [A3: set_b_9060095955432656540pace_b] :
          ( collec134500591788602811pace_b
          @ ( uminus1872129333469100512ce_b_o
            @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ A3 ) ) ) ) ) ).

% uminus_set_def
thf(fact_604_uminus__set__def,axiom,
    ( uminus471364138220980967pace_b
    = ( ^ [A3: set_a_5989463605624649374pace_b] :
          ( collec1289203422882586301pace_b
          @ ( uminus8920208993360864350ce_b_o
            @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ A3 ) ) ) ) ) ).

% uminus_set_def
thf(fact_605_uminus__set__def,axiom,
    ( uminus2441804219072651685pace_a
    = ( ^ [A3: set_a_5785126655188516188pace_a] :
          ( collec5836124869716247675pace_a
          @ ( uminus5535570598575651616ce_a_o
            @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ A3 ) ) ) ) ) ).

% uminus_set_def
thf(fact_606_uminus__set__def,axiom,
    ( uminus6731694806113723621et_a_b
    = ( ^ [A3: set_a_b] :
          ( collect_a_b
          @ ( uminus_uminus_a_b_o
            @ ^ [X2: a > b] : ( member_a_b @ X2 @ A3 ) ) ) ) ) ).

% uminus_set_def
thf(fact_607_Compl__eq,axiom,
    ( uminus2224264783410452005pace_b
    = ( ^ [A3: set_Pr7742364250814120412pace_b] :
          ( collec7915783404360165627pace_b
          @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
              ~ ( member6667749562321684925pace_b @ X2 @ A3 ) ) ) ) ).

% Compl_eq
thf(fact_608_Compl__eq,axiom,
    ( uminus9143991737638391846pace_b
    = ( ^ [A3: set_a_3263942136899480541pace_b] :
          ( collec5907158909762593660pace_b
          @ ^ [X2: a > probab4737552677800996672pace_b] :
              ~ ( member7340901614391157822pace_b @ X2 @ A3 ) ) ) ) ).

% Compl_eq
thf(fact_609_Compl__eq,axiom,
    ( uminus4698645898373782244ce_a_b
    = ( ^ [A3: set_Pr8041968334489646747ce_a_b] :
          ( collec3574973839036329274ce_a_b
          @ ^ [X2: probab4737552673497767871pace_a > b] :
              ~ ( member5008716543664893436ce_a_b @ X2 @ A3 ) ) ) ) ).

% Compl_eq
thf(fact_610_Compl__eq,axiom,
    ( uminus5716773519316792037pace_b
    = ( ^ [A3: set_b_9060095955432656540pace_b] :
          ( collec134500591788602811pace_b
          @ ^ [X2: b > probab4737552677800996672pace_b] :
              ~ ( member1568243296417166973pace_b @ X2 @ A3 ) ) ) ) ).

% Compl_eq
thf(fact_611_Compl__eq,axiom,
    ( uminus471364138220980967pace_b
    = ( ^ [A3: set_a_5989463605624649374pace_b] :
          ( collec1289203422882586301pace_b
          @ ^ [X2: a > probab8624551251471354625pace_b] :
              ~ ( member41169580844105599pace_b @ X2 @ A3 ) ) ) ) ).

% Compl_eq
thf(fact_612_Compl__eq,axiom,
    ( uminus2441804219072651685pace_a
    = ( ^ [A3: set_a_5785126655188516188pace_a] :
          ( collec5836124869716247675pace_a
          @ ^ [X2: a > probab4737552673497767871pace_a] :
              ~ ( member7269867574344811837pace_a @ X2 @ A3 ) ) ) ) ).

% Compl_eq
thf(fact_613_Compl__eq,axiom,
    ( uminus6731694806113723621et_a_b
    = ( ^ [A3: set_a_b] :
          ( collect_a_b
          @ ^ [X2: a > b] :
              ~ ( member_a_b @ X2 @ A3 ) ) ) ) ).

% Compl_eq
thf(fact_614_Collect__subset,axiom,
    ! [A2: set_Pr7742364250814120412pace_b,P: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o] :
      ( ord_le1280929228223758908pace_b
      @ ( collec7915783404360165627pace_b
        @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
            ( ( member6667749562321684925pace_b @ X2 @ A2 )
            & ( P @ X2 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_615_Collect__subset,axiom,
    ! [A2: set_a_3263942136899480541pace_b,P: ( a > probab4737552677800996672pace_b ) > $o] :
      ( ord_le130150003083865149pace_b
      @ ( collec5907158909762593660pace_b
        @ ^ [X2: a > probab4737552677800996672pace_b] :
            ( ( member7340901614391157822pace_b @ X2 @ A2 )
            & ( P @ X2 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_616_Collect__subset,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,P: ( probab4737552673497767871pace_a > b ) > $o] :
      ( ord_le4908176200674031355ce_a_b
      @ ( collec3574973839036329274ce_a_b
        @ ^ [X2: probab4737552673497767871pace_a > b] :
            ( ( member5008716543664893436ce_a_b @ X2 @ A2 )
            & ( P @ X2 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_617_Collect__subset,axiom,
    ! [A2: set_b_9060095955432656540pace_b,P: ( b > probab4737552677800996672pace_b ) > $o] :
      ( ord_le5926303821617041148pace_b
      @ ( collec134500591788602811pace_b
        @ ^ [X2: b > probab4737552677800996672pace_b] :
            ( ( member1568243296417166973pace_b @ X2 @ A2 )
            & ( P @ X2 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_618_Collect__subset,axiom,
    ! [A2: set_a_5989463605624649374pace_b,P: ( a > probab8624551251471354625pace_b ) > $o] :
      ( ord_le8751400619889063678pace_b
      @ ( collec1289203422882586301pace_b
        @ ^ [X2: a > probab8624551251471354625pace_b] :
            ( ( member41169580844105599pace_b @ X2 @ A2 )
            & ( P @ X2 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_619_Collect__subset,axiom,
    ! [A2: set_a_5785126655188516188pace_a,P: ( a > probab4737552673497767871pace_a ) > $o] :
      ( ord_le2651334521372900796pace_a
      @ ( collec5836124869716247675pace_a
        @ ^ [X2: a > probab4737552673497767871pace_a] :
            ( ( member7269867574344811837pace_a @ X2 @ A2 )
            & ( P @ X2 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_620_Collect__subset,axiom,
    ! [A2: set_a_b,P: ( a > b ) > $o] :
      ( ord_less_eq_set_a_b
      @ ( collect_a_b
        @ ^ [X2: a > b] :
            ( ( member_a_b @ X2 @ A2 )
            & ( P @ X2 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_621_Int__def,axiom,
    ( inf_in8598470101551243374pace_b
    = ( ^ [A3: set_Pr7742364250814120412pace_b,B4: set_Pr7742364250814120412pace_b] :
          ( collec7915783404360165627pace_b
          @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
              ( ( member6667749562321684925pace_b @ X2 @ A3 )
              & ( member6667749562321684925pace_b @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_622_Int__def,axiom,
    ( inf_in3860511187648227951pace_b
    = ( ^ [A3: set_a_3263942136899480541pace_b,B4: set_a_3263942136899480541pace_b] :
          ( collec5907158909762593660pace_b
          @ ^ [X2: a > probab4737552677800996672pace_b] :
              ( ( member7340901614391157822pace_b @ X2 @ A3 )
              & ( member7340901614391157822pace_b @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_623_Int__def,axiom,
    ( inf_in8638537385238394157ce_a_b
    = ( ^ [A3: set_Pr8041968334489646747ce_a_b,B4: set_Pr8041968334489646747ce_a_b] :
          ( collec3574973839036329274ce_a_b
          @ ^ [X2: probab4737552673497767871pace_a > b] :
              ( ( member5008716543664893436ce_a_b @ X2 @ A3 )
              & ( member5008716543664893436ce_a_b @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_624_Int__def,axiom,
    ( inf_in433292969326628142pace_b
    = ( ^ [A3: set_b_9060095955432656540pace_b,B4: set_b_9060095955432656540pace_b] :
          ( collec134500591788602811pace_b
          @ ^ [X2: b > probab4737552677800996672pace_b] :
              ( ( member1568243296417166973pace_b @ X2 @ A3 )
              & ( member1568243296417166973pace_b @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_625_Int__def,axiom,
    ( inf_in6845569456361772336pace_b
    = ( ^ [A3: set_a_5989463605624649374pace_b,B4: set_a_5989463605624649374pace_b] :
          ( collec1289203422882586301pace_b
          @ ^ [X2: a > probab8624551251471354625pace_b] :
              ( ( member41169580844105599pace_b @ X2 @ A3 )
              & ( member41169580844105599pace_b @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_626_Int__def,axiom,
    ( inf_in6381695705937263598pace_a
    = ( ^ [A3: set_a_5785126655188516188pace_a,B4: set_a_5785126655188516188pace_a] :
          ( collec5836124869716247675pace_a
          @ ^ [X2: a > probab4737552673497767871pace_a] :
              ( ( member7269867574344811837pace_a @ X2 @ A3 )
              & ( member7269867574344811837pace_a @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_627_Int__def,axiom,
    ( inf_inf_set_a_b
    = ( ^ [A3: set_a_b,B4: set_a_b] :
          ( collect_a_b
          @ ^ [X2: a > b] :
              ( ( member_a_b @ X2 @ A3 )
              & ( member_a_b @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_628_Int__Collect,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,P: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o] :
      ( ( member6667749562321684925pace_b @ X3 @ ( inf_in8598470101551243374pace_b @ A2 @ ( collec7915783404360165627pace_b @ P ) ) )
      = ( ( member6667749562321684925pace_b @ X3 @ A2 )
        & ( P @ X3 ) ) ) ).

% Int_Collect
thf(fact_629_Int__Collect,axiom,
    ! [X3: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,P: ( a > probab4737552677800996672pace_b ) > $o] :
      ( ( member7340901614391157822pace_b @ X3 @ ( inf_in3860511187648227951pace_b @ A2 @ ( collec5907158909762593660pace_b @ P ) ) )
      = ( ( member7340901614391157822pace_b @ X3 @ A2 )
        & ( P @ X3 ) ) ) ).

% Int_Collect
thf(fact_630_Int__Collect,axiom,
    ! [X3: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,P: ( probab4737552673497767871pace_a > b ) > $o] :
      ( ( member5008716543664893436ce_a_b @ X3 @ ( inf_in8638537385238394157ce_a_b @ A2 @ ( collec3574973839036329274ce_a_b @ P ) ) )
      = ( ( member5008716543664893436ce_a_b @ X3 @ A2 )
        & ( P @ X3 ) ) ) ).

% Int_Collect
thf(fact_631_Int__Collect,axiom,
    ! [X3: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,P: ( b > probab4737552677800996672pace_b ) > $o] :
      ( ( member1568243296417166973pace_b @ X3 @ ( inf_in433292969326628142pace_b @ A2 @ ( collec134500591788602811pace_b @ P ) ) )
      = ( ( member1568243296417166973pace_b @ X3 @ A2 )
        & ( P @ X3 ) ) ) ).

% Int_Collect
thf(fact_632_Int__Collect,axiom,
    ! [X3: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,P: ( a > probab8624551251471354625pace_b ) > $o] :
      ( ( member41169580844105599pace_b @ X3 @ ( inf_in6845569456361772336pace_b @ A2 @ ( collec1289203422882586301pace_b @ P ) ) )
      = ( ( member41169580844105599pace_b @ X3 @ A2 )
        & ( P @ X3 ) ) ) ).

% Int_Collect
thf(fact_633_Int__Collect,axiom,
    ! [X3: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,P: ( a > probab4737552673497767871pace_a ) > $o] :
      ( ( member7269867574344811837pace_a @ X3 @ ( inf_in6381695705937263598pace_a @ A2 @ ( collec5836124869716247675pace_a @ P ) ) )
      = ( ( member7269867574344811837pace_a @ X3 @ A2 )
        & ( P @ X3 ) ) ) ).

% Int_Collect
thf(fact_634_Int__Collect,axiom,
    ! [X3: a > b,A2: set_a_b,P: ( a > b ) > $o] :
      ( ( member_a_b @ X3 @ ( inf_inf_set_a_b @ A2 @ ( collect_a_b @ P ) ) )
      = ( ( member_a_b @ X3 @ A2 )
        & ( P @ X3 ) ) ) ).

% Int_Collect
thf(fact_635_subset__emptyI,axiom,
    ! [A2: set_Pr7742364250814120412pace_b] :
      ( ! [X4: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
          ~ ( member6667749562321684925pace_b @ X4 @ A2 )
     => ( ord_le1280929228223758908pace_b @ A2 @ bot_bo5050001829711205488pace_b ) ) ).

% subset_emptyI
thf(fact_636_subset__emptyI,axiom,
    ! [A2: set_a_3263942136899480541pace_b] :
      ( ! [X4: a > probab4737552677800996672pace_b] :
          ~ ( member7340901614391157822pace_b @ X4 @ A2 )
     => ( ord_le130150003083865149pace_b @ A2 @ bot_bo2617902995080265329pace_b ) ) ).

% subset_emptyI
thf(fact_637_subset__emptyI,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b] :
      ( ! [X4: probab4737552673497767871pace_a > b] :
          ~ ( member5008716543664893436ce_a_b @ X4 @ A2 )
     => ( ord_le4908176200674031355ce_a_b @ A2 @ bot_bo7395929192670431535ce_a_b ) ) ).

% subset_emptyI
thf(fact_638_subset__emptyI,axiom,
    ! [A2: set_b_9060095955432656540pace_b] :
      ( ! [X4: b > probab4737552677800996672pace_b] :
          ~ ( member1568243296417166973pace_b @ X4 @ A2 )
     => ( ord_le5926303821617041148pace_b @ A2 @ bot_bo8414056813613441328pace_b ) ) ).

% subset_emptyI
thf(fact_639_subset__emptyI,axiom,
    ! [A2: set_a_5989463605624649374pace_b] :
      ( ! [X4: a > probab8624551251471354625pace_b] :
          ~ ( member41169580844105599pace_b @ X4 @ A2 )
     => ( ord_le8751400619889063678pace_b @ A2 @ bot_bo3297101184521734450pace_b ) ) ).

% subset_emptyI
thf(fact_640_subset__emptyI,axiom,
    ! [A2: set_a_5785126655188516188pace_a] :
      ( ! [X4: a > probab4737552673497767871pace_a] :
          ~ ( member7269867574344811837pace_a @ X4 @ A2 )
     => ( ord_le2651334521372900796pace_a @ A2 @ bot_bo5139087513369300976pace_a ) ) ).

% subset_emptyI
thf(fact_641_subset__emptyI,axiom,
    ! [A2: set_a_b] :
      ( ! [X4: a > b] :
          ~ ( member_a_b @ X4 @ A2 )
     => ( ord_less_eq_set_a_b @ A2 @ bot_bot_set_a_b ) ) ).

% subset_emptyI
thf(fact_642_Int__emptyI,axiom,
    ! [A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ! [X4: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
          ( ( member6667749562321684925pace_b @ X4 @ A2 )
         => ~ ( member6667749562321684925pace_b @ X4 @ B2 ) )
     => ( ( inf_in8598470101551243374pace_b @ A2 @ B2 )
        = bot_bo5050001829711205488pace_b ) ) ).

% Int_emptyI
thf(fact_643_Int__emptyI,axiom,
    ! [A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ! [X4: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ X4 @ A2 )
         => ~ ( member7340901614391157822pace_b @ X4 @ B2 ) )
     => ( ( inf_in3860511187648227951pace_b @ A2 @ B2 )
        = bot_bo2617902995080265329pace_b ) ) ).

% Int_emptyI
thf(fact_644_Int__emptyI,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ! [X4: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ X4 @ A2 )
         => ~ ( member5008716543664893436ce_a_b @ X4 @ B2 ) )
     => ( ( inf_in8638537385238394157ce_a_b @ A2 @ B2 )
        = bot_bo7395929192670431535ce_a_b ) ) ).

% Int_emptyI
thf(fact_645_Int__emptyI,axiom,
    ! [A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ! [X4: b > probab4737552677800996672pace_b] :
          ( ( member1568243296417166973pace_b @ X4 @ A2 )
         => ~ ( member1568243296417166973pace_b @ X4 @ B2 ) )
     => ( ( inf_in433292969326628142pace_b @ A2 @ B2 )
        = bot_bo8414056813613441328pace_b ) ) ).

% Int_emptyI
thf(fact_646_Int__emptyI,axiom,
    ! [A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ! [X4: a > probab8624551251471354625pace_b] :
          ( ( member41169580844105599pace_b @ X4 @ A2 )
         => ~ ( member41169580844105599pace_b @ X4 @ B2 ) )
     => ( ( inf_in6845569456361772336pace_b @ A2 @ B2 )
        = bot_bo3297101184521734450pace_b ) ) ).

% Int_emptyI
thf(fact_647_Int__emptyI,axiom,
    ! [A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ! [X4: a > probab4737552673497767871pace_a] :
          ( ( member7269867574344811837pace_a @ X4 @ A2 )
         => ~ ( member7269867574344811837pace_a @ X4 @ B2 ) )
     => ( ( inf_in6381695705937263598pace_a @ A2 @ B2 )
        = bot_bo5139087513369300976pace_a ) ) ).

% Int_emptyI
thf(fact_648_Int__emptyI,axiom,
    ! [A2: set_a_b,B2: set_a_b] :
      ( ! [X4: a > b] :
          ( ( member_a_b @ X4 @ A2 )
         => ~ ( member_a_b @ X4 @ B2 ) )
     => ( ( inf_inf_set_a_b @ A2 @ B2 )
        = bot_bot_set_a_b ) ) ).

% Int_emptyI
thf(fact_649_disjoint__iff,axiom,
    ! [A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( ( inf_in8598470101551243374pace_b @ A2 @ B2 )
        = bot_bo5050001829711205488pace_b )
      = ( ! [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
            ( ( member6667749562321684925pace_b @ X2 @ A2 )
           => ~ ( member6667749562321684925pace_b @ X2 @ B2 ) ) ) ) ).

% disjoint_iff
thf(fact_650_disjoint__iff,axiom,
    ! [A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( ( inf_in3860511187648227951pace_b @ A2 @ B2 )
        = bot_bo2617902995080265329pace_b )
      = ( ! [X2: a > probab4737552677800996672pace_b] :
            ( ( member7340901614391157822pace_b @ X2 @ A2 )
           => ~ ( member7340901614391157822pace_b @ X2 @ B2 ) ) ) ) ).

% disjoint_iff
thf(fact_651_disjoint__iff,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( ( inf_in8638537385238394157ce_a_b @ A2 @ B2 )
        = bot_bo7395929192670431535ce_a_b )
      = ( ! [X2: probab4737552673497767871pace_a > b] :
            ( ( member5008716543664893436ce_a_b @ X2 @ A2 )
           => ~ ( member5008716543664893436ce_a_b @ X2 @ B2 ) ) ) ) ).

% disjoint_iff
thf(fact_652_disjoint__iff,axiom,
    ! [A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( ( inf_in433292969326628142pace_b @ A2 @ B2 )
        = bot_bo8414056813613441328pace_b )
      = ( ! [X2: b > probab4737552677800996672pace_b] :
            ( ( member1568243296417166973pace_b @ X2 @ A2 )
           => ~ ( member1568243296417166973pace_b @ X2 @ B2 ) ) ) ) ).

% disjoint_iff
thf(fact_653_disjoint__iff,axiom,
    ! [A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( ( inf_in6845569456361772336pace_b @ A2 @ B2 )
        = bot_bo3297101184521734450pace_b )
      = ( ! [X2: a > probab8624551251471354625pace_b] :
            ( ( member41169580844105599pace_b @ X2 @ A2 )
           => ~ ( member41169580844105599pace_b @ X2 @ B2 ) ) ) ) ).

% disjoint_iff
thf(fact_654_disjoint__iff,axiom,
    ! [A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( ( inf_in6381695705937263598pace_a @ A2 @ B2 )
        = bot_bo5139087513369300976pace_a )
      = ( ! [X2: a > probab4737552673497767871pace_a] :
            ( ( member7269867574344811837pace_a @ X2 @ A2 )
           => ~ ( member7269867574344811837pace_a @ X2 @ B2 ) ) ) ) ).

% disjoint_iff
thf(fact_655_disjoint__iff,axiom,
    ! [A2: set_a_b,B2: set_a_b] :
      ( ( ( inf_inf_set_a_b @ A2 @ B2 )
        = bot_bot_set_a_b )
      = ( ! [X2: a > b] :
            ( ( member_a_b @ X2 @ A2 )
           => ~ ( member_a_b @ X2 @ B2 ) ) ) ) ).

% disjoint_iff
thf(fact_656_image__subsetI,axiom,
    ! [A2: set_a_b,F: ( a > b ) > a > b,B2: set_a_b] :
      ( ! [X4: a > b] :
          ( ( member_a_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ B2 ) )
     => ( ord_less_eq_set_a_b @ ( image_a_b_a_b @ F @ A2 ) @ B2 ) ) ).

% image_subsetI
thf(fact_657_image__subsetI,axiom,
    ! [A2: set_a_3263942136899480541pace_b,F: ( a > probab4737552677800996672pace_b ) > a > b,B2: set_a_b] :
      ( ! [X4: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ B2 ) )
     => ( ord_less_eq_set_a_b @ ( image_5357422296895858068_b_a_b @ F @ A2 ) @ B2 ) ) ).

% image_subsetI
thf(fact_658_image__subsetI,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,F: ( probab4737552673497767871pace_a > b ) > a > b,B2: set_a_b] :
      ( ! [X4: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ B2 ) )
     => ( ord_less_eq_set_a_b @ ( image_2665524599124622162_b_a_b @ F @ A2 ) @ B2 ) ) ).

% image_subsetI
thf(fact_659_image__subsetI,axiom,
    ! [A2: set_b_9060095955432656540pace_b,F: ( b > probab4737552677800996672pace_b ) > a > b,B2: set_a_b] :
      ( ! [X4: b > probab4737552677800996672pace_b] :
          ( ( member1568243296417166973pace_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ B2 ) )
     => ( ord_less_eq_set_a_b @ ( image_8215988703474630099_b_a_b @ F @ A2 ) @ B2 ) ) ).

% image_subsetI
thf(fact_660_image__subsetI,axiom,
    ! [A2: set_a_5785126655188516188pace_a,F: ( a > probab4737552673497767871pace_a ) > a > b,B2: set_a_b] :
      ( ! [X4: a > probab4737552673497767871pace_a] :
          ( ( member7269867574344811837pace_a @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ B2 ) )
     => ( ord_less_eq_set_a_b @ ( image_7482003829499661459_a_a_b @ F @ A2 ) @ B2 ) ) ).

% image_subsetI
thf(fact_661_image__subsetI,axiom,
    ! [A2: set_a_b,F: ( a > b ) > a > probab4737552677800996672pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ! [X4: a > b] :
          ( ( member_a_b @ X4 @ A2 )
         => ( member7340901614391157822pace_b @ ( F @ X4 ) @ B2 ) )
     => ( ord_le130150003083865149pace_b @ ( image_6394579700060191636pace_b @ F @ A2 ) @ B2 ) ) ).

% image_subsetI
thf(fact_662_image__subsetI,axiom,
    ! [A2: set_a_b,F: ( a > b ) > probab4737552673497767871pace_a > b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ! [X4: a > b] :
          ( ( member_a_b @ X4 @ A2 )
         => ( member5008716543664893436ce_a_b @ ( F @ X4 ) @ B2 ) )
     => ( ord_le4908176200674031355ce_a_b @ ( image_4062394629333927250ce_a_b @ F @ A2 ) @ B2 ) ) ).

% image_subsetI
thf(fact_663_image__subsetI,axiom,
    ! [A2: set_a_b,F: ( a > b ) > b > probab4737552677800996672pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ! [X4: a > b] :
          ( ( member_a_b @ X4 @ A2 )
         => ( member1568243296417166973pace_b @ ( F @ X4 ) @ B2 ) )
     => ( ord_le5926303821617041148pace_b @ ( image_621921382086200787pace_b @ F @ A2 ) @ B2 ) ) ).

% image_subsetI
thf(fact_664_image__subsetI,axiom,
    ! [A2: set_a_b,F: ( a > b ) > a > probab4737552673497767871pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ! [X4: a > b] :
          ( ( member_a_b @ X4 @ A2 )
         => ( member7269867574344811837pace_a @ ( F @ X4 ) @ B2 ) )
     => ( ord_le2651334521372900796pace_a @ ( image_6323545660013845651pace_a @ F @ A2 ) @ B2 ) ) ).

% image_subsetI
thf(fact_665_image__subsetI,axiom,
    ! [A2: set_Pr7742364250814120412pace_b,F: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > a > b,B2: set_a_b] :
      ( ! [X4: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
          ( ( member6667749562321684925pace_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ B2 ) )
     => ( ord_less_eq_set_a_b @ ( image_750332364051833107_b_a_b @ F @ A2 ) @ B2 ) ) ).

% image_subsetI
thf(fact_666_image__subset__iff__funcset,axiom,
    ! [F3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr8456636223741192351pace_a,B2: set_Pr8527670263787538336pace_b] :
      ( ( ord_le6835030988992847680pace_b @ ( image_2686409134298894662pace_b @ F3 @ A2 ) @ B2 )
      = ( member6667749562321684925pace_b @ F3
        @ ( pi_Pro4287250843231025420pace_b @ A2
          @ ^ [Uu: probab4737552673497767871pace_a] : B2 ) ) ) ).

% image_subset_iff_funcset
thf(fact_667_image__subset__iff__funcset,axiom,
    ! [F3: a > probab4737552677800996672pace_b,A2: set_a,B2: set_Pr8527670263787538336pace_b] :
      ( ( ord_le6835030988992847680pace_b @ ( image_2612207334979447751pace_b @ F3 @ A2 ) @ B2 )
      = ( member7340901614391157822pace_b @ F3
        @ ( pi_a_P1132609506902963085pace_b @ A2
          @ ^ [Uu: a] : B2 ) ) ) ).

% image_subset_iff_funcset
thf(fact_668_image__subset__iff__funcset,axiom,
    ! [F3: probab4737552673497767871pace_a > b,A2: set_Pr8456636223741192351pace_a,B2: set_b] :
      ( ( ord_less_eq_set_b @ ( image_514102633767150853ce_a_b @ F3 @ A2 ) @ B2 )
      = ( member5008716543664893436ce_a_b @ F3
        @ ( pi_Pro8257876842545441995ce_a_b @ A2
          @ ^ [Uu: probab4737552673497767871pace_a] : B2 ) ) ) ).

% image_subset_iff_funcset
thf(fact_669_image__subset__iff__funcset,axiom,
    ! [F3: b > probab4737552677800996672pace_b,A2: set_b,B2: set_Pr8527670263787538336pace_b] :
      ( ( ord_le6835030988992847680pace_b @ ( image_6062921053860232710pace_b @ F3 @ A2 ) @ B2 )
      = ( member1568243296417166973pace_b @ F3
        @ ( pi_b_P4583323225783748044pace_b @ A2
          @ ^ [Uu: b] : B2 ) ) ) ).

% image_subset_iff_funcset
thf(fact_670_image__subset__iff__funcset,axiom,
    ! [F3: a > probab8624551251471354625pace_b,A2: set_a,B2: set_Pr2974436765678502625pace_b] :
      ( ( ord_le991005684472732289pace_b @ ( image_1260092861389117320pace_b @ F3 @ A2 ) @ B2 )
      = ( member41169580844105599pace_b @ F3
        @ ( pi_a_P2860934570321248078pace_b @ A2
          @ ^ [Uu: a] : B2 ) ) ) ).

% image_subset_iff_funcset
thf(fact_671_image__subset__iff__funcset,axiom,
    ! [F3: a > probab4737552673497767871pace_a,A2: set_a,B2: set_Pr8456636223741192351pace_a] :
      ( ( ord_le6763996948946501695pace_a @ ( image_2612207330676218950pace_a @ F3 @ A2 ) @ B2 )
      = ( member7269867574344811837pace_a @ F3
        @ ( pi_a_P1132609502599734284pace_a @ A2
          @ ^ [Uu: a] : B2 ) ) ) ).

% image_subset_iff_funcset
thf(fact_672_image__subset__iff__funcset,axiom,
    ! [F3: a > b,A2: set_a,B2: set_b] :
      ( ( ord_less_eq_set_b @ ( image_a_b @ F3 @ A2 ) @ B2 )
      = ( member_a_b @ F3
        @ ( pi_a_b @ A2
          @ ^ [Uu: a] : B2 ) ) ) ).

% image_subset_iff_funcset
thf(fact_673_funcset__image,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr8456636223741192351pace_a,B2: set_Pr8527670263787538336pace_b] :
      ( ( member6667749562321684925pace_b @ F
        @ ( pi_Pro4287250843231025420pace_b @ A2
          @ ^ [Uu: probab4737552673497767871pace_a] : B2 ) )
     => ( ord_le6835030988992847680pace_b @ ( image_2686409134298894662pace_b @ F @ A2 ) @ B2 ) ) ).

% funcset_image
thf(fact_674_funcset__image,axiom,
    ! [F: a > probab4737552677800996672pace_b,A2: set_a,B2: set_Pr8527670263787538336pace_b] :
      ( ( member7340901614391157822pace_b @ F
        @ ( pi_a_P1132609506902963085pace_b @ A2
          @ ^ [Uu: a] : B2 ) )
     => ( ord_le6835030988992847680pace_b @ ( image_2612207334979447751pace_b @ F @ A2 ) @ B2 ) ) ).

% funcset_image
thf(fact_675_funcset__image,axiom,
    ! [F: probab4737552673497767871pace_a > b,A2: set_Pr8456636223741192351pace_a,B2: set_b] :
      ( ( member5008716543664893436ce_a_b @ F
        @ ( pi_Pro8257876842545441995ce_a_b @ A2
          @ ^ [Uu: probab4737552673497767871pace_a] : B2 ) )
     => ( ord_less_eq_set_b @ ( image_514102633767150853ce_a_b @ F @ A2 ) @ B2 ) ) ).

% funcset_image
thf(fact_676_funcset__image,axiom,
    ! [F: b > probab4737552677800996672pace_b,A2: set_b,B2: set_Pr8527670263787538336pace_b] :
      ( ( member1568243296417166973pace_b @ F
        @ ( pi_b_P4583323225783748044pace_b @ A2
          @ ^ [Uu: b] : B2 ) )
     => ( ord_le6835030988992847680pace_b @ ( image_6062921053860232710pace_b @ F @ A2 ) @ B2 ) ) ).

% funcset_image
thf(fact_677_funcset__image,axiom,
    ! [F: a > probab8624551251471354625pace_b,A2: set_a,B2: set_Pr2974436765678502625pace_b] :
      ( ( member41169580844105599pace_b @ F
        @ ( pi_a_P2860934570321248078pace_b @ A2
          @ ^ [Uu: a] : B2 ) )
     => ( ord_le991005684472732289pace_b @ ( image_1260092861389117320pace_b @ F @ A2 ) @ B2 ) ) ).

% funcset_image
thf(fact_678_funcset__image,axiom,
    ! [F: a > probab4737552673497767871pace_a,A2: set_a,B2: set_Pr8456636223741192351pace_a] :
      ( ( member7269867574344811837pace_a @ F
        @ ( pi_a_P1132609502599734284pace_a @ A2
          @ ^ [Uu: a] : B2 ) )
     => ( ord_le6763996948946501695pace_a @ ( image_2612207330676218950pace_a @ F @ A2 ) @ B2 ) ) ).

% funcset_image
thf(fact_679_funcset__image,axiom,
    ! [F: a > b,A2: set_a,B2: set_b] :
      ( ( member_a_b @ F
        @ ( pi_a_b @ A2
          @ ^ [Uu: a] : B2 ) )
     => ( ord_less_eq_set_b @ ( image_a_b @ F @ A2 ) @ B2 ) ) ).

% funcset_image
thf(fact_680_monadP__qbs__f,axiom,
    ! [X: quasi_borel_b] :
      ( ord_le148948439097960011pace_b @ ( monad_4223963853064302126_MPx_b @ X )
      @ ( pi_rea6523506394092168711pace_b @ top_top_set_real
        @ ^ [Uu: real] : ( monad_3932415646498543857s_Px_b @ X ) ) ) ).

% monadP_qbs_f
thf(fact_681_monadP__qbs__f,axiom,
    ! [X: quasi_borel_a] :
      ( ord_le2670132957386995658pace_a @ ( monad_4223963853064302125_MPx_a @ X )
      @ ( pi_rea6523506389788939910pace_a @ top_top_set_real
        @ ^ [Uu: real] : ( monad_3932415646498543856s_Px_a @ X ) ) ) ).

% monadP_qbs_f
thf(fact_682_monadP__qbs__def,axiom,
    ( monad_1549008831671149082pace_b
    = ( ^ [X5: quasi_3431323906171122406pace_b] : ( quasi_6710520835166146883pace_b @ ( produc7684423503814015074pace_b @ ( monad_8082909354289562930pace_b @ X5 ) @ ( monad_2041073082211224175pace_b @ X5 ) ) ) ) ) ).

% monadP_qbs_def
thf(fact_683_monadP__qbs__def,axiom,
    ( monad_monadP_qbs_b
    = ( ^ [X5: quasi_borel_b] : ( quasi_7051621126577149314pace_b @ ( produc5532427567629089954pace_b @ ( monad_3932415646498543857s_Px_b @ X5 ) @ ( monad_4223963853064302126_MPx_b @ X5 ) ) ) ) ) ).

% monadP_qbs_def
thf(fact_684_monadP__qbs__def,axiom,
    ( monad_monadP_qbs_a
    = ( ^ [X5: quasi_borel_a] : ( quasi_7051621122273920513pace_a @ ( produc6037706855006621922pace_a @ ( monad_3932415646498543856s_Px_a @ X5 ) @ ( monad_4223963853064302125_MPx_a @ X5 ) ) ) ) ) ).

% monadP_qbs_def
thf(fact_685_sub__qbs__closed_I3_J,axiom,
    ! [X: quasi_3431323906171122406pace_b,U: set_Pr8527670263787538336pace_b] :
      ( qbs_cl4771842943276419957pace_b
      @ ( collec7038231833220187958pace_b
        @ ^ [F2: real > probab4737552677800996672pace_b] :
            ( ( member5892728515905534708pace_b @ F2
              @ ( pi_rea6523506394092168711pace_b @ top_top_set_real
                @ ^ [Uu: real] : ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ U ) ) )
            & ( member5892728515905534708pace_b @ F2 @ ( qbs_Mx4221877620443553463pace_b @ X ) ) ) ) ) ).

% sub_qbs_closed(3)
thf(fact_686_sub__qbs__closed_I3_J,axiom,
    ! [X: quasi_3360289866124776421pace_a,U: set_Pr8456636223741192351pace_a] :
      ( qbs_cl4771842938973191156pace_a
      @ ( collec6967197793173841973pace_a
        @ ^ [F2: real > probab4737552673497767871pace_a] :
            ( ( member5821694475859188723pace_a @ F2
              @ ( pi_rea6523506389788939910pace_a @ top_top_set_real
                @ ^ [Uu: real] : ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ U ) ) )
            & ( member5821694475859188723pace_a @ F2 @ ( qbs_Mx4221877616140324662pace_a @ X ) ) ) ) ) ).

% sub_qbs_closed(3)
thf(fact_687_sub__qbs__correct,axiom,
    ! [X: quasi_3431323906171122406pace_b,U: set_Pr8527670263787538336pace_b] :
      ( ( quasi_159326149610617975pace_b @ ( sub_qb625756744037846968pace_b @ X @ U ) )
      = ( produc5532427567629089954pace_b @ ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ U )
        @ ( collec7038231833220187958pace_b
          @ ^ [F2: real > probab4737552677800996672pace_b] :
              ( ( member5892728515905534708pace_b @ F2
                @ ( pi_rea6523506394092168711pace_b @ top_top_set_real
                  @ ^ [Uu: real] : ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ U ) ) )
              & ( member5892728515905534708pace_b @ F2 @ ( qbs_Mx4221877620443553463pace_b @ X ) ) ) ) ) ) ).

% sub_qbs_correct
thf(fact_688_sub__qbs__correct,axiom,
    ! [X: quasi_3360289866124776421pace_a,U: set_Pr8456636223741192351pace_a] :
      ( ( quasi_159326145307389174pace_a @ ( sub_qb625756739734618167pace_a @ X @ U ) )
      = ( produc6037706855006621922pace_a @ ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ U )
        @ ( collec6967197793173841973pace_a
          @ ^ [F2: real > probab4737552673497767871pace_a] :
              ( ( member5821694475859188723pace_a @ F2
                @ ( pi_rea6523506389788939910pace_a @ top_top_set_real
                  @ ^ [Uu: real] : ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ U ) ) )
              & ( member5821694475859188723pace_a @ F2 @ ( qbs_Mx4221877616140324662pace_a @ X ) ) ) ) ) ) ).

% sub_qbs_correct
thf(fact_689_sub__qbs__Mx,axiom,
    ! [X: quasi_3431323906171122406pace_b,U: set_Pr8527670263787538336pace_b] :
      ( ( qbs_Mx4221877620443553463pace_b @ ( sub_qb625756744037846968pace_b @ X @ U ) )
      = ( collec7038231833220187958pace_b
        @ ^ [F2: real > probab4737552677800996672pace_b] :
            ( ( member5892728515905534708pace_b @ F2
              @ ( pi_rea6523506394092168711pace_b @ top_top_set_real
                @ ^ [Uu: real] : ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ U ) ) )
            & ( member5892728515905534708pace_b @ F2 @ ( qbs_Mx4221877620443553463pace_b @ X ) ) ) ) ) ).

% sub_qbs_Mx
thf(fact_690_sub__qbs__Mx,axiom,
    ! [X: quasi_3360289866124776421pace_a,U: set_Pr8456636223741192351pace_a] :
      ( ( qbs_Mx4221877616140324662pace_a @ ( sub_qb625756739734618167pace_a @ X @ U ) )
      = ( collec6967197793173841973pace_a
        @ ^ [F2: real > probab4737552673497767871pace_a] :
            ( ( member5821694475859188723pace_a @ F2
              @ ( pi_rea6523506389788939910pace_a @ top_top_set_real
                @ ^ [Uu: real] : ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ U ) ) )
            & ( member5821694475859188723pace_a @ F2 @ ( qbs_Mx4221877616140324662pace_a @ X ) ) ) ) ) ).

% sub_qbs_Mx
thf(fact_691_sub__qbs__def,axiom,
    ( sub_qb625756744037846968pace_b
    = ( ^ [X5: quasi_3431323906171122406pace_b,U2: set_Pr8527670263787538336pace_b] :
          ( quasi_7051621126577149314pace_b
          @ ( produc5532427567629089954pace_b @ ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X5 ) @ U2 )
            @ ( collec7038231833220187958pace_b
              @ ^ [F2: real > probab4737552677800996672pace_b] :
                  ( ( member5892728515905534708pace_b @ F2
                    @ ( pi_rea6523506394092168711pace_b @ top_top_set_real
                      @ ^ [Uu: real] : ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X5 ) @ U2 ) ) )
                  & ( member5892728515905534708pace_b @ F2 @ ( qbs_Mx4221877620443553463pace_b @ X5 ) ) ) ) ) ) ) ) ).

% sub_qbs_def
thf(fact_692_sub__qbs__def,axiom,
    ( sub_qb625756739734618167pace_a
    = ( ^ [X5: quasi_3360289866124776421pace_a,U2: set_Pr8456636223741192351pace_a] :
          ( quasi_7051621122273920513pace_a
          @ ( produc6037706855006621922pace_a @ ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X5 ) @ U2 )
            @ ( collec6967197793173841973pace_a
              @ ^ [F2: real > probab4737552673497767871pace_a] :
                  ( ( member5821694475859188723pace_a @ F2
                    @ ( pi_rea6523506389788939910pace_a @ top_top_set_real
                      @ ^ [Uu: real] : ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X5 ) @ U2 ) ) )
                  & ( member5821694475859188723pace_a @ F2 @ ( qbs_Mx4221877616140324662pace_a @ X5 ) ) ) ) ) ) ) ) ).

% sub_qbs_def
thf(fact_693_sub__qbs,axiom,
    ! [U: set_Pr8527670263787538336pace_b,X: quasi_3431323906171122406pace_b] :
      ( ( ord_le6835030988992847680pace_b @ U @ ( qbs_sp9192884687904738934pace_b @ X ) )
     => ( ( produc5532427567629089954pace_b @ ( qbs_sp9192884687904738934pace_b @ ( sub_qb625756744037846968pace_b @ X @ U ) ) @ ( qbs_Mx4221877620443553463pace_b @ ( sub_qb625756744037846968pace_b @ X @ U ) ) )
        = ( produc5532427567629089954pace_b @ U
          @ ( collec7038231833220187958pace_b
            @ ^ [F2: real > probab4737552677800996672pace_b] :
                ( ( member5892728515905534708pace_b @ F2
                  @ ( pi_rea6523506394092168711pace_b @ top_top_set_real
                    @ ^ [Uu: real] : U ) )
                & ( member5892728515905534708pace_b @ F2 @ ( qbs_Mx4221877620443553463pace_b @ X ) ) ) ) ) ) ) ).

% sub_qbs
thf(fact_694_sub__qbs,axiom,
    ! [U: set_Pr8456636223741192351pace_a,X: quasi_3360289866124776421pace_a] :
      ( ( ord_le6763996948946501695pace_a @ U @ ( qbs_sp9192884683601510133pace_a @ X ) )
     => ( ( produc6037706855006621922pace_a @ ( qbs_sp9192884683601510133pace_a @ ( sub_qb625756739734618167pace_a @ X @ U ) ) @ ( qbs_Mx4221877616140324662pace_a @ ( sub_qb625756739734618167pace_a @ X @ U ) ) )
        = ( produc6037706855006621922pace_a @ U
          @ ( collec6967197793173841973pace_a
            @ ^ [F2: real > probab4737552673497767871pace_a] :
                ( ( member5821694475859188723pace_a @ F2
                  @ ( pi_rea6523506389788939910pace_a @ top_top_set_real
                    @ ^ [Uu: real] : U ) )
                & ( member5821694475859188723pace_a @ F2 @ ( qbs_Mx4221877616140324662pace_a @ X ) ) ) ) ) ) ) ).

% sub_qbs
thf(fact_695_inf__quasi__borel__def,axiom,
    ( inf_qu8610821493433791850pace_b
    = ( ^ [X5: quasi_3431323906171122406pace_b,X6: quasi_3431323906171122406pace_b] : ( quasi_7051621126577149314pace_b @ ( produc5532427567629089954pace_b @ ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X5 ) @ ( qbs_sp9192884687904738934pace_b @ X6 ) ) @ ( inf_in2124724585691125913pace_b @ ( qbs_Mx4221877620443553463pace_b @ X5 ) @ ( qbs_Mx4221877620443553463pace_b @ X6 ) ) ) ) ) ) ).

% inf_quasi_borel_def
thf(fact_696_inf__quasi__borel__def,axiom,
    ( inf_qu8610821489130563049pace_a
    = ( ^ [X5: quasi_3360289866124776421pace_a,X6: quasi_3360289866124776421pace_a] : ( quasi_7051621122273920513pace_a @ ( produc6037706855006621922pace_a @ ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X5 ) @ ( qbs_sp9192884683601510133pace_a @ X6 ) ) @ ( inf_in4645909103980161560pace_a @ ( qbs_Mx4221877616140324662pace_a @ X5 ) @ ( qbs_Mx4221877616140324662pace_a @ X6 ) ) ) ) ) ) ).

% inf_quasi_borel_def
thf(fact_697_inf__quasi__borel__correct,axiom,
    ! [X: quasi_3431323906171122406pace_b,X7: quasi_3431323906171122406pace_b] :
      ( ( quasi_159326149610617975pace_b @ ( inf_qu8610821493433791850pace_b @ X @ X7 ) )
      = ( produc5532427567629089954pace_b @ ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ ( qbs_sp9192884687904738934pace_b @ X7 ) ) @ ( inf_in2124724585691125913pace_b @ ( qbs_Mx4221877620443553463pace_b @ X ) @ ( qbs_Mx4221877620443553463pace_b @ X7 ) ) ) ) ).

% inf_quasi_borel_correct
thf(fact_698_inf__quasi__borel__correct,axiom,
    ! [X: quasi_3360289866124776421pace_a,X7: quasi_3360289866124776421pace_a] :
      ( ( quasi_159326145307389174pace_a @ ( inf_qu8610821489130563049pace_a @ X @ X7 ) )
      = ( produc6037706855006621922pace_a @ ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ ( qbs_sp9192884683601510133pace_a @ X7 ) ) @ ( inf_in4645909103980161560pace_a @ ( qbs_Mx4221877616140324662pace_a @ X ) @ ( qbs_Mx4221877616140324662pace_a @ X7 ) ) ) ) ).

% inf_quasi_borel_correct
thf(fact_699_sub__qbs__space,axiom,
    ! [X: quasi_3431323906171122406pace_b,U: set_Pr8527670263787538336pace_b] :
      ( ( qbs_sp9192884687904738934pace_b @ ( sub_qb625756744037846968pace_b @ X @ U ) )
      = ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ U ) ) ).

% sub_qbs_space
thf(fact_700_sub__qbs__space,axiom,
    ! [X: quasi_3360289866124776421pace_a,U: set_Pr8456636223741192351pace_a] :
      ( ( qbs_sp9192884683601510133pace_a @ ( sub_qb625756739734618167pace_a @ X @ U ) )
      = ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ U ) ) ).

% sub_qbs_space
thf(fact_701_inf__qbs__space,axiom,
    ! [X: quasi_3431323906171122406pace_b,X7: quasi_3431323906171122406pace_b] :
      ( ( qbs_sp9192884687904738934pace_b @ ( inf_qu8610821493433791850pace_b @ X @ X7 ) )
      = ( inf_in8913089558028559758pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ ( qbs_sp9192884687904738934pace_b @ X7 ) ) ) ).

% inf_qbs_space
thf(fact_702_inf__qbs__space,axiom,
    ! [X: quasi_3360289866124776421pace_a,X7: quasi_3360289866124776421pace_a] :
      ( ( qbs_sp9192884683601510133pace_a @ ( inf_qu8610821489130563049pace_a @ X @ X7 ) )
      = ( inf_in8842055517982213773pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ ( qbs_sp9192884683601510133pace_a @ X7 ) ) ) ).

% inf_qbs_space
thf(fact_703_inf__qbs__Mx,axiom,
    ! [X: quasi_3431323906171122406pace_b,X7: quasi_3431323906171122406pace_b] :
      ( ( qbs_Mx4221877620443553463pace_b @ ( inf_qu8610821493433791850pace_b @ X @ X7 ) )
      = ( inf_in2124724585691125913pace_b @ ( qbs_Mx4221877620443553463pace_b @ X ) @ ( qbs_Mx4221877620443553463pace_b @ X7 ) ) ) ).

% inf_qbs_Mx
thf(fact_704_inf__qbs__Mx,axiom,
    ! [X: quasi_3360289866124776421pace_a,X7: quasi_3360289866124776421pace_a] :
      ( ( qbs_Mx4221877616140324662pace_a @ ( inf_qu8610821489130563049pace_a @ X @ X7 ) )
      = ( inf_in4645909103980161560pace_a @ ( qbs_Mx4221877616140324662pace_a @ X ) @ ( qbs_Mx4221877616140324662pace_a @ X7 ) ) ) ).

% inf_qbs_Mx
thf(fact_705_inf__Int__eq,axiom,
    ! [R3: set_Pr7742364250814120412pace_b,S3: set_Pr7742364250814120412pace_b] :
      ( ( inf_in5826830131739084183ce_b_o
        @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ R3 )
        @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ S3 ) )
      = ( ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ ( inf_in8598470101551243374pace_b @ R3 @ S3 ) ) ) ) ).

% inf_Int_eq
thf(fact_706_inf__Int__eq,axiom,
    ! [R3: set_a_3263942136899480541pace_b,S3: set_a_3263942136899480541pace_b] :
      ( ( inf_in7481488465596882134ce_b_o
        @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ R3 )
        @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ S3 ) )
      = ( ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ ( inf_in3860511187648227951pace_b @ R3 @ S3 ) ) ) ) ).

% inf_Int_eq
thf(fact_707_inf__Int__eq,axiom,
    ! [R3: set_Pr8041968334489646747ce_a_b,S3: set_Pr8041968334489646747ce_a_b] :
      ( ( inf_in4158870736502718360_a_b_o
        @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ R3 )
        @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ S3 ) )
      = ( ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ ( inf_in8638537385238394157ce_a_b @ R3 @ S3 ) ) ) ) ).

% inf_Int_eq
thf(fact_708_inf__Int__eq,axiom,
    ! [R3: set_b_9060095955432656540pace_b,S3: set_b_9060095955432656540pace_b] :
      ( ( inf_in4453696201095317719ce_b_o
        @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ R3 )
        @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ S3 ) )
      = ( ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ ( inf_in433292969326628142pace_b @ R3 @ S3 ) ) ) ) ).

% inf_Int_eq
thf(fact_709_inf__Int__eq,axiom,
    ! [R3: set_a_5989463605624649374pace_b,S3: set_a_5989463605624649374pace_b] :
      ( ( inf_in1454270903699293013ce_b_o
        @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ R3 )
        @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ S3 ) )
      = ( ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ ( inf_in6845569456361772336pace_b @ R3 @ S3 ) ) ) ) ).

% inf_Int_eq
thf(fact_710_inf__Int__eq,axiom,
    ! [R3: set_a_5785126655188516188pace_a,S3: set_a_5785126655188516188pace_a] :
      ( ( inf_in8117137466201868823ce_a_o
        @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ R3 )
        @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ S3 ) )
      = ( ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ ( inf_in6381695705937263598pace_a @ R3 @ S3 ) ) ) ) ).

% inf_Int_eq
thf(fact_711_inf__Int__eq,axiom,
    ! [R3: set_a_b,S3: set_a_b] :
      ( ( inf_inf_a_b_o
        @ ^ [X2: a > b] : ( member_a_b @ X2 @ R3 )
        @ ^ [X2: a > b] : ( member_a_b @ X2 @ S3 ) )
      = ( ^ [X2: a > b] : ( member_a_b @ X2 @ ( inf_inf_set_a_b @ R3 @ S3 ) ) ) ) ).

% inf_Int_eq
thf(fact_712_inf__set__def,axiom,
    ( inf_in8598470101551243374pace_b
    = ( ^ [A3: set_Pr7742364250814120412pace_b,B4: set_Pr7742364250814120412pace_b] :
          ( collec7915783404360165627pace_b
          @ ( inf_in5826830131739084183ce_b_o
            @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ A3 )
            @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_713_inf__set__def,axiom,
    ( inf_in3860511187648227951pace_b
    = ( ^ [A3: set_a_3263942136899480541pace_b,B4: set_a_3263942136899480541pace_b] :
          ( collec5907158909762593660pace_b
          @ ( inf_in7481488465596882134ce_b_o
            @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ A3 )
            @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_714_inf__set__def,axiom,
    ( inf_in8638537385238394157ce_a_b
    = ( ^ [A3: set_Pr8041968334489646747ce_a_b,B4: set_Pr8041968334489646747ce_a_b] :
          ( collec3574973839036329274ce_a_b
          @ ( inf_in4158870736502718360_a_b_o
            @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ A3 )
            @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_715_inf__set__def,axiom,
    ( inf_in433292969326628142pace_b
    = ( ^ [A3: set_b_9060095955432656540pace_b,B4: set_b_9060095955432656540pace_b] :
          ( collec134500591788602811pace_b
          @ ( inf_in4453696201095317719ce_b_o
            @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ A3 )
            @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_716_inf__set__def,axiom,
    ( inf_in6845569456361772336pace_b
    = ( ^ [A3: set_a_5989463605624649374pace_b,B4: set_a_5989463605624649374pace_b] :
          ( collec1289203422882586301pace_b
          @ ( inf_in1454270903699293013ce_b_o
            @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ A3 )
            @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_717_inf__set__def,axiom,
    ( inf_in6381695705937263598pace_a
    = ( ^ [A3: set_a_5785126655188516188pace_a,B4: set_a_5785126655188516188pace_a] :
          ( collec5836124869716247675pace_a
          @ ( inf_in8117137466201868823ce_a_o
            @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ A3 )
            @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_718_inf__set__def,axiom,
    ( inf_inf_set_a_b
    = ( ^ [A3: set_a_b,B4: set_a_b] :
          ( collect_a_b
          @ ( inf_inf_a_b_o
            @ ^ [X2: a > b] : ( member_a_b @ X2 @ A3 )
            @ ^ [X2: a > b] : ( member_a_b @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_719_pred__subset__eq,axiom,
    ! [R3: set_Pr7742364250814120412pace_b,S3: set_Pr7742364250814120412pace_b] :
      ( ( ord_le5572460138280733001ce_b_o
        @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ R3 )
        @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ S3 ) )
      = ( ord_le1280929228223758908pace_b @ R3 @ S3 ) ) ).

% pred_subset_eq
thf(fact_720_pred__subset__eq,axiom,
    ! [R3: set_a_3263942136899480541pace_b,S3: set_a_3263942136899480541pace_b] :
      ( ( ord_le4998732279864508552ce_b_o
        @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ R3 )
        @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ S3 ) )
      = ( ord_le130150003083865149pace_b @ R3 @ S3 ) ) ).

% pred_subset_eq
thf(fact_721_pred__subset__eq,axiom,
    ! [R3: set_Pr8041968334489646747ce_a_b,S3: set_Pr8041968334489646747ce_a_b] :
      ( ( ord_le1676114550770344778_a_b_o
        @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ R3 )
        @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ S3 ) )
      = ( ord_le4908176200674031355ce_a_b @ R3 @ S3 ) ) ).

% pred_subset_eq
thf(fact_722_pred__subset__eq,axiom,
    ! [R3: set_b_9060095955432656540pace_b,S3: set_b_9060095955432656540pace_b] :
      ( ( ord_le1970940015362944137ce_b_o
        @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ R3 )
        @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ S3 ) )
      = ( ord_le5926303821617041148pace_b @ R3 @ S3 ) ) ).

% pred_subset_eq
thf(fact_723_pred__subset__eq,axiom,
    ! [R3: set_a_5989463605624649374pace_b,S3: set_a_5989463605624649374pace_b] :
      ( ( ord_le1199900910240941831ce_b_o
        @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ R3 )
        @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ S3 ) )
      = ( ord_le8751400619889063678pace_b @ R3 @ S3 ) ) ).

% pred_subset_eq
thf(fact_724_pred__subset__eq,axiom,
    ! [R3: set_a_5785126655188516188pace_a,S3: set_a_5785126655188516188pace_a] :
      ( ( ord_le5634381280469495241ce_a_o
        @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ R3 )
        @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ S3 ) )
      = ( ord_le2651334521372900796pace_a @ R3 @ S3 ) ) ).

% pred_subset_eq
thf(fact_725_pred__subset__eq,axiom,
    ! [R3: set_a_b,S3: set_a_b] :
      ( ( ord_less_eq_a_b_o
        @ ^ [X2: a > b] : ( member_a_b @ X2 @ R3 )
        @ ^ [X2: a > b] : ( member_a_b @ X2 @ S3 ) )
      = ( ord_less_eq_set_a_b @ R3 @ S3 ) ) ).

% pred_subset_eq
thf(fact_726_less__eq__set__def,axiom,
    ( ord_le1280929228223758908pace_b
    = ( ^ [A3: set_Pr7742364250814120412pace_b,B4: set_Pr7742364250814120412pace_b] :
          ( ord_le5572460138280733001ce_b_o
          @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ A3 )
          @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ B4 ) ) ) ) ).

% less_eq_set_def
thf(fact_727_less__eq__set__def,axiom,
    ( ord_le130150003083865149pace_b
    = ( ^ [A3: set_a_3263942136899480541pace_b,B4: set_a_3263942136899480541pace_b] :
          ( ord_le4998732279864508552ce_b_o
          @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ A3 )
          @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ B4 ) ) ) ) ).

% less_eq_set_def
thf(fact_728_less__eq__set__def,axiom,
    ( ord_le4908176200674031355ce_a_b
    = ( ^ [A3: set_Pr8041968334489646747ce_a_b,B4: set_Pr8041968334489646747ce_a_b] :
          ( ord_le1676114550770344778_a_b_o
          @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ A3 )
          @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ B4 ) ) ) ) ).

% less_eq_set_def
thf(fact_729_less__eq__set__def,axiom,
    ( ord_le5926303821617041148pace_b
    = ( ^ [A3: set_b_9060095955432656540pace_b,B4: set_b_9060095955432656540pace_b] :
          ( ord_le1970940015362944137ce_b_o
          @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ A3 )
          @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ B4 ) ) ) ) ).

% less_eq_set_def
thf(fact_730_less__eq__set__def,axiom,
    ( ord_le8751400619889063678pace_b
    = ( ^ [A3: set_a_5989463605624649374pace_b,B4: set_a_5989463605624649374pace_b] :
          ( ord_le1199900910240941831ce_b_o
          @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ A3 )
          @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ B4 ) ) ) ) ).

% less_eq_set_def
thf(fact_731_less__eq__set__def,axiom,
    ( ord_le2651334521372900796pace_a
    = ( ^ [A3: set_a_5785126655188516188pace_a,B4: set_a_5785126655188516188pace_a] :
          ( ord_le5634381280469495241ce_a_o
          @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ A3 )
          @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ B4 ) ) ) ) ).

% less_eq_set_def
thf(fact_732_less__eq__set__def,axiom,
    ( ord_less_eq_set_a_b
    = ( ^ [A3: set_a_b,B4: set_a_b] :
          ( ord_less_eq_a_b_o
          @ ^ [X2: a > b] : ( member_a_b @ X2 @ A3 )
          @ ^ [X2: a > b] : ( member_a_b @ X2 @ B4 ) ) ) ) ).

% less_eq_set_def
thf(fact_733_less__eq__quasi__borel_Ointros_I2_J,axiom,
    ! [X: quasi_3431323906171122406pace_b,Y: quasi_3431323906171122406pace_b] :
      ( ( ( qbs_sp9192884687904738934pace_b @ X )
        = ( qbs_sp9192884687904738934pace_b @ Y ) )
     => ( ( ord_le148948439097960011pace_b @ ( qbs_Mx4221877620443553463pace_b @ Y ) @ ( qbs_Mx4221877620443553463pace_b @ X ) )
       => ( ord_le2345554537223240326pace_b @ X @ Y ) ) ) ).

% less_eq_quasi_borel.intros(2)
thf(fact_734_less__eq__quasi__borel_Ointros_I2_J,axiom,
    ! [X: quasi_3360289866124776421pace_a,Y: quasi_3360289866124776421pace_a] :
      ( ( ( qbs_sp9192884683601510133pace_a @ X )
        = ( qbs_sp9192884683601510133pace_a @ Y ) )
     => ( ( ord_le2670132957386995658pace_a @ ( qbs_Mx4221877616140324662pace_a @ Y ) @ ( qbs_Mx4221877616140324662pace_a @ X ) )
       => ( ord_le2274520497176894341pace_a @ X @ Y ) ) ) ).

% less_eq_quasi_borel.intros(2)
thf(fact_735_qbs__decomp,axiom,
    ! [X: quasi_3431323906171122406pace_b] : ( member2497209941670631003pace_b @ ( produc5532427567629089954pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ ( qbs_Mx4221877620443553463pace_b @ X ) ) @ ( collec1864026394871242909pace_b @ ( produc963543601085603617ce_b_o @ is_qua6571408881302630775pace_b ) ) ) ).

% qbs_decomp
thf(fact_736_qbs__decomp,axiom,
    ! [X: quasi_3360289866124776421pace_a] : ( member640087230083980059pace_a @ ( produc6037706855006621922pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ ( qbs_Mx4221877616140324662pace_a @ X ) ) @ ( collec6903683284591965pace_a @ ( produc7896180074483694305ce_a_o @ is_qua6571408876999401974pace_a ) ) ) ).

% qbs_decomp
thf(fact_737_subset__CollectI,axiom,
    ! [B2: set_Pr7742364250814120412pace_b,A2: set_Pr7742364250814120412pace_b,Q: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o,P: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o] :
      ( ( ord_le1280929228223758908pace_b @ B2 @ A2 )
     => ( ! [X4: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
            ( ( member6667749562321684925pace_b @ X4 @ B2 )
           => ( ( Q @ X4 )
             => ( P @ X4 ) ) )
       => ( ord_le1280929228223758908pace_b
          @ ( collec7915783404360165627pace_b
            @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
                ( ( member6667749562321684925pace_b @ X2 @ B2 )
                & ( Q @ X2 ) ) )
          @ ( collec7915783404360165627pace_b
            @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
                ( ( member6667749562321684925pace_b @ X2 @ A2 )
                & ( P @ X2 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_738_subset__CollectI,axiom,
    ! [B2: set_a_3263942136899480541pace_b,A2: set_a_3263942136899480541pace_b,Q: ( a > probab4737552677800996672pace_b ) > $o,P: ( a > probab4737552677800996672pace_b ) > $o] :
      ( ( ord_le130150003083865149pace_b @ B2 @ A2 )
     => ( ! [X4: a > probab4737552677800996672pace_b] :
            ( ( member7340901614391157822pace_b @ X4 @ B2 )
           => ( ( Q @ X4 )
             => ( P @ X4 ) ) )
       => ( ord_le130150003083865149pace_b
          @ ( collec5907158909762593660pace_b
            @ ^ [X2: a > probab4737552677800996672pace_b] :
                ( ( member7340901614391157822pace_b @ X2 @ B2 )
                & ( Q @ X2 ) ) )
          @ ( collec5907158909762593660pace_b
            @ ^ [X2: a > probab4737552677800996672pace_b] :
                ( ( member7340901614391157822pace_b @ X2 @ A2 )
                & ( P @ X2 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_739_subset__CollectI,axiom,
    ! [B2: set_Pr8041968334489646747ce_a_b,A2: set_Pr8041968334489646747ce_a_b,Q: ( probab4737552673497767871pace_a > b ) > $o,P: ( probab4737552673497767871pace_a > b ) > $o] :
      ( ( ord_le4908176200674031355ce_a_b @ B2 @ A2 )
     => ( ! [X4: probab4737552673497767871pace_a > b] :
            ( ( member5008716543664893436ce_a_b @ X4 @ B2 )
           => ( ( Q @ X4 )
             => ( P @ X4 ) ) )
       => ( ord_le4908176200674031355ce_a_b
          @ ( collec3574973839036329274ce_a_b
            @ ^ [X2: probab4737552673497767871pace_a > b] :
                ( ( member5008716543664893436ce_a_b @ X2 @ B2 )
                & ( Q @ X2 ) ) )
          @ ( collec3574973839036329274ce_a_b
            @ ^ [X2: probab4737552673497767871pace_a > b] :
                ( ( member5008716543664893436ce_a_b @ X2 @ A2 )
                & ( P @ X2 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_740_subset__CollectI,axiom,
    ! [B2: set_b_9060095955432656540pace_b,A2: set_b_9060095955432656540pace_b,Q: ( b > probab4737552677800996672pace_b ) > $o,P: ( b > probab4737552677800996672pace_b ) > $o] :
      ( ( ord_le5926303821617041148pace_b @ B2 @ A2 )
     => ( ! [X4: b > probab4737552677800996672pace_b] :
            ( ( member1568243296417166973pace_b @ X4 @ B2 )
           => ( ( Q @ X4 )
             => ( P @ X4 ) ) )
       => ( ord_le5926303821617041148pace_b
          @ ( collec134500591788602811pace_b
            @ ^ [X2: b > probab4737552677800996672pace_b] :
                ( ( member1568243296417166973pace_b @ X2 @ B2 )
                & ( Q @ X2 ) ) )
          @ ( collec134500591788602811pace_b
            @ ^ [X2: b > probab4737552677800996672pace_b] :
                ( ( member1568243296417166973pace_b @ X2 @ A2 )
                & ( P @ X2 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_741_subset__CollectI,axiom,
    ! [B2: set_a_5989463605624649374pace_b,A2: set_a_5989463605624649374pace_b,Q: ( a > probab8624551251471354625pace_b ) > $o,P: ( a > probab8624551251471354625pace_b ) > $o] :
      ( ( ord_le8751400619889063678pace_b @ B2 @ A2 )
     => ( ! [X4: a > probab8624551251471354625pace_b] :
            ( ( member41169580844105599pace_b @ X4 @ B2 )
           => ( ( Q @ X4 )
             => ( P @ X4 ) ) )
       => ( ord_le8751400619889063678pace_b
          @ ( collec1289203422882586301pace_b
            @ ^ [X2: a > probab8624551251471354625pace_b] :
                ( ( member41169580844105599pace_b @ X2 @ B2 )
                & ( Q @ X2 ) ) )
          @ ( collec1289203422882586301pace_b
            @ ^ [X2: a > probab8624551251471354625pace_b] :
                ( ( member41169580844105599pace_b @ X2 @ A2 )
                & ( P @ X2 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_742_subset__CollectI,axiom,
    ! [B2: set_a_5785126655188516188pace_a,A2: set_a_5785126655188516188pace_a,Q: ( a > probab4737552673497767871pace_a ) > $o,P: ( a > probab4737552673497767871pace_a ) > $o] :
      ( ( ord_le2651334521372900796pace_a @ B2 @ A2 )
     => ( ! [X4: a > probab4737552673497767871pace_a] :
            ( ( member7269867574344811837pace_a @ X4 @ B2 )
           => ( ( Q @ X4 )
             => ( P @ X4 ) ) )
       => ( ord_le2651334521372900796pace_a
          @ ( collec5836124869716247675pace_a
            @ ^ [X2: a > probab4737552673497767871pace_a] :
                ( ( member7269867574344811837pace_a @ X2 @ B2 )
                & ( Q @ X2 ) ) )
          @ ( collec5836124869716247675pace_a
            @ ^ [X2: a > probab4737552673497767871pace_a] :
                ( ( member7269867574344811837pace_a @ X2 @ A2 )
                & ( P @ X2 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_743_subset__CollectI,axiom,
    ! [B2: set_a_b,A2: set_a_b,Q: ( a > b ) > $o,P: ( a > b ) > $o] :
      ( ( ord_less_eq_set_a_b @ B2 @ A2 )
     => ( ! [X4: a > b] :
            ( ( member_a_b @ X4 @ B2 )
           => ( ( Q @ X4 )
             => ( P @ X4 ) ) )
       => ( ord_less_eq_set_a_b
          @ ( collect_a_b
            @ ^ [X2: a > b] :
                ( ( member_a_b @ X2 @ B2 )
                & ( Q @ X2 ) ) )
          @ ( collect_a_b
            @ ^ [X2: a > b] :
                ( ( member_a_b @ X2 @ A2 )
                & ( P @ X2 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_744_subset__Collect__iff,axiom,
    ! [B2: set_Pr7742364250814120412pace_b,A2: set_Pr7742364250814120412pace_b,P: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > $o] :
      ( ( ord_le1280929228223758908pace_b @ B2 @ A2 )
     => ( ( ord_le1280929228223758908pace_b @ B2
          @ ( collec7915783404360165627pace_b
            @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
                ( ( member6667749562321684925pace_b @ X2 @ A2 )
                & ( P @ X2 ) ) ) )
        = ( ! [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
              ( ( member6667749562321684925pace_b @ X2 @ B2 )
             => ( P @ X2 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_745_subset__Collect__iff,axiom,
    ! [B2: set_a_3263942136899480541pace_b,A2: set_a_3263942136899480541pace_b,P: ( a > probab4737552677800996672pace_b ) > $o] :
      ( ( ord_le130150003083865149pace_b @ B2 @ A2 )
     => ( ( ord_le130150003083865149pace_b @ B2
          @ ( collec5907158909762593660pace_b
            @ ^ [X2: a > probab4737552677800996672pace_b] :
                ( ( member7340901614391157822pace_b @ X2 @ A2 )
                & ( P @ X2 ) ) ) )
        = ( ! [X2: a > probab4737552677800996672pace_b] :
              ( ( member7340901614391157822pace_b @ X2 @ B2 )
             => ( P @ X2 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_746_subset__Collect__iff,axiom,
    ! [B2: set_Pr8041968334489646747ce_a_b,A2: set_Pr8041968334489646747ce_a_b,P: ( probab4737552673497767871pace_a > b ) > $o] :
      ( ( ord_le4908176200674031355ce_a_b @ B2 @ A2 )
     => ( ( ord_le4908176200674031355ce_a_b @ B2
          @ ( collec3574973839036329274ce_a_b
            @ ^ [X2: probab4737552673497767871pace_a > b] :
                ( ( member5008716543664893436ce_a_b @ X2 @ A2 )
                & ( P @ X2 ) ) ) )
        = ( ! [X2: probab4737552673497767871pace_a > b] :
              ( ( member5008716543664893436ce_a_b @ X2 @ B2 )
             => ( P @ X2 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_747_subset__Collect__iff,axiom,
    ! [B2: set_b_9060095955432656540pace_b,A2: set_b_9060095955432656540pace_b,P: ( b > probab4737552677800996672pace_b ) > $o] :
      ( ( ord_le5926303821617041148pace_b @ B2 @ A2 )
     => ( ( ord_le5926303821617041148pace_b @ B2
          @ ( collec134500591788602811pace_b
            @ ^ [X2: b > probab4737552677800996672pace_b] :
                ( ( member1568243296417166973pace_b @ X2 @ A2 )
                & ( P @ X2 ) ) ) )
        = ( ! [X2: b > probab4737552677800996672pace_b] :
              ( ( member1568243296417166973pace_b @ X2 @ B2 )
             => ( P @ X2 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_748_subset__Collect__iff,axiom,
    ! [B2: set_a_5989463605624649374pace_b,A2: set_a_5989463605624649374pace_b,P: ( a > probab8624551251471354625pace_b ) > $o] :
      ( ( ord_le8751400619889063678pace_b @ B2 @ A2 )
     => ( ( ord_le8751400619889063678pace_b @ B2
          @ ( collec1289203422882586301pace_b
            @ ^ [X2: a > probab8624551251471354625pace_b] :
                ( ( member41169580844105599pace_b @ X2 @ A2 )
                & ( P @ X2 ) ) ) )
        = ( ! [X2: a > probab8624551251471354625pace_b] :
              ( ( member41169580844105599pace_b @ X2 @ B2 )
             => ( P @ X2 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_749_subset__Collect__iff,axiom,
    ! [B2: set_a_5785126655188516188pace_a,A2: set_a_5785126655188516188pace_a,P: ( a > probab4737552673497767871pace_a ) > $o] :
      ( ( ord_le2651334521372900796pace_a @ B2 @ A2 )
     => ( ( ord_le2651334521372900796pace_a @ B2
          @ ( collec5836124869716247675pace_a
            @ ^ [X2: a > probab4737552673497767871pace_a] :
                ( ( member7269867574344811837pace_a @ X2 @ A2 )
                & ( P @ X2 ) ) ) )
        = ( ! [X2: a > probab4737552673497767871pace_a] :
              ( ( member7269867574344811837pace_a @ X2 @ B2 )
             => ( P @ X2 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_750_subset__Collect__iff,axiom,
    ! [B2: set_a_b,A2: set_a_b,P: ( a > b ) > $o] :
      ( ( ord_less_eq_set_a_b @ B2 @ A2 )
     => ( ( ord_less_eq_set_a_b @ B2
          @ ( collect_a_b
            @ ^ [X2: a > b] :
                ( ( member_a_b @ X2 @ A2 )
                & ( P @ X2 ) ) ) )
        = ( ! [X2: a > b] :
              ( ( member_a_b @ X2 @ B2 )
             => ( P @ X2 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_751_less__eq__quasi__borel_Ocases,axiom,
    ! [A1: quasi_3431323906171122406pace_b,A22: quasi_3431323906171122406pace_b] :
      ( ( ord_le2345554537223240326pace_b @ A1 @ A22 )
     => ( ~ ( ord_le8230322567725371980pace_b @ ( qbs_sp9192884687904738934pace_b @ A1 ) @ ( qbs_sp9192884687904738934pace_b @ A22 ) )
       => ~ ( ( ( qbs_sp9192884687904738934pace_b @ A1 )
              = ( qbs_sp9192884687904738934pace_b @ A22 ) )
           => ~ ( ord_le148948439097960011pace_b @ ( qbs_Mx4221877620443553463pace_b @ A22 ) @ ( qbs_Mx4221877620443553463pace_b @ A1 ) ) ) ) ) ).

% less_eq_quasi_borel.cases
thf(fact_752_less__eq__quasi__borel_Ocases,axiom,
    ! [A1: quasi_3360289866124776421pace_a,A22: quasi_3360289866124776421pace_a] :
      ( ( ord_le2274520497176894341pace_a @ A1 @ A22 )
     => ( ~ ( ord_le8159288527679025995pace_a @ ( qbs_sp9192884683601510133pace_a @ A1 ) @ ( qbs_sp9192884683601510133pace_a @ A22 ) )
       => ~ ( ( ( qbs_sp9192884683601510133pace_a @ A1 )
              = ( qbs_sp9192884683601510133pace_a @ A22 ) )
           => ~ ( ord_le2670132957386995658pace_a @ ( qbs_Mx4221877616140324662pace_a @ A22 ) @ ( qbs_Mx4221877616140324662pace_a @ A1 ) ) ) ) ) ).

% less_eq_quasi_borel.cases
thf(fact_753_less__eq__quasi__borel_Osimps,axiom,
    ( ord_le2345554537223240326pace_b
    = ( ^ [A12: quasi_3431323906171122406pace_b,A23: quasi_3431323906171122406pace_b] :
          ( ? [X5: quasi_3431323906171122406pace_b,Y4: quasi_3431323906171122406pace_b] :
              ( ( A12 = X5 )
              & ( A23 = Y4 )
              & ( ord_le8230322567725371980pace_b @ ( qbs_sp9192884687904738934pace_b @ X5 ) @ ( qbs_sp9192884687904738934pace_b @ Y4 ) ) )
          | ? [X5: quasi_3431323906171122406pace_b,Y4: quasi_3431323906171122406pace_b] :
              ( ( A12 = X5 )
              & ( A23 = Y4 )
              & ( ( qbs_sp9192884687904738934pace_b @ X5 )
                = ( qbs_sp9192884687904738934pace_b @ Y4 ) )
              & ( ord_le148948439097960011pace_b @ ( qbs_Mx4221877620443553463pace_b @ Y4 ) @ ( qbs_Mx4221877620443553463pace_b @ X5 ) ) ) ) ) ) ).

% less_eq_quasi_borel.simps
thf(fact_754_less__eq__quasi__borel_Osimps,axiom,
    ( ord_le2274520497176894341pace_a
    = ( ^ [A12: quasi_3360289866124776421pace_a,A23: quasi_3360289866124776421pace_a] :
          ( ? [X5: quasi_3360289866124776421pace_a,Y4: quasi_3360289866124776421pace_a] :
              ( ( A12 = X5 )
              & ( A23 = Y4 )
              & ( ord_le8159288527679025995pace_a @ ( qbs_sp9192884683601510133pace_a @ X5 ) @ ( qbs_sp9192884683601510133pace_a @ Y4 ) ) )
          | ? [X5: quasi_3360289866124776421pace_a,Y4: quasi_3360289866124776421pace_a] :
              ( ( A12 = X5 )
              & ( A23 = Y4 )
              & ( ( qbs_sp9192884683601510133pace_a @ X5 )
                = ( qbs_sp9192884683601510133pace_a @ Y4 ) )
              & ( ord_le2670132957386995658pace_a @ ( qbs_Mx4221877616140324662pace_a @ Y4 ) @ ( qbs_Mx4221877616140324662pace_a @ X5 ) ) ) ) ) ) ).

% less_eq_quasi_borel.simps
thf(fact_755_le__quasi__borel__iff,axiom,
    ( ord_le2345554537223240326pace_b
    = ( ^ [X5: quasi_3431323906171122406pace_b,Y4: quasi_3431323906171122406pace_b] :
          ( ( ( ( qbs_sp9192884687904738934pace_b @ X5 )
              = ( qbs_sp9192884687904738934pace_b @ Y4 ) )
           => ( ord_le148948439097960011pace_b @ ( qbs_Mx4221877620443553463pace_b @ Y4 ) @ ( qbs_Mx4221877620443553463pace_b @ X5 ) ) )
          & ( ( ( qbs_sp9192884687904738934pace_b @ X5 )
             != ( qbs_sp9192884687904738934pace_b @ Y4 ) )
           => ( ord_le8230322567725371980pace_b @ ( qbs_sp9192884687904738934pace_b @ X5 ) @ ( qbs_sp9192884687904738934pace_b @ Y4 ) ) ) ) ) ) ).

% le_quasi_borel_iff
thf(fact_756_le__quasi__borel__iff,axiom,
    ( ord_le2274520497176894341pace_a
    = ( ^ [X5: quasi_3360289866124776421pace_a,Y4: quasi_3360289866124776421pace_a] :
          ( ( ( ( qbs_sp9192884683601510133pace_a @ X5 )
              = ( qbs_sp9192884683601510133pace_a @ Y4 ) )
           => ( ord_le2670132957386995658pace_a @ ( qbs_Mx4221877616140324662pace_a @ Y4 ) @ ( qbs_Mx4221877616140324662pace_a @ X5 ) ) )
          & ( ( ( qbs_sp9192884683601510133pace_a @ X5 )
             != ( qbs_sp9192884683601510133pace_a @ Y4 ) )
           => ( ord_le8159288527679025995pace_a @ ( qbs_sp9192884683601510133pace_a @ X5 ) @ ( qbs_sp9192884683601510133pace_a @ Y4 ) ) ) ) ) ) ).

% le_quasi_borel_iff
thf(fact_757_psubsetD,axiom,
    ! [A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b,C: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ( ( ord_le3404582512095951920pace_b @ A2 @ B2 )
     => ( ( member6667749562321684925pace_b @ C @ A2 )
       => ( member6667749562321684925pace_b @ C @ B2 ) ) ) ).

% psubsetD
thf(fact_758_psubsetD,axiom,
    ! [A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b,C: a > probab4737552677800996672pace_b] :
      ( ( ord_le4992135731509388849pace_b @ A2 @ B2 )
     => ( ( member7340901614391157822pace_b @ C @ A2 )
       => ( member7340901614391157822pace_b @ C @ B2 ) ) ) ).

% psubsetD
thf(fact_759_psubsetD,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b,C: probab4737552673497767871pace_a > b] :
      ( ( ord_le546789892244779247ce_a_b @ A2 @ B2 )
     => ( ( member5008716543664893436ce_a_b @ C @ A2 )
       => ( member5008716543664893436ce_a_b @ C @ B2 ) ) ) ).

% psubsetD
thf(fact_760_psubsetD,axiom,
    ! [A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b,C: b > probab4737552677800996672pace_b] :
      ( ( ord_le1564917513187789040pace_b @ A2 @ B2 )
     => ( ( member1568243296417166973pace_b @ C @ A2 )
       => ( member1568243296417166973pace_b @ C @ B2 ) ) ) ).

% psubsetD
thf(fact_761_psubsetD,axiom,
    ! [A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b,C: a > probab8624551251471354625pace_b] :
      ( ( ord_le1651681866906480882pace_b @ A2 @ B2 )
     => ( ( member41169580844105599pace_b @ C @ A2 )
       => ( member41169580844105599pace_b @ C @ B2 ) ) ) ).

% psubsetD
thf(fact_762_psubsetD,axiom,
    ! [A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a,C: a > probab4737552673497767871pace_a] :
      ( ( ord_le7513320249798424496pace_a @ A2 @ B2 )
     => ( ( member7269867574344811837pace_a @ C @ A2 )
       => ( member7269867574344811837pace_a @ C @ B2 ) ) ) ).

% psubsetD
thf(fact_763_psubsetD,axiom,
    ! [A2: set_a_b,B2: set_a_b,C: a > b] :
      ( ( ord_less_set_a_b @ A2 @ B2 )
     => ( ( member_a_b @ C @ A2 )
       => ( member_a_b @ C @ B2 ) ) ) ).

% psubsetD
thf(fact_764_less__eq__quasi__borel_Ointros_I1_J,axiom,
    ! [X: quasi_3431323906171122406pace_b,Y: quasi_3431323906171122406pace_b] :
      ( ( ord_le8230322567725371980pace_b @ ( qbs_sp9192884687904738934pace_b @ X ) @ ( qbs_sp9192884687904738934pace_b @ Y ) )
     => ( ord_le2345554537223240326pace_b @ X @ Y ) ) ).

% less_eq_quasi_borel.intros(1)
thf(fact_765_less__eq__quasi__borel_Ointros_I1_J,axiom,
    ! [X: quasi_3360289866124776421pace_a,Y: quasi_3360289866124776421pace_a] :
      ( ( ord_le8159288527679025995pace_a @ ( qbs_sp9192884683601510133pace_a @ X ) @ ( qbs_sp9192884683601510133pace_a @ Y ) )
     => ( ord_le2274520497176894341pace_a @ X @ Y ) ) ).

% less_eq_quasi_borel.intros(1)
thf(fact_766_less__set__def,axiom,
    ( ord_le3404582512095951920pace_b
    = ( ^ [A3: set_Pr7742364250814120412pace_b,B4: set_Pr7742364250814120412pace_b] :
          ( ord_le6391347287134640213ce_b_o
          @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ A3 )
          @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ B4 ) ) ) ) ).

% less_set_def
thf(fact_767_less__set__def,axiom,
    ( ord_le4992135731509388849pace_b
    = ( ^ [A3: set_a_3263942136899480541pace_b,B4: set_a_3263942136899480541pace_b] :
          ( ord_le5661718335121051540ce_b_o
          @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ A3 )
          @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ B4 ) ) ) ) ).

% less_set_def
thf(fact_768_less__set__def,axiom,
    ( ord_le546789892244779247ce_a_b
    = ( ^ [A3: set_Pr8041968334489646747ce_a_b,B4: set_Pr8041968334489646747ce_a_b] :
          ( ord_le2339100606026887766_a_b_o
          @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ A3 )
          @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ B4 ) ) ) ) ).

% less_set_def
thf(fact_769_less__set__def,axiom,
    ( ord_le1564917513187789040pace_b
    = ( ^ [A3: set_b_9060095955432656540pace_b,B4: set_b_9060095955432656540pace_b] :
          ( ord_le2633926070619487125ce_b_o
          @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ A3 )
          @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ B4 ) ) ) ) ).

% less_set_def
thf(fact_770_less__set__def,axiom,
    ( ord_le1651681866906480882pace_b
    = ( ^ [A3: set_a_5989463605624649374pace_b,B4: set_a_5989463605624649374pace_b] :
          ( ord_le2018788059094849043ce_b_o
          @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ A3 )
          @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ B4 ) ) ) ) ).

% less_set_def
thf(fact_771_less__set__def,axiom,
    ( ord_le7513320249798424496pace_a
    = ( ^ [A3: set_a_5785126655188516188pace_a,B4: set_a_5785126655188516188pace_a] :
          ( ord_le6297367335726038229ce_a_o
          @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ A3 )
          @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ B4 ) ) ) ) ).

% less_set_def
thf(fact_772_less__set__def,axiom,
    ( ord_less_set_a_b
    = ( ^ [A3: set_a_b,B4: set_a_b] :
          ( ord_less_a_b_o
          @ ^ [X2: a > b] : ( member_a_b @ X2 @ A3 )
          @ ^ [X2: a > b] : ( member_a_b @ X2 @ B4 ) ) ) ) ).

% less_set_def
thf(fact_773_Pi__split__domain,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,I2: set_Pr8456636223741192351pace_a,J: set_Pr8456636223741192351pace_a,X: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ ( sup_su2422338781931550323pace_a @ I2 @ J ) @ X ) )
      = ( ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ X ) )
        & ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ J @ X ) ) ) ) ).

% Pi_split_domain
thf(fact_774_Pi__split__domain,axiom,
    ! [X3: a > probab4737552677800996672pace_b,I2: set_a,J: set_a,X: a > set_Pr8527670263787538336pace_b] :
      ( ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ ( sup_sup_set_a @ I2 @ J ) @ X ) )
      = ( ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ X ) )
        & ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ J @ X ) ) ) ) ).

% Pi_split_domain
thf(fact_775_Pi__split__domain,axiom,
    ! [X3: probab4737552673497767871pace_a > b,I2: set_Pr8456636223741192351pace_a,J: set_Pr8456636223741192351pace_a,X: probab4737552673497767871pace_a > set_b] :
      ( ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ ( sup_su2422338781931550323pace_a @ I2 @ J ) @ X ) )
      = ( ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ X ) )
        & ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ J @ X ) ) ) ) ).

% Pi_split_domain
thf(fact_776_Pi__split__domain,axiom,
    ! [X3: b > probab4737552677800996672pace_b,I2: set_b,J: set_b,X: b > set_Pr8527670263787538336pace_b] :
      ( ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ ( sup_sup_set_b @ I2 @ J ) @ X ) )
      = ( ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ X ) )
        & ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ J @ X ) ) ) ) ).

% Pi_split_domain
thf(fact_777_Pi__split__domain,axiom,
    ! [X3: a > probab8624551251471354625pace_b,I2: set_a,J: set_a,X: a > set_Pr2974436765678502625pace_b] :
      ( ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ ( sup_sup_set_a @ I2 @ J ) @ X ) )
      = ( ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ X ) )
        & ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ J @ X ) ) ) ) ).

% Pi_split_domain
thf(fact_778_Pi__split__domain,axiom,
    ! [X3: a > probab4737552673497767871pace_a,I2: set_a,J: set_a,X: a > set_Pr8456636223741192351pace_a] :
      ( ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ ( sup_sup_set_a @ I2 @ J ) @ X ) )
      = ( ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ X ) )
        & ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ J @ X ) ) ) ) ).

% Pi_split_domain
thf(fact_779_Pi__split__domain,axiom,
    ! [X3: a > b,I2: set_a,J: set_a,X: a > set_b] :
      ( ( member_a_b @ X3 @ ( pi_a_b @ ( sup_sup_set_a @ I2 @ J ) @ X ) )
      = ( ( member_a_b @ X3 @ ( pi_a_b @ I2 @ X ) )
        & ( member_a_b @ X3 @ ( pi_a_b @ J @ X ) ) ) ) ).

% Pi_split_domain
thf(fact_780_sup__quasi__borel__def,axiom,
    ( sup_su2195192086808692410pace_b
    = ( ^ [X5: quasi_3431323906171122406pace_b,Y4: quasi_3431323906171122406pace_b] :
          ( if_qua2367494438840067244pace_b
          @ ( ( qbs_sp9192884687904738934pace_b @ X5 )
            = ( qbs_sp9192884687904738934pace_b @ Y4 ) )
          @ ( inf_qu8610821493433791850pace_b @ X5 @ Y4 )
          @ ( if_qua2367494438840067244pace_b @ ( ord_le8230322567725371980pace_b @ ( qbs_sp9192884687904738934pace_b @ X5 ) @ ( qbs_sp9192884687904738934pace_b @ Y4 ) ) @ Y4 @ ( if_qua2367494438840067244pace_b @ ( ord_le8230322567725371980pace_b @ ( qbs_sp9192884687904738934pace_b @ Y4 ) @ ( qbs_sp9192884687904738934pace_b @ X5 ) ) @ X5 @ ( max_qu2338019691940189127pace_b @ ( sup_su2493372821977896308pace_b @ ( qbs_sp9192884687904738934pace_b @ X5 ) @ ( qbs_sp9192884687904738934pace_b @ Y4 ) ) ) ) ) ) ) ) ).

% sup_quasi_borel_def
thf(fact_781_sup__quasi__borel__def,axiom,
    ( sup_su2124158046762346425pace_a
    = ( ^ [X5: quasi_3360289866124776421pace_a,Y4: quasi_3360289866124776421pace_a] :
          ( if_qua2296460398793721259pace_a
          @ ( ( qbs_sp9192884683601510133pace_a @ X5 )
            = ( qbs_sp9192884683601510133pace_a @ Y4 ) )
          @ ( inf_qu8610821489130563049pace_a @ X5 @ Y4 )
          @ ( if_qua2296460398793721259pace_a @ ( ord_le8159288527679025995pace_a @ ( qbs_sp9192884683601510133pace_a @ X5 ) @ ( qbs_sp9192884683601510133pace_a @ Y4 ) ) @ Y4 @ ( if_qua2296460398793721259pace_a @ ( ord_le8159288527679025995pace_a @ ( qbs_sp9192884683601510133pace_a @ Y4 ) @ ( qbs_sp9192884683601510133pace_a @ X5 ) ) @ X5 @ ( max_qu2338019687636960326pace_a @ ( sup_su2422338781931550323pace_a @ ( qbs_sp9192884683601510133pace_a @ X5 ) @ ( qbs_sp9192884683601510133pace_a @ Y4 ) ) ) ) ) ) ) ) ).

% sup_quasi_borel_def
thf(fact_782_Un__iff,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ C @ ( sup_su4215213818124963592pace_b @ A2 @ B2 ) )
      = ( ( member6667749562321684925pace_b @ C @ A2 )
        | ( member6667749562321684925pace_b @ C @ B2 ) ) ) ).

% Un_iff
thf(fact_783_Un__iff,axiom,
    ! [C: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ C @ ( sup_su5431229879208114441pace_b @ A2 @ B2 ) )
      = ( ( member7340901614391157822pace_b @ C @ A2 )
        | ( member7340901614391157822pace_b @ C @ B2 ) ) ) ).

% Un_iff
thf(fact_784_Un__iff,axiom,
    ! [C: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ C @ ( sup_su985884039943504839ce_a_b @ A2 @ B2 ) )
      = ( ( member5008716543664893436ce_a_b @ C @ A2 )
        | ( member5008716543664893436ce_a_b @ C @ B2 ) ) ) ).

% Un_iff
thf(fact_785_Un__iff,axiom,
    ! [C: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ C @ ( sup_su2004011660886514632pace_b @ A2 @ B2 ) )
      = ( ( member1568243296417166973pace_b @ C @ A2 )
        | ( member1568243296417166973pace_b @ C @ B2 ) ) ) ).

% Un_iff
thf(fact_786_Un__iff,axiom,
    ! [C: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ C @ ( sup_su2462313172935492554pace_b @ A2 @ B2 ) )
      = ( ( member41169580844105599pace_b @ C @ A2 )
        | ( member41169580844105599pace_b @ C @ B2 ) ) ) ).

% Un_iff
thf(fact_787_Un__iff,axiom,
    ! [C: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ C @ ( sup_su7952414397497150088pace_a @ A2 @ B2 ) )
      = ( ( member7269867574344811837pace_a @ C @ A2 )
        | ( member7269867574344811837pace_a @ C @ B2 ) ) ) ).

% Un_iff
thf(fact_788_Un__iff,axiom,
    ! [C: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( member_a_b @ C @ ( sup_sup_set_a_b @ A2 @ B2 ) )
      = ( ( member_a_b @ C @ A2 )
        | ( member_a_b @ C @ B2 ) ) ) ).

% Un_iff
thf(fact_789_UnCI,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: set_Pr7742364250814120412pace_b,A2: set_Pr7742364250814120412pace_b] :
      ( ( ~ ( member6667749562321684925pace_b @ C @ B2 )
       => ( member6667749562321684925pace_b @ C @ A2 ) )
     => ( member6667749562321684925pace_b @ C @ ( sup_su4215213818124963592pace_b @ A2 @ B2 ) ) ) ).

% UnCI
thf(fact_790_UnCI,axiom,
    ! [C: a > probab4737552677800996672pace_b,B2: set_a_3263942136899480541pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ( ~ ( member7340901614391157822pace_b @ C @ B2 )
       => ( member7340901614391157822pace_b @ C @ A2 ) )
     => ( member7340901614391157822pace_b @ C @ ( sup_su5431229879208114441pace_b @ A2 @ B2 ) ) ) ).

% UnCI
thf(fact_791_UnCI,axiom,
    ! [C: probab4737552673497767871pace_a > b,B2: set_Pr8041968334489646747ce_a_b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( ~ ( member5008716543664893436ce_a_b @ C @ B2 )
       => ( member5008716543664893436ce_a_b @ C @ A2 ) )
     => ( member5008716543664893436ce_a_b @ C @ ( sup_su985884039943504839ce_a_b @ A2 @ B2 ) ) ) ).

% UnCI
thf(fact_792_UnCI,axiom,
    ! [C: b > probab4737552677800996672pace_b,B2: set_b_9060095955432656540pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ( ~ ( member1568243296417166973pace_b @ C @ B2 )
       => ( member1568243296417166973pace_b @ C @ A2 ) )
     => ( member1568243296417166973pace_b @ C @ ( sup_su2004011660886514632pace_b @ A2 @ B2 ) ) ) ).

% UnCI
thf(fact_793_UnCI,axiom,
    ! [C: a > probab8624551251471354625pace_b,B2: set_a_5989463605624649374pace_b,A2: set_a_5989463605624649374pace_b] :
      ( ( ~ ( member41169580844105599pace_b @ C @ B2 )
       => ( member41169580844105599pace_b @ C @ A2 ) )
     => ( member41169580844105599pace_b @ C @ ( sup_su2462313172935492554pace_b @ A2 @ B2 ) ) ) ).

% UnCI
thf(fact_794_UnCI,axiom,
    ! [C: a > probab4737552673497767871pace_a,B2: set_a_5785126655188516188pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ( ~ ( member7269867574344811837pace_a @ C @ B2 )
       => ( member7269867574344811837pace_a @ C @ A2 ) )
     => ( member7269867574344811837pace_a @ C @ ( sup_su7952414397497150088pace_a @ A2 @ B2 ) ) ) ).

% UnCI
thf(fact_795_UnCI,axiom,
    ! [C: a > b,B2: set_a_b,A2: set_a_b] :
      ( ( ~ ( member_a_b @ C @ B2 )
       => ( member_a_b @ C @ A2 ) )
     => ( member_a_b @ C @ ( sup_sup_set_a_b @ A2 @ B2 ) ) ) ).

% UnCI
thf(fact_796_Un__def,axiom,
    ( sup_su4215213818124963592pace_b
    = ( ^ [A3: set_Pr7742364250814120412pace_b,B4: set_Pr7742364250814120412pace_b] :
          ( collec7915783404360165627pace_b
          @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
              ( ( member6667749562321684925pace_b @ X2 @ A3 )
              | ( member6667749562321684925pace_b @ X2 @ B4 ) ) ) ) ) ).

% Un_def
thf(fact_797_Un__def,axiom,
    ( sup_su5431229879208114441pace_b
    = ( ^ [A3: set_a_3263942136899480541pace_b,B4: set_a_3263942136899480541pace_b] :
          ( collec5907158909762593660pace_b
          @ ^ [X2: a > probab4737552677800996672pace_b] :
              ( ( member7340901614391157822pace_b @ X2 @ A3 )
              | ( member7340901614391157822pace_b @ X2 @ B4 ) ) ) ) ) ).

% Un_def
thf(fact_798_Un__def,axiom,
    ( sup_su985884039943504839ce_a_b
    = ( ^ [A3: set_Pr8041968334489646747ce_a_b,B4: set_Pr8041968334489646747ce_a_b] :
          ( collec3574973839036329274ce_a_b
          @ ^ [X2: probab4737552673497767871pace_a > b] :
              ( ( member5008716543664893436ce_a_b @ X2 @ A3 )
              | ( member5008716543664893436ce_a_b @ X2 @ B4 ) ) ) ) ) ).

% Un_def
thf(fact_799_Un__def,axiom,
    ( sup_su2004011660886514632pace_b
    = ( ^ [A3: set_b_9060095955432656540pace_b,B4: set_b_9060095955432656540pace_b] :
          ( collec134500591788602811pace_b
          @ ^ [X2: b > probab4737552677800996672pace_b] :
              ( ( member1568243296417166973pace_b @ X2 @ A3 )
              | ( member1568243296417166973pace_b @ X2 @ B4 ) ) ) ) ) ).

% Un_def
thf(fact_800_Un__def,axiom,
    ( sup_su2462313172935492554pace_b
    = ( ^ [A3: set_a_5989463605624649374pace_b,B4: set_a_5989463605624649374pace_b] :
          ( collec1289203422882586301pace_b
          @ ^ [X2: a > probab8624551251471354625pace_b] :
              ( ( member41169580844105599pace_b @ X2 @ A3 )
              | ( member41169580844105599pace_b @ X2 @ B4 ) ) ) ) ) ).

% Un_def
thf(fact_801_Un__def,axiom,
    ( sup_su7952414397497150088pace_a
    = ( ^ [A3: set_a_5785126655188516188pace_a,B4: set_a_5785126655188516188pace_a] :
          ( collec5836124869716247675pace_a
          @ ^ [X2: a > probab4737552673497767871pace_a] :
              ( ( member7269867574344811837pace_a @ X2 @ A3 )
              | ( member7269867574344811837pace_a @ X2 @ B4 ) ) ) ) ) ).

% Un_def
thf(fact_802_Un__def,axiom,
    ( sup_sup_set_a_b
    = ( ^ [A3: set_a_b,B4: set_a_b] :
          ( collect_a_b
          @ ^ [X2: a > b] :
              ( ( member_a_b @ X2 @ A3 )
              | ( member_a_b @ X2 @ B4 ) ) ) ) ) ).

% Un_def
thf(fact_803_sup__set__def,axiom,
    ( sup_su4215213818124963592pace_b
    = ( ^ [A3: set_Pr7742364250814120412pace_b,B4: set_Pr7742364250814120412pace_b] :
          ( collec7915783404360165627pace_b
          @ ( sup_su5183789638013051773ce_b_o
            @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ A3 )
            @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ B4 ) ) ) ) ) ).

% sup_set_def
thf(fact_804_sup__set__def,axiom,
    ( sup_su5431229879208114441pace_b
    = ( ^ [A3: set_a_3263942136899480541pace_b,B4: set_a_3263942136899480541pace_b] :
          ( collec5907158909762593660pace_b
          @ ( sup_su1325753604073888444ce_b_o
            @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ A3 )
            @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ B4 ) ) ) ) ) ).

% sup_set_def
thf(fact_805_sup__set__def,axiom,
    ( sup_su985884039943504839ce_a_b
    = ( ^ [A3: set_Pr8041968334489646747ce_a_b,B4: set_Pr8041968334489646747ce_a_b] :
          ( collec3574973839036329274ce_a_b
          @ ( sup_su7226507911834500478_a_b_o
            @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ A3 )
            @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ B4 ) ) ) ) ) ).

% sup_set_def
thf(fact_806_sup__set__def,axiom,
    ( sup_su2004011660886514632pace_b
    = ( ^ [A3: set_b_9060095955432656540pace_b,B4: set_b_9060095955432656540pace_b] :
          ( collec134500591788602811pace_b
          @ ( sup_su7521333376427099837ce_b_o
            @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ A3 )
            @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ B4 ) ) ) ) ) ).

% sup_set_def
thf(fact_807_sup__set__def,axiom,
    ( sup_su2462313172935492554pace_b
    = ( ^ [A3: set_a_5989463605624649374pace_b,B4: set_a_5989463605624649374pace_b] :
          ( collec1289203422882586301pace_b
          @ ( sup_su811230409973260603ce_b_o
            @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ A3 )
            @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ B4 ) ) ) ) ) ).

% sup_set_def
thf(fact_808_sup__set__def,axiom,
    ( sup_su7952414397497150088pace_a
    = ( ^ [A3: set_a_5785126655188516188pace_a,B4: set_a_5785126655188516188pace_a] :
          ( collec5836124869716247675pace_a
          @ ( sup_su1961402604678875133ce_a_o
            @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ A3 )
            @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ B4 ) ) ) ) ) ).

% sup_set_def
thf(fact_809_sup__set__def,axiom,
    ( sup_sup_set_a_b
    = ( ^ [A3: set_a_b,B4: set_a_b] :
          ( collect_a_b
          @ ( sup_sup_a_b_o
            @ ^ [X2: a > b] : ( member_a_b @ X2 @ A3 )
            @ ^ [X2: a > b] : ( member_a_b @ X2 @ B4 ) ) ) ) ) ).

% sup_set_def
thf(fact_810_UnI2,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: set_Pr7742364250814120412pace_b,A2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ C @ B2 )
     => ( member6667749562321684925pace_b @ C @ ( sup_su4215213818124963592pace_b @ A2 @ B2 ) ) ) ).

% UnI2
thf(fact_811_UnI2,axiom,
    ! [C: a > probab4737552677800996672pace_b,B2: set_a_3263942136899480541pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ C @ B2 )
     => ( member7340901614391157822pace_b @ C @ ( sup_su5431229879208114441pace_b @ A2 @ B2 ) ) ) ).

% UnI2
thf(fact_812_UnI2,axiom,
    ! [C: probab4737552673497767871pace_a > b,B2: set_Pr8041968334489646747ce_a_b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ C @ B2 )
     => ( member5008716543664893436ce_a_b @ C @ ( sup_su985884039943504839ce_a_b @ A2 @ B2 ) ) ) ).

% UnI2
thf(fact_813_UnI2,axiom,
    ! [C: b > probab4737552677800996672pace_b,B2: set_b_9060095955432656540pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ C @ B2 )
     => ( member1568243296417166973pace_b @ C @ ( sup_su2004011660886514632pace_b @ A2 @ B2 ) ) ) ).

% UnI2
thf(fact_814_UnI2,axiom,
    ! [C: a > probab8624551251471354625pace_b,B2: set_a_5989463605624649374pace_b,A2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ C @ B2 )
     => ( member41169580844105599pace_b @ C @ ( sup_su2462313172935492554pace_b @ A2 @ B2 ) ) ) ).

% UnI2
thf(fact_815_UnI2,axiom,
    ! [C: a > probab4737552673497767871pace_a,B2: set_a_5785126655188516188pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ C @ B2 )
     => ( member7269867574344811837pace_a @ C @ ( sup_su7952414397497150088pace_a @ A2 @ B2 ) ) ) ).

% UnI2
thf(fact_816_UnI2,axiom,
    ! [C: a > b,B2: set_a_b,A2: set_a_b] :
      ( ( member_a_b @ C @ B2 )
     => ( member_a_b @ C @ ( sup_sup_set_a_b @ A2 @ B2 ) ) ) ).

% UnI2
thf(fact_817_UnI1,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ C @ A2 )
     => ( member6667749562321684925pace_b @ C @ ( sup_su4215213818124963592pace_b @ A2 @ B2 ) ) ) ).

% UnI1
thf(fact_818_UnI1,axiom,
    ! [C: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ C @ A2 )
     => ( member7340901614391157822pace_b @ C @ ( sup_su5431229879208114441pace_b @ A2 @ B2 ) ) ) ).

% UnI1
thf(fact_819_UnI1,axiom,
    ! [C: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ C @ A2 )
     => ( member5008716543664893436ce_a_b @ C @ ( sup_su985884039943504839ce_a_b @ A2 @ B2 ) ) ) ).

% UnI1
thf(fact_820_UnI1,axiom,
    ! [C: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ C @ A2 )
     => ( member1568243296417166973pace_b @ C @ ( sup_su2004011660886514632pace_b @ A2 @ B2 ) ) ) ).

% UnI1
thf(fact_821_UnI1,axiom,
    ! [C: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ C @ A2 )
     => ( member41169580844105599pace_b @ C @ ( sup_su2462313172935492554pace_b @ A2 @ B2 ) ) ) ).

% UnI1
thf(fact_822_UnI1,axiom,
    ! [C: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ C @ A2 )
     => ( member7269867574344811837pace_a @ C @ ( sup_su7952414397497150088pace_a @ A2 @ B2 ) ) ) ).

% UnI1
thf(fact_823_UnI1,axiom,
    ! [C: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( member_a_b @ C @ A2 )
     => ( member_a_b @ C @ ( sup_sup_set_a_b @ A2 @ B2 ) ) ) ).

% UnI1
thf(fact_824_UnE,axiom,
    ! [C: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ C @ ( sup_su4215213818124963592pace_b @ A2 @ B2 ) )
     => ( ~ ( member6667749562321684925pace_b @ C @ A2 )
       => ( member6667749562321684925pace_b @ C @ B2 ) ) ) ).

% UnE
thf(fact_825_UnE,axiom,
    ! [C: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ C @ ( sup_su5431229879208114441pace_b @ A2 @ B2 ) )
     => ( ~ ( member7340901614391157822pace_b @ C @ A2 )
       => ( member7340901614391157822pace_b @ C @ B2 ) ) ) ).

% UnE
thf(fact_826_UnE,axiom,
    ! [C: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ C @ ( sup_su985884039943504839ce_a_b @ A2 @ B2 ) )
     => ( ~ ( member5008716543664893436ce_a_b @ C @ A2 )
       => ( member5008716543664893436ce_a_b @ C @ B2 ) ) ) ).

% UnE
thf(fact_827_UnE,axiom,
    ! [C: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ C @ ( sup_su2004011660886514632pace_b @ A2 @ B2 ) )
     => ( ~ ( member1568243296417166973pace_b @ C @ A2 )
       => ( member1568243296417166973pace_b @ C @ B2 ) ) ) ).

% UnE
thf(fact_828_UnE,axiom,
    ! [C: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ C @ ( sup_su2462313172935492554pace_b @ A2 @ B2 ) )
     => ( ~ ( member41169580844105599pace_b @ C @ A2 )
       => ( member41169580844105599pace_b @ C @ B2 ) ) ) ).

% UnE
thf(fact_829_UnE,axiom,
    ! [C: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ C @ ( sup_su7952414397497150088pace_a @ A2 @ B2 ) )
     => ( ~ ( member7269867574344811837pace_a @ C @ A2 )
       => ( member7269867574344811837pace_a @ C @ B2 ) ) ) ).

% UnE
thf(fact_830_UnE,axiom,
    ! [C: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( member_a_b @ C @ ( sup_sup_set_a_b @ A2 @ B2 ) )
     => ( ~ ( member_a_b @ C @ A2 )
       => ( member_a_b @ C @ B2 ) ) ) ).

% UnE
thf(fact_831_sup__Un__eq,axiom,
    ! [R3: set_Pr7742364250814120412pace_b,S3: set_Pr7742364250814120412pace_b] :
      ( ( sup_su5183789638013051773ce_b_o
        @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ R3 )
        @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ S3 ) )
      = ( ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ X2 @ ( sup_su4215213818124963592pace_b @ R3 @ S3 ) ) ) ) ).

% sup_Un_eq
thf(fact_832_sup__Un__eq,axiom,
    ! [R3: set_a_3263942136899480541pace_b,S3: set_a_3263942136899480541pace_b] :
      ( ( sup_su1325753604073888444ce_b_o
        @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ R3 )
        @ ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ S3 ) )
      = ( ^ [X2: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ X2 @ ( sup_su5431229879208114441pace_b @ R3 @ S3 ) ) ) ) ).

% sup_Un_eq
thf(fact_833_sup__Un__eq,axiom,
    ! [R3: set_Pr8041968334489646747ce_a_b,S3: set_Pr8041968334489646747ce_a_b] :
      ( ( sup_su7226507911834500478_a_b_o
        @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ R3 )
        @ ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ S3 ) )
      = ( ^ [X2: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ X2 @ ( sup_su985884039943504839ce_a_b @ R3 @ S3 ) ) ) ) ).

% sup_Un_eq
thf(fact_834_sup__Un__eq,axiom,
    ! [R3: set_b_9060095955432656540pace_b,S3: set_b_9060095955432656540pace_b] :
      ( ( sup_su7521333376427099837ce_b_o
        @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ R3 )
        @ ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ S3 ) )
      = ( ^ [X2: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ X2 @ ( sup_su2004011660886514632pace_b @ R3 @ S3 ) ) ) ) ).

% sup_Un_eq
thf(fact_835_sup__Un__eq,axiom,
    ! [R3: set_a_5989463605624649374pace_b,S3: set_a_5989463605624649374pace_b] :
      ( ( sup_su811230409973260603ce_b_o
        @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ R3 )
        @ ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ S3 ) )
      = ( ^ [X2: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ X2 @ ( sup_su2462313172935492554pace_b @ R3 @ S3 ) ) ) ) ).

% sup_Un_eq
thf(fact_836_sup__Un__eq,axiom,
    ! [R3: set_a_5785126655188516188pace_a,S3: set_a_5785126655188516188pace_a] :
      ( ( sup_su1961402604678875133ce_a_o
        @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ R3 )
        @ ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ S3 ) )
      = ( ^ [X2: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ X2 @ ( sup_su7952414397497150088pace_a @ R3 @ S3 ) ) ) ) ).

% sup_Un_eq
thf(fact_837_sup__Un__eq,axiom,
    ! [R3: set_a_b,S3: set_a_b] :
      ( ( sup_sup_a_b_o
        @ ^ [X2: a > b] : ( member_a_b @ X2 @ R3 )
        @ ^ [X2: a > b] : ( member_a_b @ X2 @ S3 ) )
      = ( ^ [X2: a > b] : ( member_a_b @ X2 @ ( sup_sup_set_a_b @ R3 @ S3 ) ) ) ) ).

% sup_Un_eq
thf(fact_838_PiE__cancel__merge,axiom,
    ! [I2: set_Pr8456636223741192351pace_a,J: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,Y2: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_in8842055517982213773pace_a @ I2 @ J )
        = bot_bo2798762229408049931pace_a )
     => ( ( member6667749562321684925pace_b @ ( finite5780851627059721263pace_b @ I2 @ J @ ( produc6052399650957384421pace_b @ X3 @ Y2 ) ) @ ( piE_Pr1548282726383880571pace_b @ ( sup_su2422338781931550323pace_a @ I2 @ J ) @ B2 ) )
        = ( ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ B2 ) )
          & ( member6667749562321684925pace_b @ Y2 @ ( pi_Pro4287250843231025420pace_b @ J @ B2 ) ) ) ) ) ).

% PiE_cancel_merge
thf(fact_839_PiE__cancel__merge,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab4737552677800996672pace_b,Y2: a > probab4737552677800996672pace_b,B2: a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member7340901614391157822pace_b @ ( finite6055857901040393904pace_b @ I2 @ J @ ( produc2364966598166989287pace_b @ X3 @ Y2 ) ) @ ( piE_a_4194508618861114364pace_b @ ( sup_sup_set_a @ I2 @ J ) @ B2 ) )
        = ( ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ B2 ) )
          & ( member7340901614391157822pace_b @ Y2 @ ( pi_a_P1132609506902963085pace_b @ J @ B2 ) ) ) ) ) ).

% PiE_cancel_merge
thf(fact_840_PiE__cancel__merge,axiom,
    ! [I2: set_Pr8456636223741192351pace_a,J: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > b,Y2: probab4737552673497767871pace_a > b,B2: probab4737552673497767871pace_a > set_b] :
      ( ( ( inf_in8842055517982213773pace_a @ I2 @ J )
        = bot_bo2798762229408049931pace_a )
     => ( ( member5008716543664893436ce_a_b @ ( finite3957753199828097006ce_a_b @ I2 @ J @ ( produc258301278392420707ce_a_b @ X3 @ Y2 ) ) @ ( piE_Pr2096403917648817466ce_a_b @ ( sup_su2422338781931550323pace_a @ I2 @ J ) @ B2 ) )
        = ( ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ B2 ) )
          & ( member5008716543664893436ce_a_b @ Y2 @ ( pi_Pro8257876842545441995ce_a_b @ J @ B2 ) ) ) ) ) ).

% PiE_cancel_merge
thf(fact_841_PiE__cancel__merge,axiom,
    ! [I2: set_b,J: set_b,X3: b > probab4737552677800996672pace_b,Y2: b > probab4737552677800996672pace_b,B2: b > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_b @ I2 @ J )
        = bot_bot_set_b )
     => ( ( member1568243296417166973pace_b @ ( finite283199583066403055pace_b @ I2 @ J @ ( produc6520359691314873445pace_b @ X3 @ Y2 ) ) @ ( piE_b_7645222337741899323pace_b @ ( sup_sup_set_b @ I2 @ J ) @ B2 ) )
        = ( ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ B2 ) )
          & ( member1568243296417166973pace_b @ Y2 @ ( pi_b_P4583323225783748044pace_b @ J @ B2 ) ) ) ) ) ).

% PiE_cancel_merge
thf(fact_842_PiE__cancel__merge,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab8624551251471354625pace_b,Y2: a > probab8624551251471354625pace_b,B2: a > set_Pr2974436765678502625pace_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member41169580844105599pace_b @ ( finite4354535354149943921pace_b @ I2 @ J @ ( produc1199162346724129385pace_b @ X3 @ Y2 ) ) @ ( piE_a_121966453474103229pace_b @ ( sup_sup_set_a @ I2 @ J ) @ B2 ) )
        = ( ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ B2 ) )
          & ( member41169580844105599pace_b @ Y2 @ ( pi_a_P2860934570321248078pace_b @ J @ B2 ) ) ) ) ) ).

% PiE_cancel_merge
thf(fact_843_PiE__cancel__merge,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab4737552673497767871pace_a,Y2: a > probab4737552673497767871pace_a,B2: a > set_Pr8456636223741192351pace_a] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member7269867574344811837pace_a @ ( finite6055857896737165103pace_a @ I2 @ J @ ( produc9067851722357105125pace_a @ X3 @ Y2 ) ) @ ( piE_a_4194508614557885563pace_a @ ( sup_sup_set_a @ I2 @ J ) @ B2 ) )
        = ( ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ B2 ) )
          & ( member7269867574344811837pace_a @ Y2 @ ( pi_a_P1132609502599734284pace_a @ J @ B2 ) ) ) ) ) ).

% PiE_cancel_merge
thf(fact_844_PiE__cancel__merge,axiom,
    ! [I2: set_a,J: set_a,X3: a > b,Y2: a > b,B2: a > set_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member_a_b @ ( finite2735608678046798447ge_a_b @ I2 @ J @ ( product_Pair_a_b_a_b @ X3 @ Y2 ) ) @ ( piE_a_b @ ( sup_sup_set_a @ I2 @ J ) @ B2 ) )
        = ( ( member_a_b @ X3 @ ( pi_a_b @ I2 @ B2 ) )
          & ( member_a_b @ Y2 @ ( pi_a_b @ J @ B2 ) ) ) ) ) ).

% PiE_cancel_merge
thf(fact_845_Pi__cancel__merge__range_I1_J,axiom,
    ! [I2: set_Pr8456636223741192351pace_a,J: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_in8842055517982213773pace_a @ I2 @ J )
        = bot_bo2798762229408049931pace_a )
     => ( ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ ( finite2812723535947976847pace_b @ I2 @ J @ ( produc881681157476890533pace_b @ A2 @ B2 ) ) ) )
        = ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(1)
thf(fact_846_Pi__cancel__merge__range_I1_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab4737552677800996672pace_b,A2: a > set_Pr8527670263787538336pace_b,B2: a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ ( finite8461668838746617616pace_b @ I2 @ J @ ( produc5089952577834195623pace_b @ A2 @ B2 ) ) ) )
        = ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(1)
thf(fact_847_Pi__cancel__merge__range_I1_J,axiom,
    ! [I2: set_Pr8456636223741192351pace_a,J: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > b,A2: probab4737552673497767871pace_a > set_b,B2: probab4737552673497767871pace_a > set_b] :
      ( ( ( inf_in8842055517982213773pace_a @ I2 @ J )
        = bot_bo2798762229408049931pace_a )
     => ( ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ ( finite4108965814801126606_set_b @ I2 @ J @ ( produc6944462652351720227_set_b @ A2 @ B2 ) ) ) )
        = ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(1)
thf(fact_848_Pi__cancel__merge__range_I1_J,axiom,
    ! [I2: set_b,J: set_b,X3: b > probab4737552677800996672pace_b,A2: b > set_Pr8527670263787538336pace_b,B2: b > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_b @ I2 @ J )
        = bot_bot_set_b )
     => ( ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ ( finite2633747095815736655pace_b @ I2 @ J @ ( produc6518286030610866469pace_b @ A2 @ B2 ) ) ) )
        = ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(1)
thf(fact_849_Pi__cancel__merge__range_I1_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab8624551251471354625pace_b,A2: a > set_Pr2974436765678502625pace_b,B2: a > set_Pr2974436765678502625pace_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ ( finite3412154840674873937pace_b @ I2 @ J @ ( produc7259445117708109353pace_b @ A2 @ B2 ) ) ) )
        = ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(1)
thf(fact_850_Pi__cancel__merge__range_I1_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab4737552673497767871pace_a,A2: a > set_Pr8456636223741192351pace_a,B2: a > set_Pr8456636223741192351pace_a] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ ( finite8390634798700271631pace_a @ I2 @ J @ ( produc4013479291510626213pace_a @ A2 @ B2 ) ) ) )
        = ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(1)
thf(fact_851_Pi__cancel__merge__range_I1_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > b,A2: a > set_b,B2: a > set_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member_a_b @ X3 @ ( pi_a_b @ I2 @ ( finite1260387632014723919_set_b @ I2 @ J @ ( produc1220256858021801509_set_b @ A2 @ B2 ) ) ) )
        = ( member_a_b @ X3 @ ( pi_a_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(1)
thf(fact_852_Pi__cancel__merge__range_I2_J,axiom,
    ! [I2: set_Pr8456636223741192351pace_a,J: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b,A2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_in8842055517982213773pace_a @ I2 @ J )
        = bot_bo2798762229408049931pace_a )
     => ( ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ ( finite2812723535947976847pace_b @ J @ I2 @ ( produc881681157476890533pace_b @ B2 @ A2 ) ) ) )
        = ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(2)
thf(fact_853_Pi__cancel__merge__range_I2_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab4737552677800996672pace_b,B2: a > set_Pr8527670263787538336pace_b,A2: a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ ( finite8461668838746617616pace_b @ J @ I2 @ ( produc5089952577834195623pace_b @ B2 @ A2 ) ) ) )
        = ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(2)
thf(fact_854_Pi__cancel__merge__range_I2_J,axiom,
    ! [I2: set_Pr8456636223741192351pace_a,J: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > b,B2: probab4737552673497767871pace_a > set_b,A2: probab4737552673497767871pace_a > set_b] :
      ( ( ( inf_in8842055517982213773pace_a @ I2 @ J )
        = bot_bo2798762229408049931pace_a )
     => ( ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ ( finite4108965814801126606_set_b @ J @ I2 @ ( produc6944462652351720227_set_b @ B2 @ A2 ) ) ) )
        = ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(2)
thf(fact_855_Pi__cancel__merge__range_I2_J,axiom,
    ! [I2: set_b,J: set_b,X3: b > probab4737552677800996672pace_b,B2: b > set_Pr8527670263787538336pace_b,A2: b > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_b @ I2 @ J )
        = bot_bot_set_b )
     => ( ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ ( finite2633747095815736655pace_b @ J @ I2 @ ( produc6518286030610866469pace_b @ B2 @ A2 ) ) ) )
        = ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(2)
thf(fact_856_Pi__cancel__merge__range_I2_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab8624551251471354625pace_b,B2: a > set_Pr2974436765678502625pace_b,A2: a > set_Pr2974436765678502625pace_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ ( finite3412154840674873937pace_b @ J @ I2 @ ( produc7259445117708109353pace_b @ B2 @ A2 ) ) ) )
        = ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(2)
thf(fact_857_Pi__cancel__merge__range_I2_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab4737552673497767871pace_a,B2: a > set_Pr8456636223741192351pace_a,A2: a > set_Pr8456636223741192351pace_a] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ ( finite8390634798700271631pace_a @ J @ I2 @ ( produc4013479291510626213pace_a @ B2 @ A2 ) ) ) )
        = ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(2)
thf(fact_858_Pi__cancel__merge__range_I2_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > b,B2: a > set_b,A2: a > set_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member_a_b @ X3 @ ( pi_a_b @ I2 @ ( finite1260387632014723919_set_b @ J @ I2 @ ( produc1220256858021801509_set_b @ B2 @ A2 ) ) ) )
        = ( member_a_b @ X3 @ ( pi_a_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(2)
thf(fact_859_Pi__cancel__merge__range_I3_J,axiom,
    ! [J: set_Pr8456636223741192351pace_a,I2: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_in8842055517982213773pace_a @ J @ I2 )
        = bot_bo2798762229408049931pace_a )
     => ( ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ ( finite2812723535947976847pace_b @ I2 @ J @ ( produc881681157476890533pace_b @ A2 @ B2 ) ) ) )
        = ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(3)
thf(fact_860_Pi__cancel__merge__range_I3_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > probab4737552677800996672pace_b,A2: a > set_Pr8527670263787538336pace_b,B2: a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ ( finite8461668838746617616pace_b @ I2 @ J @ ( produc5089952577834195623pace_b @ A2 @ B2 ) ) ) )
        = ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(3)
thf(fact_861_Pi__cancel__merge__range_I3_J,axiom,
    ! [J: set_Pr8456636223741192351pace_a,I2: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > b,A2: probab4737552673497767871pace_a > set_b,B2: probab4737552673497767871pace_a > set_b] :
      ( ( ( inf_in8842055517982213773pace_a @ J @ I2 )
        = bot_bo2798762229408049931pace_a )
     => ( ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ ( finite4108965814801126606_set_b @ I2 @ J @ ( produc6944462652351720227_set_b @ A2 @ B2 ) ) ) )
        = ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(3)
thf(fact_862_Pi__cancel__merge__range_I3_J,axiom,
    ! [J: set_b,I2: set_b,X3: b > probab4737552677800996672pace_b,A2: b > set_Pr8527670263787538336pace_b,B2: b > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_b @ J @ I2 )
        = bot_bot_set_b )
     => ( ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ ( finite2633747095815736655pace_b @ I2 @ J @ ( produc6518286030610866469pace_b @ A2 @ B2 ) ) ) )
        = ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(3)
thf(fact_863_Pi__cancel__merge__range_I3_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > probab8624551251471354625pace_b,A2: a > set_Pr2974436765678502625pace_b,B2: a > set_Pr2974436765678502625pace_b] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ ( finite3412154840674873937pace_b @ I2 @ J @ ( produc7259445117708109353pace_b @ A2 @ B2 ) ) ) )
        = ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(3)
thf(fact_864_Pi__cancel__merge__range_I3_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > probab4737552673497767871pace_a,A2: a > set_Pr8456636223741192351pace_a,B2: a > set_Pr8456636223741192351pace_a] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ ( finite8390634798700271631pace_a @ I2 @ J @ ( produc4013479291510626213pace_a @ A2 @ B2 ) ) ) )
        = ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(3)
thf(fact_865_Pi__cancel__merge__range_I3_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > b,A2: a > set_b,B2: a > set_b] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member_a_b @ X3 @ ( pi_a_b @ I2 @ ( finite1260387632014723919_set_b @ I2 @ J @ ( produc1220256858021801509_set_b @ A2 @ B2 ) ) ) )
        = ( member_a_b @ X3 @ ( pi_a_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(3)
thf(fact_866_Pi__cancel__merge__range_I4_J,axiom,
    ! [J: set_Pr8456636223741192351pace_a,I2: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b,A2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_in8842055517982213773pace_a @ J @ I2 )
        = bot_bo2798762229408049931pace_a )
     => ( ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ ( finite2812723535947976847pace_b @ J @ I2 @ ( produc881681157476890533pace_b @ B2 @ A2 ) ) ) )
        = ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(4)
thf(fact_867_Pi__cancel__merge__range_I4_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > probab4737552677800996672pace_b,B2: a > set_Pr8527670263787538336pace_b,A2: a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ ( finite8461668838746617616pace_b @ J @ I2 @ ( produc5089952577834195623pace_b @ B2 @ A2 ) ) ) )
        = ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(4)
thf(fact_868_Pi__cancel__merge__range_I4_J,axiom,
    ! [J: set_Pr8456636223741192351pace_a,I2: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > b,B2: probab4737552673497767871pace_a > set_b,A2: probab4737552673497767871pace_a > set_b] :
      ( ( ( inf_in8842055517982213773pace_a @ J @ I2 )
        = bot_bo2798762229408049931pace_a )
     => ( ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ ( finite4108965814801126606_set_b @ J @ I2 @ ( produc6944462652351720227_set_b @ B2 @ A2 ) ) ) )
        = ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(4)
thf(fact_869_Pi__cancel__merge__range_I4_J,axiom,
    ! [J: set_b,I2: set_b,X3: b > probab4737552677800996672pace_b,B2: b > set_Pr8527670263787538336pace_b,A2: b > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_b @ J @ I2 )
        = bot_bot_set_b )
     => ( ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ ( finite2633747095815736655pace_b @ J @ I2 @ ( produc6518286030610866469pace_b @ B2 @ A2 ) ) ) )
        = ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(4)
thf(fact_870_Pi__cancel__merge__range_I4_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > probab8624551251471354625pace_b,B2: a > set_Pr2974436765678502625pace_b,A2: a > set_Pr2974436765678502625pace_b] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ ( finite3412154840674873937pace_b @ J @ I2 @ ( produc7259445117708109353pace_b @ B2 @ A2 ) ) ) )
        = ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(4)
thf(fact_871_Pi__cancel__merge__range_I4_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > probab4737552673497767871pace_a,B2: a > set_Pr8456636223741192351pace_a,A2: a > set_Pr8456636223741192351pace_a] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ ( finite8390634798700271631pace_a @ J @ I2 @ ( produc4013479291510626213pace_a @ B2 @ A2 ) ) ) )
        = ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(4)
thf(fact_872_Pi__cancel__merge__range_I4_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > b,B2: a > set_b,A2: a > set_b] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member_a_b @ X3 @ ( pi_a_b @ I2 @ ( finite1260387632014723919_set_b @ J @ I2 @ ( produc1220256858021801509_set_b @ B2 @ A2 ) ) ) )
        = ( member_a_b @ X3 @ ( pi_a_b @ I2 @ A2 ) ) ) ) ).

% Pi_cancel_merge_range(4)
thf(fact_873_Pi__cancel__merge_I1_J,axiom,
    ! [I2: set_Pr8456636223741192351pace_a,J: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,Y2: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_in8842055517982213773pace_a @ I2 @ J )
        = bot_bo2798762229408049931pace_a )
     => ( ( member6667749562321684925pace_b @ ( finite5780851627059721263pace_b @ I2 @ J @ ( produc6052399650957384421pace_b @ X3 @ Y2 ) ) @ ( pi_Pro4287250843231025420pace_b @ I2 @ B2 ) )
        = ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(1)
thf(fact_874_Pi__cancel__merge_I1_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab4737552677800996672pace_b,Y2: a > probab4737552677800996672pace_b,B2: a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member7340901614391157822pace_b @ ( finite6055857901040393904pace_b @ I2 @ J @ ( produc2364966598166989287pace_b @ X3 @ Y2 ) ) @ ( pi_a_P1132609506902963085pace_b @ I2 @ B2 ) )
        = ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(1)
thf(fact_875_Pi__cancel__merge_I1_J,axiom,
    ! [I2: set_Pr8456636223741192351pace_a,J: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > b,Y2: probab4737552673497767871pace_a > b,B2: probab4737552673497767871pace_a > set_b] :
      ( ( ( inf_in8842055517982213773pace_a @ I2 @ J )
        = bot_bo2798762229408049931pace_a )
     => ( ( member5008716543664893436ce_a_b @ ( finite3957753199828097006ce_a_b @ I2 @ J @ ( produc258301278392420707ce_a_b @ X3 @ Y2 ) ) @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ B2 ) )
        = ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(1)
thf(fact_876_Pi__cancel__merge_I1_J,axiom,
    ! [I2: set_b,J: set_b,X3: b > probab4737552677800996672pace_b,Y2: b > probab4737552677800996672pace_b,B2: b > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_b @ I2 @ J )
        = bot_bot_set_b )
     => ( ( member1568243296417166973pace_b @ ( finite283199583066403055pace_b @ I2 @ J @ ( produc6520359691314873445pace_b @ X3 @ Y2 ) ) @ ( pi_b_P4583323225783748044pace_b @ I2 @ B2 ) )
        = ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(1)
thf(fact_877_Pi__cancel__merge_I1_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab8624551251471354625pace_b,Y2: a > probab8624551251471354625pace_b,B2: a > set_Pr2974436765678502625pace_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member41169580844105599pace_b @ ( finite4354535354149943921pace_b @ I2 @ J @ ( produc1199162346724129385pace_b @ X3 @ Y2 ) ) @ ( pi_a_P2860934570321248078pace_b @ I2 @ B2 ) )
        = ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(1)
thf(fact_878_Pi__cancel__merge_I1_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab4737552673497767871pace_a,Y2: a > probab4737552673497767871pace_a,B2: a > set_Pr8456636223741192351pace_a] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member7269867574344811837pace_a @ ( finite6055857896737165103pace_a @ I2 @ J @ ( produc9067851722357105125pace_a @ X3 @ Y2 ) ) @ ( pi_a_P1132609502599734284pace_a @ I2 @ B2 ) )
        = ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(1)
thf(fact_879_Pi__cancel__merge_I1_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > b,Y2: a > b,B2: a > set_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member_a_b @ ( finite2735608678046798447ge_a_b @ I2 @ J @ ( product_Pair_a_b_a_b @ X3 @ Y2 ) ) @ ( pi_a_b @ I2 @ B2 ) )
        = ( member_a_b @ X3 @ ( pi_a_b @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(1)
thf(fact_880_Pi__cancel__merge_I2_J,axiom,
    ! [J: set_Pr8456636223741192351pace_a,I2: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,Y2: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_in8842055517982213773pace_a @ J @ I2 )
        = bot_bo2798762229408049931pace_a )
     => ( ( member6667749562321684925pace_b @ ( finite5780851627059721263pace_b @ I2 @ J @ ( produc6052399650957384421pace_b @ X3 @ Y2 ) ) @ ( pi_Pro4287250843231025420pace_b @ I2 @ B2 ) )
        = ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(2)
thf(fact_881_Pi__cancel__merge_I2_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > probab4737552677800996672pace_b,Y2: a > probab4737552677800996672pace_b,B2: a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member7340901614391157822pace_b @ ( finite6055857901040393904pace_b @ I2 @ J @ ( produc2364966598166989287pace_b @ X3 @ Y2 ) ) @ ( pi_a_P1132609506902963085pace_b @ I2 @ B2 ) )
        = ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(2)
thf(fact_882_Pi__cancel__merge_I2_J,axiom,
    ! [J: set_Pr8456636223741192351pace_a,I2: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > b,Y2: probab4737552673497767871pace_a > b,B2: probab4737552673497767871pace_a > set_b] :
      ( ( ( inf_in8842055517982213773pace_a @ J @ I2 )
        = bot_bo2798762229408049931pace_a )
     => ( ( member5008716543664893436ce_a_b @ ( finite3957753199828097006ce_a_b @ I2 @ J @ ( produc258301278392420707ce_a_b @ X3 @ Y2 ) ) @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ B2 ) )
        = ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(2)
thf(fact_883_Pi__cancel__merge_I2_J,axiom,
    ! [J: set_b,I2: set_b,X3: b > probab4737552677800996672pace_b,Y2: b > probab4737552677800996672pace_b,B2: b > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_b @ J @ I2 )
        = bot_bot_set_b )
     => ( ( member1568243296417166973pace_b @ ( finite283199583066403055pace_b @ I2 @ J @ ( produc6520359691314873445pace_b @ X3 @ Y2 ) ) @ ( pi_b_P4583323225783748044pace_b @ I2 @ B2 ) )
        = ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(2)
thf(fact_884_Pi__cancel__merge_I2_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > probab8624551251471354625pace_b,Y2: a > probab8624551251471354625pace_b,B2: a > set_Pr2974436765678502625pace_b] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member41169580844105599pace_b @ ( finite4354535354149943921pace_b @ I2 @ J @ ( produc1199162346724129385pace_b @ X3 @ Y2 ) ) @ ( pi_a_P2860934570321248078pace_b @ I2 @ B2 ) )
        = ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(2)
thf(fact_885_Pi__cancel__merge_I2_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > probab4737552673497767871pace_a,Y2: a > probab4737552673497767871pace_a,B2: a > set_Pr8456636223741192351pace_a] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member7269867574344811837pace_a @ ( finite6055857896737165103pace_a @ I2 @ J @ ( produc9067851722357105125pace_a @ X3 @ Y2 ) ) @ ( pi_a_P1132609502599734284pace_a @ I2 @ B2 ) )
        = ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(2)
thf(fact_886_Pi__cancel__merge_I2_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > b,Y2: a > b,B2: a > set_b] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member_a_b @ ( finite2735608678046798447ge_a_b @ I2 @ J @ ( product_Pair_a_b_a_b @ X3 @ Y2 ) ) @ ( pi_a_b @ I2 @ B2 ) )
        = ( member_a_b @ X3 @ ( pi_a_b @ I2 @ B2 ) ) ) ) ).

% Pi_cancel_merge(2)
thf(fact_887_Pi__cancel__merge_I3_J,axiom,
    ! [I2: set_Pr8456636223741192351pace_a,J: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,Y2: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_in8842055517982213773pace_a @ I2 @ J )
        = bot_bo2798762229408049931pace_a )
     => ( ( member6667749562321684925pace_b @ ( finite5780851627059721263pace_b @ I2 @ J @ ( produc6052399650957384421pace_b @ X3 @ Y2 ) ) @ ( pi_Pro4287250843231025420pace_b @ J @ B2 ) )
        = ( member6667749562321684925pace_b @ Y2 @ ( pi_Pro4287250843231025420pace_b @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(3)
thf(fact_888_Pi__cancel__merge_I3_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab4737552677800996672pace_b,Y2: a > probab4737552677800996672pace_b,B2: a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member7340901614391157822pace_b @ ( finite6055857901040393904pace_b @ I2 @ J @ ( produc2364966598166989287pace_b @ X3 @ Y2 ) ) @ ( pi_a_P1132609506902963085pace_b @ J @ B2 ) )
        = ( member7340901614391157822pace_b @ Y2 @ ( pi_a_P1132609506902963085pace_b @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(3)
thf(fact_889_Pi__cancel__merge_I3_J,axiom,
    ! [I2: set_Pr8456636223741192351pace_a,J: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > b,Y2: probab4737552673497767871pace_a > b,B2: probab4737552673497767871pace_a > set_b] :
      ( ( ( inf_in8842055517982213773pace_a @ I2 @ J )
        = bot_bo2798762229408049931pace_a )
     => ( ( member5008716543664893436ce_a_b @ ( finite3957753199828097006ce_a_b @ I2 @ J @ ( produc258301278392420707ce_a_b @ X3 @ Y2 ) ) @ ( pi_Pro8257876842545441995ce_a_b @ J @ B2 ) )
        = ( member5008716543664893436ce_a_b @ Y2 @ ( pi_Pro8257876842545441995ce_a_b @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(3)
thf(fact_890_Pi__cancel__merge_I3_J,axiom,
    ! [I2: set_b,J: set_b,X3: b > probab4737552677800996672pace_b,Y2: b > probab4737552677800996672pace_b,B2: b > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_b @ I2 @ J )
        = bot_bot_set_b )
     => ( ( member1568243296417166973pace_b @ ( finite283199583066403055pace_b @ I2 @ J @ ( produc6520359691314873445pace_b @ X3 @ Y2 ) ) @ ( pi_b_P4583323225783748044pace_b @ J @ B2 ) )
        = ( member1568243296417166973pace_b @ Y2 @ ( pi_b_P4583323225783748044pace_b @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(3)
thf(fact_891_Pi__cancel__merge_I3_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab8624551251471354625pace_b,Y2: a > probab8624551251471354625pace_b,B2: a > set_Pr2974436765678502625pace_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member41169580844105599pace_b @ ( finite4354535354149943921pace_b @ I2 @ J @ ( produc1199162346724129385pace_b @ X3 @ Y2 ) ) @ ( pi_a_P2860934570321248078pace_b @ J @ B2 ) )
        = ( member41169580844105599pace_b @ Y2 @ ( pi_a_P2860934570321248078pace_b @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(3)
thf(fact_892_Pi__cancel__merge_I3_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > probab4737552673497767871pace_a,Y2: a > probab4737552673497767871pace_a,B2: a > set_Pr8456636223741192351pace_a] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member7269867574344811837pace_a @ ( finite6055857896737165103pace_a @ I2 @ J @ ( produc9067851722357105125pace_a @ X3 @ Y2 ) ) @ ( pi_a_P1132609502599734284pace_a @ J @ B2 ) )
        = ( member7269867574344811837pace_a @ Y2 @ ( pi_a_P1132609502599734284pace_a @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(3)
thf(fact_893_Pi__cancel__merge_I3_J,axiom,
    ! [I2: set_a,J: set_a,X3: a > b,Y2: a > b,B2: a > set_b] :
      ( ( ( inf_inf_set_a @ I2 @ J )
        = bot_bot_set_a )
     => ( ( member_a_b @ ( finite2735608678046798447ge_a_b @ I2 @ J @ ( product_Pair_a_b_a_b @ X3 @ Y2 ) ) @ ( pi_a_b @ J @ B2 ) )
        = ( member_a_b @ Y2 @ ( pi_a_b @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(3)
thf(fact_894_Pi__cancel__merge_I4_J,axiom,
    ! [J: set_Pr8456636223741192351pace_a,I2: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,Y2: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_in8842055517982213773pace_a @ J @ I2 )
        = bot_bo2798762229408049931pace_a )
     => ( ( member6667749562321684925pace_b @ ( finite5780851627059721263pace_b @ I2 @ J @ ( produc6052399650957384421pace_b @ X3 @ Y2 ) ) @ ( pi_Pro4287250843231025420pace_b @ J @ B2 ) )
        = ( member6667749562321684925pace_b @ Y2 @ ( pi_Pro4287250843231025420pace_b @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(4)
thf(fact_895_Pi__cancel__merge_I4_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > probab4737552677800996672pace_b,Y2: a > probab4737552677800996672pace_b,B2: a > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member7340901614391157822pace_b @ ( finite6055857901040393904pace_b @ I2 @ J @ ( produc2364966598166989287pace_b @ X3 @ Y2 ) ) @ ( pi_a_P1132609506902963085pace_b @ J @ B2 ) )
        = ( member7340901614391157822pace_b @ Y2 @ ( pi_a_P1132609506902963085pace_b @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(4)
thf(fact_896_Pi__cancel__merge_I4_J,axiom,
    ! [J: set_Pr8456636223741192351pace_a,I2: set_Pr8456636223741192351pace_a,X3: probab4737552673497767871pace_a > b,Y2: probab4737552673497767871pace_a > b,B2: probab4737552673497767871pace_a > set_b] :
      ( ( ( inf_in8842055517982213773pace_a @ J @ I2 )
        = bot_bo2798762229408049931pace_a )
     => ( ( member5008716543664893436ce_a_b @ ( finite3957753199828097006ce_a_b @ I2 @ J @ ( produc258301278392420707ce_a_b @ X3 @ Y2 ) ) @ ( pi_Pro8257876842545441995ce_a_b @ J @ B2 ) )
        = ( member5008716543664893436ce_a_b @ Y2 @ ( pi_Pro8257876842545441995ce_a_b @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(4)
thf(fact_897_Pi__cancel__merge_I4_J,axiom,
    ! [J: set_b,I2: set_b,X3: b > probab4737552677800996672pace_b,Y2: b > probab4737552677800996672pace_b,B2: b > set_Pr8527670263787538336pace_b] :
      ( ( ( inf_inf_set_b @ J @ I2 )
        = bot_bot_set_b )
     => ( ( member1568243296417166973pace_b @ ( finite283199583066403055pace_b @ I2 @ J @ ( produc6520359691314873445pace_b @ X3 @ Y2 ) ) @ ( pi_b_P4583323225783748044pace_b @ J @ B2 ) )
        = ( member1568243296417166973pace_b @ Y2 @ ( pi_b_P4583323225783748044pace_b @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(4)
thf(fact_898_Pi__cancel__merge_I4_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > probab8624551251471354625pace_b,Y2: a > probab8624551251471354625pace_b,B2: a > set_Pr2974436765678502625pace_b] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member41169580844105599pace_b @ ( finite4354535354149943921pace_b @ I2 @ J @ ( produc1199162346724129385pace_b @ X3 @ Y2 ) ) @ ( pi_a_P2860934570321248078pace_b @ J @ B2 ) )
        = ( member41169580844105599pace_b @ Y2 @ ( pi_a_P2860934570321248078pace_b @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(4)
thf(fact_899_Pi__cancel__merge_I4_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > probab4737552673497767871pace_a,Y2: a > probab4737552673497767871pace_a,B2: a > set_Pr8456636223741192351pace_a] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member7269867574344811837pace_a @ ( finite6055857896737165103pace_a @ I2 @ J @ ( produc9067851722357105125pace_a @ X3 @ Y2 ) ) @ ( pi_a_P1132609502599734284pace_a @ J @ B2 ) )
        = ( member7269867574344811837pace_a @ Y2 @ ( pi_a_P1132609502599734284pace_a @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(4)
thf(fact_900_Pi__cancel__merge_I4_J,axiom,
    ! [J: set_a,I2: set_a,X3: a > b,Y2: a > b,B2: a > set_b] :
      ( ( ( inf_inf_set_a @ J @ I2 )
        = bot_bot_set_a )
     => ( ( member_a_b @ ( finite2735608678046798447ge_a_b @ I2 @ J @ ( product_Pair_a_b_a_b @ X3 @ Y2 ) ) @ ( pi_a_b @ J @ B2 ) )
        = ( member_a_b @ Y2 @ ( pi_a_b @ J @ B2 ) ) ) ) ).

% Pi_cancel_merge(4)
thf(fact_901_PiE__restrict,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr8456636223741192351pace_a,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( member6667749562321684925pace_b @ F @ ( piE_Pr1548282726383880571pace_b @ A2 @ B2 ) )
     => ( ( restri5846393312276451823pace_b @ F @ A2 )
        = F ) ) ).

% PiE_restrict
thf(fact_902_PiE__restrict,axiom,
    ! [F: a > probab4737552677800996672pace_b,A2: set_a,B2: a > set_Pr8527670263787538336pace_b] :
      ( ( member7340901614391157822pace_b @ F @ ( piE_a_4194508618861114364pace_b @ A2 @ B2 ) )
     => ( ( restri4927025876843904112pace_b @ F @ A2 )
        = F ) ) ).

% PiE_restrict
thf(fact_903_PiE__restrict,axiom,
    ! [F: probab4737552673497767871pace_a > b,A2: set_Pr8456636223741192351pace_a,B2: probab4737552673497767871pace_a > set_b] :
      ( ( member5008716543664893436ce_a_b @ F @ ( piE_Pr2096403917648817466ce_a_b @ A2 @ B2 ) )
     => ( ( restri2828921175631607214ce_a_b @ F @ A2 )
        = F ) ) ).

% PiE_restrict
thf(fact_904_PiE__restrict,axiom,
    ! [F: b > probab4737552677800996672pace_b,A2: set_b,B2: b > set_Pr8527670263787538336pace_b] :
      ( ( member1568243296417166973pace_b @ F @ ( piE_b_7645222337741899323pace_b @ A2 @ B2 ) )
     => ( ( restri8377739595724689071pace_b @ F @ A2 )
        = F ) ) ).

% PiE_restrict
thf(fact_905_PiE__restrict,axiom,
    ! [F: a > probab8624551251471354625pace_b,A2: set_a,B2: a > set_Pr2974436765678502625pace_b] :
      ( ( member41169580844105599pace_b @ F @ ( piE_a_121966453474103229pace_b @ A2 @ B2 ) )
     => ( ( restri4420077039366674481pace_b @ F @ A2 )
        = F ) ) ).

% PiE_restrict
thf(fact_906_PiE__restrict,axiom,
    ! [F: a > probab4737552673497767871pace_a,A2: set_a,B2: a > set_Pr8456636223741192351pace_a] :
      ( ( member7269867574344811837pace_a @ F @ ( piE_a_4194508614557885563pace_a @ A2 @ B2 ) )
     => ( ( restri4927025872540675311pace_a @ F @ A2 )
        = F ) ) ).

% PiE_restrict
thf(fact_907_PiE__restrict,axiom,
    ! [F: a > b,A2: set_a,B2: a > set_b] :
      ( ( member_a_b @ F @ ( piE_a_b @ A2 @ B2 ) )
     => ( ( restrict_a_b @ F @ A2 )
        = F ) ) ).

% PiE_restrict
thf(fact_908_restrictI,axiom,
    ! [A2: set_a,F: a > b,B2: a > set_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member_a_b @ ( restrict_a_b @ F @ A2 ) @ ( pi_a_b @ A2 @ B2 ) ) ) ).

% restrictI
thf(fact_909_restrictI,axiom,
    ! [A2: set_a,F: a > probab4737552677800996672pace_b,B2: a > set_Pr8527670263787538336pace_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member6485455078948787817pace_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member7340901614391157822pace_b @ ( restri4927025876843904112pace_b @ F @ A2 ) @ ( pi_a_P1132609506902963085pace_b @ A2 @ B2 ) ) ) ).

% restrictI
thf(fact_910_restrictI,axiom,
    ! [A2: set_Pr8456636223741192351pace_a,F: probab4737552673497767871pace_a > b,B2: probab4737552673497767871pace_a > set_b] :
      ( ! [X4: probab4737552673497767871pace_a] :
          ( ( member6485455074645559016pace_a @ X4 @ A2 )
         => ( member_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member5008716543664893436ce_a_b @ ( restri2828921175631607214ce_a_b @ F @ A2 ) @ ( pi_Pro8257876842545441995ce_a_b @ A2 @ B2 ) ) ) ).

% restrictI
thf(fact_911_restrictI,axiom,
    ! [A2: set_b,F: b > probab4737552677800996672pace_b,B2: b > set_Pr8527670263787538336pace_b] :
      ( ! [X4: b] :
          ( ( member_b @ X4 @ A2 )
         => ( member6485455078948787817pace_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member1568243296417166973pace_b @ ( restri8377739595724689071pace_b @ F @ A2 ) @ ( pi_b_P4583323225783748044pace_b @ A2 @ B2 ) ) ) ).

% restrictI
thf(fact_912_restrictI,axiom,
    ! [A2: set_a,F: a > probab4737552673497767871pace_a,B2: a > set_Pr8456636223741192351pace_a] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member6485455074645559016pace_a @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member7269867574344811837pace_a @ ( restri4927025872540675311pace_a @ F @ A2 ) @ ( pi_a_P1132609502599734284pace_a @ A2 @ B2 ) ) ) ).

% restrictI
thf(fact_913_restrictI,axiom,
    ! [A2: set_Pr8456636223741192351pace_a,F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ! [X4: probab4737552673497767871pace_a] :
          ( ( member6485455074645559016pace_a @ X4 @ A2 )
         => ( member6485455078948787817pace_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member6667749562321684925pace_b @ ( restri5846393312276451823pace_b @ F @ A2 ) @ ( pi_Pro4287250843231025420pace_b @ A2 @ B2 ) ) ) ).

% restrictI
thf(fact_914_restrictI,axiom,
    ! [A2: set_a,F: a > probab8624551251471354625pace_b,B2: a > set_Pr2974436765678502625pace_b] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ A2 )
         => ( member7462078926031725098pace_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member41169580844105599pace_b @ ( restri4420077039366674481pace_b @ F @ A2 ) @ ( pi_a_P2860934570321248078pace_b @ A2 @ B2 ) ) ) ).

% restrictI
thf(fact_915_restrictI,axiom,
    ! [A2: set_a_b,F: ( a > b ) > a > b,B2: ( a > b ) > set_a_b] :
      ( ! [X4: a > b] :
          ( ( member_a_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member_a_b_a_b @ ( restrict_a_b_a_b @ F @ A2 ) @ ( pi_a_b_a_b @ A2 @ B2 ) ) ) ).

% restrictI
thf(fact_916_restrictI,axiom,
    ! [A2: set_a_3263942136899480541pace_b,F: ( a > probab4737552677800996672pace_b ) > a > b,B2: ( a > probab4737552677800996672pace_b ) > set_a_b] :
      ( ! [X4: a > probab4737552677800996672pace_b] :
          ( ( member7340901614391157822pace_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member4717814410477825091_b_a_b @ ( restri290663758601482941_b_a_b @ F @ A2 ) @ ( pi_a_P7357289706263199834_b_a_b @ A2 @ B2 ) ) ) ).

% restrictI
thf(fact_917_restrictI,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,F: ( probab4737552673497767871pace_a > b ) > a > b,B2: ( probab4737552673497767871pace_a > b ) > set_a_b] :
      ( ! [X4: probab4737552673497767871pace_a > b] :
          ( ( member5008716543664893436ce_a_b @ X4 @ A2 )
         => ( member_a_b @ ( F @ X4 ) @ ( B2 @ X4 ) ) )
     => ( member2025916712706589185_b_a_b @ ( restri6822138097685022843_b_a_b @ F @ A2 ) @ ( pi_Pro4665392008491963928_b_a_b @ A2 @ B2 ) ) ) ).

% restrictI
thf(fact_918_restrict__PiE,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,I2: set_Pr8456636223741192351pace_a,S3: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( member6667749562321684925pace_b @ ( restri5846393312276451823pace_b @ F @ I2 ) @ ( piE_Pr1548282726383880571pace_b @ I2 @ S3 ) )
      = ( member6667749562321684925pace_b @ F @ ( pi_Pro4287250843231025420pace_b @ I2 @ S3 ) ) ) ).

% restrict_PiE
thf(fact_919_restrict__PiE,axiom,
    ! [F: a > probab4737552677800996672pace_b,I2: set_a,S3: a > set_Pr8527670263787538336pace_b] :
      ( ( member7340901614391157822pace_b @ ( restri4927025876843904112pace_b @ F @ I2 ) @ ( piE_a_4194508618861114364pace_b @ I2 @ S3 ) )
      = ( member7340901614391157822pace_b @ F @ ( pi_a_P1132609506902963085pace_b @ I2 @ S3 ) ) ) ).

% restrict_PiE
thf(fact_920_restrict__PiE,axiom,
    ! [F: probab4737552673497767871pace_a > b,I2: set_Pr8456636223741192351pace_a,S3: probab4737552673497767871pace_a > set_b] :
      ( ( member5008716543664893436ce_a_b @ ( restri2828921175631607214ce_a_b @ F @ I2 ) @ ( piE_Pr2096403917648817466ce_a_b @ I2 @ S3 ) )
      = ( member5008716543664893436ce_a_b @ F @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ S3 ) ) ) ).

% restrict_PiE
thf(fact_921_restrict__PiE,axiom,
    ! [F: b > probab4737552677800996672pace_b,I2: set_b,S3: b > set_Pr8527670263787538336pace_b] :
      ( ( member1568243296417166973pace_b @ ( restri8377739595724689071pace_b @ F @ I2 ) @ ( piE_b_7645222337741899323pace_b @ I2 @ S3 ) )
      = ( member1568243296417166973pace_b @ F @ ( pi_b_P4583323225783748044pace_b @ I2 @ S3 ) ) ) ).

% restrict_PiE
thf(fact_922_restrict__PiE,axiom,
    ! [F: a > probab8624551251471354625pace_b,I2: set_a,S3: a > set_Pr2974436765678502625pace_b] :
      ( ( member41169580844105599pace_b @ ( restri4420077039366674481pace_b @ F @ I2 ) @ ( piE_a_121966453474103229pace_b @ I2 @ S3 ) )
      = ( member41169580844105599pace_b @ F @ ( pi_a_P2860934570321248078pace_b @ I2 @ S3 ) ) ) ).

% restrict_PiE
thf(fact_923_restrict__PiE,axiom,
    ! [F: a > probab4737552673497767871pace_a,I2: set_a,S3: a > set_Pr8456636223741192351pace_a] :
      ( ( member7269867574344811837pace_a @ ( restri4927025872540675311pace_a @ F @ I2 ) @ ( piE_a_4194508614557885563pace_a @ I2 @ S3 ) )
      = ( member7269867574344811837pace_a @ F @ ( pi_a_P1132609502599734284pace_a @ I2 @ S3 ) ) ) ).

% restrict_PiE
thf(fact_924_restrict__PiE,axiom,
    ! [F: a > b,I2: set_a,S3: a > set_b] :
      ( ( member_a_b @ ( restrict_a_b @ F @ I2 ) @ ( piE_a_b @ I2 @ S3 ) )
      = ( member_a_b @ F @ ( pi_a_b @ I2 @ S3 ) ) ) ).

% restrict_PiE
thf(fact_925_restrict__PiE__iff,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,I2: set_Pr8456636223741192351pace_a,X: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( member6667749562321684925pace_b @ ( restri5846393312276451823pace_b @ F @ I2 ) @ ( piE_Pr1548282726383880571pace_b @ I2 @ X ) )
      = ( ! [X2: probab4737552673497767871pace_a] :
            ( ( member6485455074645559016pace_a @ X2 @ I2 )
           => ( member6485455078948787817pace_b @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% restrict_PiE_iff
thf(fact_926_restrict__PiE__iff,axiom,
    ! [F: a > probab4737552677800996672pace_b,I2: set_a,X: a > set_Pr8527670263787538336pace_b] :
      ( ( member7340901614391157822pace_b @ ( restri4927025876843904112pace_b @ F @ I2 ) @ ( piE_a_4194508618861114364pace_b @ I2 @ X ) )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ I2 )
           => ( member6485455078948787817pace_b @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% restrict_PiE_iff
thf(fact_927_restrict__PiE__iff,axiom,
    ! [F: probab4737552673497767871pace_a > b,I2: set_Pr8456636223741192351pace_a,X: probab4737552673497767871pace_a > set_b] :
      ( ( member5008716543664893436ce_a_b @ ( restri2828921175631607214ce_a_b @ F @ I2 ) @ ( piE_Pr2096403917648817466ce_a_b @ I2 @ X ) )
      = ( ! [X2: probab4737552673497767871pace_a] :
            ( ( member6485455074645559016pace_a @ X2 @ I2 )
           => ( member_b @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% restrict_PiE_iff
thf(fact_928_restrict__PiE__iff,axiom,
    ! [F: b > probab4737552677800996672pace_b,I2: set_b,X: b > set_Pr8527670263787538336pace_b] :
      ( ( member1568243296417166973pace_b @ ( restri8377739595724689071pace_b @ F @ I2 ) @ ( piE_b_7645222337741899323pace_b @ I2 @ X ) )
      = ( ! [X2: b] :
            ( ( member_b @ X2 @ I2 )
           => ( member6485455078948787817pace_b @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% restrict_PiE_iff
thf(fact_929_restrict__PiE__iff,axiom,
    ! [F: a > probab8624551251471354625pace_b,I2: set_a,X: a > set_Pr2974436765678502625pace_b] :
      ( ( member41169580844105599pace_b @ ( restri4420077039366674481pace_b @ F @ I2 ) @ ( piE_a_121966453474103229pace_b @ I2 @ X ) )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ I2 )
           => ( member7462078926031725098pace_b @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% restrict_PiE_iff
thf(fact_930_restrict__PiE__iff,axiom,
    ! [F: a > probab4737552673497767871pace_a,I2: set_a,X: a > set_Pr8456636223741192351pace_a] :
      ( ( member7269867574344811837pace_a @ ( restri4927025872540675311pace_a @ F @ I2 ) @ ( piE_a_4194508614557885563pace_a @ I2 @ X ) )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ I2 )
           => ( member6485455074645559016pace_a @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% restrict_PiE_iff
thf(fact_931_restrict__PiE__iff,axiom,
    ! [F: a > b,I2: set_a,X: a > set_b] :
      ( ( member_a_b @ ( restrict_a_b @ F @ I2 ) @ ( piE_a_b @ I2 @ X ) )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ I2 )
           => ( member_b @ ( F @ X2 ) @ ( X @ X2 ) ) ) ) ) ).

% restrict_PiE_iff
thf(fact_932_restrict__Pi__cancel,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,I2: set_Pr8456636223741192351pace_a,A2: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( member6667749562321684925pace_b @ ( restri5846393312276451823pace_b @ X3 @ I2 ) @ ( pi_Pro4287250843231025420pace_b @ I2 @ A2 ) )
      = ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ A2 ) ) ) ).

% restrict_Pi_cancel
thf(fact_933_restrict__Pi__cancel,axiom,
    ! [X3: a > probab4737552677800996672pace_b,I2: set_a,A2: a > set_Pr8527670263787538336pace_b] :
      ( ( member7340901614391157822pace_b @ ( restri4927025876843904112pace_b @ X3 @ I2 ) @ ( pi_a_P1132609506902963085pace_b @ I2 @ A2 ) )
      = ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ A2 ) ) ) ).

% restrict_Pi_cancel
thf(fact_934_restrict__Pi__cancel,axiom,
    ! [X3: probab4737552673497767871pace_a > b,I2: set_Pr8456636223741192351pace_a,A2: probab4737552673497767871pace_a > set_b] :
      ( ( member5008716543664893436ce_a_b @ ( restri2828921175631607214ce_a_b @ X3 @ I2 ) @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ A2 ) )
      = ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ A2 ) ) ) ).

% restrict_Pi_cancel
thf(fact_935_restrict__Pi__cancel,axiom,
    ! [X3: b > probab4737552677800996672pace_b,I2: set_b,A2: b > set_Pr8527670263787538336pace_b] :
      ( ( member1568243296417166973pace_b @ ( restri8377739595724689071pace_b @ X3 @ I2 ) @ ( pi_b_P4583323225783748044pace_b @ I2 @ A2 ) )
      = ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ A2 ) ) ) ).

% restrict_Pi_cancel
thf(fact_936_restrict__Pi__cancel,axiom,
    ! [X3: a > probab8624551251471354625pace_b,I2: set_a,A2: a > set_Pr2974436765678502625pace_b] :
      ( ( member41169580844105599pace_b @ ( restri4420077039366674481pace_b @ X3 @ I2 ) @ ( pi_a_P2860934570321248078pace_b @ I2 @ A2 ) )
      = ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ A2 ) ) ) ).

% restrict_Pi_cancel
thf(fact_937_restrict__Pi__cancel,axiom,
    ! [X3: a > probab4737552673497767871pace_a,I2: set_a,A2: a > set_Pr8456636223741192351pace_a] :
      ( ( member7269867574344811837pace_a @ ( restri4927025872540675311pace_a @ X3 @ I2 ) @ ( pi_a_P1132609502599734284pace_a @ I2 @ A2 ) )
      = ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ A2 ) ) ) ).

% restrict_Pi_cancel
thf(fact_938_restrict__Pi__cancel,axiom,
    ! [X3: a > b,I2: set_a,A2: a > set_b] :
      ( ( member_a_b @ ( restrict_a_b @ X3 @ I2 ) @ ( pi_a_b @ I2 @ A2 ) )
      = ( member_a_b @ X3 @ ( pi_a_b @ I2 @ A2 ) ) ) ).

% restrict_Pi_cancel
thf(fact_939_vimage__eq,axiom,
    ! [A: a > b,F: ( a > b ) > a > b,B2: set_a_b] :
      ( ( member_a_b @ A @ ( vimage_a_b_a_b @ F @ B2 ) )
      = ( member_a_b @ ( F @ A ) @ B2 ) ) ).

% vimage_eq
thf(fact_940_vimage__eq,axiom,
    ! [A: a > probab4737552677800996672pace_b,F: ( a > probab4737552677800996672pace_b ) > a > b,B2: set_a_b] :
      ( ( member7340901614391157822pace_b @ A @ ( vimage6332008315180197450_b_a_b @ F @ B2 ) )
      = ( member_a_b @ ( F @ A ) @ B2 ) ) ).

% vimage_eq
thf(fact_941_vimage__eq,axiom,
    ! [A: probab4737552673497767871pace_a > b,F: ( probab4737552673497767871pace_a > b ) > a > b,B2: set_a_b] :
      ( ( member5008716543664893436ce_a_b @ A @ ( vimage3640110617408961544_b_a_b @ F @ B2 ) )
      = ( member_a_b @ ( F @ A ) @ B2 ) ) ).

% vimage_eq
thf(fact_942_vimage__eq,axiom,
    ! [A: b > probab4737552677800996672pace_b,F: ( b > probab4737552677800996672pace_b ) > a > b,B2: set_a_b] :
      ( ( member1568243296417166973pace_b @ A @ ( vimage9190574721758969481_b_a_b @ F @ B2 ) )
      = ( member_a_b @ ( F @ A ) @ B2 ) ) ).

% vimage_eq
thf(fact_943_vimage__eq,axiom,
    ! [A: a > probab4737552673497767871pace_a,F: ( a > probab4737552673497767871pace_a ) > a > b,B2: set_a_b] :
      ( ( member7269867574344811837pace_a @ A @ ( vimage8456589847784000841_a_a_b @ F @ B2 ) )
      = ( member_a_b @ ( F @ A ) @ B2 ) ) ).

% vimage_eq
thf(fact_944_vimage__eq,axiom,
    ! [A: a > b,F: ( a > b ) > a > probab4737552677800996672pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( member_a_b @ A @ ( vimage7369165718344531018pace_b @ F @ B2 ) )
      = ( member7340901614391157822pace_b @ ( F @ A ) @ B2 ) ) ).

% vimage_eq
thf(fact_945_vimage__eq,axiom,
    ! [A: a > b,F: ( a > b ) > probab4737552673497767871pace_a > b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( member_a_b @ A @ ( vimage5036980647618266632ce_a_b @ F @ B2 ) )
      = ( member5008716543664893436ce_a_b @ ( F @ A ) @ B2 ) ) ).

% vimage_eq
thf(fact_946_vimage__eq,axiom,
    ! [A: a > b,F: ( a > b ) > b > probab4737552677800996672pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( member_a_b @ A @ ( vimage1596507400370540169pace_b @ F @ B2 ) )
      = ( member1568243296417166973pace_b @ ( F @ A ) @ B2 ) ) ).

% vimage_eq
thf(fact_947_vimage__eq,axiom,
    ! [A: a > b,F: ( a > b ) > a > probab4737552673497767871pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( member_a_b @ A @ ( vimage7298131678298185033pace_a @ F @ B2 ) )
      = ( member7269867574344811837pace_a @ ( F @ A ) @ B2 ) ) ).

% vimage_eq
thf(fact_948_vimage__eq,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,F: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > a > b,B2: set_a_b] :
      ( ( member6667749562321684925pace_b @ A @ ( vimage7679194320585949641_b_a_b @ F @ B2 ) )
      = ( member_a_b @ ( F @ A ) @ B2 ) ) ).

% vimage_eq
thf(fact_949_vimageI,axiom,
    ! [F: ( a > b ) > a > b,A: a > b,B: a > b,B2: set_a_b] :
      ( ( ( F @ A )
        = B )
     => ( ( member_a_b @ B @ B2 )
       => ( member_a_b @ A @ ( vimage_a_b_a_b @ F @ B2 ) ) ) ) ).

% vimageI
thf(fact_950_vimageI,axiom,
    ! [F: ( a > b ) > a > probab4737552677800996672pace_b,A: a > b,B: a > probab4737552677800996672pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( ( F @ A )
        = B )
     => ( ( member7340901614391157822pace_b @ B @ B2 )
       => ( member_a_b @ A @ ( vimage7369165718344531018pace_b @ F @ B2 ) ) ) ) ).

% vimageI
thf(fact_951_vimageI,axiom,
    ! [F: ( a > b ) > probab4737552673497767871pace_a > b,A: a > b,B: probab4737552673497767871pace_a > b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( ( F @ A )
        = B )
     => ( ( member5008716543664893436ce_a_b @ B @ B2 )
       => ( member_a_b @ A @ ( vimage5036980647618266632ce_a_b @ F @ B2 ) ) ) ) ).

% vimageI
thf(fact_952_vimageI,axiom,
    ! [F: ( a > b ) > b > probab4737552677800996672pace_b,A: a > b,B: b > probab4737552677800996672pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( ( F @ A )
        = B )
     => ( ( member1568243296417166973pace_b @ B @ B2 )
       => ( member_a_b @ A @ ( vimage1596507400370540169pace_b @ F @ B2 ) ) ) ) ).

% vimageI
thf(fact_953_vimageI,axiom,
    ! [F: ( a > b ) > a > probab4737552673497767871pace_a,A: a > b,B: a > probab4737552673497767871pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( ( F @ A )
        = B )
     => ( ( member7269867574344811837pace_a @ B @ B2 )
       => ( member_a_b @ A @ ( vimage7298131678298185033pace_a @ F @ B2 ) ) ) ) ).

% vimageI
thf(fact_954_vimageI,axiom,
    ! [F: ( a > probab4737552677800996672pace_b ) > a > b,A: a > probab4737552677800996672pace_b,B: a > b,B2: set_a_b] :
      ( ( ( F @ A )
        = B )
     => ( ( member_a_b @ B @ B2 )
       => ( member7340901614391157822pace_b @ A @ ( vimage6332008315180197450_b_a_b @ F @ B2 ) ) ) ) ).

% vimageI
thf(fact_955_vimageI,axiom,
    ! [F: ( probab4737552673497767871pace_a > b ) > a > b,A: probab4737552673497767871pace_a > b,B: a > b,B2: set_a_b] :
      ( ( ( F @ A )
        = B )
     => ( ( member_a_b @ B @ B2 )
       => ( member5008716543664893436ce_a_b @ A @ ( vimage3640110617408961544_b_a_b @ F @ B2 ) ) ) ) ).

% vimageI
thf(fact_956_vimageI,axiom,
    ! [F: ( b > probab4737552677800996672pace_b ) > a > b,A: b > probab4737552677800996672pace_b,B: a > b,B2: set_a_b] :
      ( ( ( F @ A )
        = B )
     => ( ( member_a_b @ B @ B2 )
       => ( member1568243296417166973pace_b @ A @ ( vimage9190574721758969481_b_a_b @ F @ B2 ) ) ) ) ).

% vimageI
thf(fact_957_vimageI,axiom,
    ! [F: ( a > probab4737552673497767871pace_a ) > a > b,A: a > probab4737552673497767871pace_a,B: a > b,B2: set_a_b] :
      ( ( ( F @ A )
        = B )
     => ( ( member_a_b @ B @ B2 )
       => ( member7269867574344811837pace_a @ A @ ( vimage8456589847784000841_a_a_b @ F @ B2 ) ) ) ) ).

% vimageI
thf(fact_958_vimageI,axiom,
    ! [F: ( a > b ) > probab4737552673497767871pace_a > probab4737552677800996672pace_b,A: a > b,B: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( ( F @ A )
        = B )
     => ( ( member6667749562321684925pace_b @ B @ B2 )
       => ( member_a_b @ A @ ( vimage6033027822411555273pace_b @ F @ B2 ) ) ) ) ).

% vimageI
thf(fact_959_vimage__if,axiom,
    ! [C: a > b,A2: set_a_b,D: a > b,B2: set_a_b] :
      ( ( ( member_a_b @ C @ A2 )
       => ( ( ( member_a_b @ D @ A2 )
           => ( ( vimage_a_b_a_b
                @ ^ [X2: a > b] : ( if_a_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = top_top_set_a_b ) )
          & ( ~ ( member_a_b @ D @ A2 )
           => ( ( vimage_a_b_a_b
                @ ^ [X2: a > b] : ( if_a_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = B2 ) ) ) )
      & ( ~ ( member_a_b @ C @ A2 )
       => ( ( ( member_a_b @ D @ A2 )
           => ( ( vimage_a_b_a_b
                @ ^ [X2: a > b] : ( if_a_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = ( uminus6731694806113723621et_a_b @ B2 ) ) )
          & ( ~ ( member_a_b @ D @ A2 )
           => ( ( vimage_a_b_a_b
                @ ^ [X2: a > b] : ( if_a_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = bot_bot_set_a_b ) ) ) ) ) ).

% vimage_if
thf(fact_960_vimage__if,axiom,
    ! [C: a > b,A2: set_a_b,D: a > b,B2: set_a_3263942136899480541pace_b] :
      ( ( ( member_a_b @ C @ A2 )
       => ( ( ( member_a_b @ D @ A2 )
           => ( ( vimage6332008315180197450_b_a_b
                @ ^ [X2: a > probab4737552677800996672pace_b] : ( if_a_b @ ( member7340901614391157822pace_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = top_to1927542458104261261pace_b ) )
          & ( ~ ( member_a_b @ D @ A2 )
           => ( ( vimage6332008315180197450_b_a_b
                @ ^ [X2: a > probab4737552677800996672pace_b] : ( if_a_b @ ( member7340901614391157822pace_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = B2 ) ) ) )
      & ( ~ ( member_a_b @ C @ A2 )
       => ( ( ( member_a_b @ D @ A2 )
           => ( ( vimage6332008315180197450_b_a_b
                @ ^ [X2: a > probab4737552677800996672pace_b] : ( if_a_b @ ( member7340901614391157822pace_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = ( uminus9143991737638391846pace_b @ B2 ) ) )
          & ( ~ ( member_a_b @ D @ A2 )
           => ( ( vimage6332008315180197450_b_a_b
                @ ^ [X2: a > probab4737552677800996672pace_b] : ( if_a_b @ ( member7340901614391157822pace_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = bot_bo2617902995080265329pace_b ) ) ) ) ) ).

% vimage_if
thf(fact_961_vimage__if,axiom,
    ! [C: a > b,A2: set_a_b,D: a > b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( ( member_a_b @ C @ A2 )
       => ( ( ( member_a_b @ D @ A2 )
           => ( ( vimage3640110617408961544_b_a_b
                @ ^ [X2: probab4737552673497767871pace_a > b] : ( if_a_b @ ( member5008716543664893436ce_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = top_to6705568655694427467ce_a_b ) )
          & ( ~ ( member_a_b @ D @ A2 )
           => ( ( vimage3640110617408961544_b_a_b
                @ ^ [X2: probab4737552673497767871pace_a > b] : ( if_a_b @ ( member5008716543664893436ce_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = B2 ) ) ) )
      & ( ~ ( member_a_b @ C @ A2 )
       => ( ( ( member_a_b @ D @ A2 )
           => ( ( vimage3640110617408961544_b_a_b
                @ ^ [X2: probab4737552673497767871pace_a > b] : ( if_a_b @ ( member5008716543664893436ce_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = ( uminus4698645898373782244ce_a_b @ B2 ) ) )
          & ( ~ ( member_a_b @ D @ A2 )
           => ( ( vimage3640110617408961544_b_a_b
                @ ^ [X2: probab4737552673497767871pace_a > b] : ( if_a_b @ ( member5008716543664893436ce_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = bot_bo7395929192670431535ce_a_b ) ) ) ) ) ).

% vimage_if
thf(fact_962_vimage__if,axiom,
    ! [C: a > b,A2: set_a_b,D: a > b,B2: set_b_9060095955432656540pace_b] :
      ( ( ( member_a_b @ C @ A2 )
       => ( ( ( member_a_b @ D @ A2 )
           => ( ( vimage9190574721758969481_b_a_b
                @ ^ [X2: b > probab4737552677800996672pace_b] : ( if_a_b @ ( member1568243296417166973pace_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = top_to7723696276637437260pace_b ) )
          & ( ~ ( member_a_b @ D @ A2 )
           => ( ( vimage9190574721758969481_b_a_b
                @ ^ [X2: b > probab4737552677800996672pace_b] : ( if_a_b @ ( member1568243296417166973pace_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = B2 ) ) ) )
      & ( ~ ( member_a_b @ C @ A2 )
       => ( ( ( member_a_b @ D @ A2 )
           => ( ( vimage9190574721758969481_b_a_b
                @ ^ [X2: b > probab4737552677800996672pace_b] : ( if_a_b @ ( member1568243296417166973pace_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = ( uminus5716773519316792037pace_b @ B2 ) ) )
          & ( ~ ( member_a_b @ D @ A2 )
           => ( ( vimage9190574721758969481_b_a_b
                @ ^ [X2: b > probab4737552677800996672pace_b] : ( if_a_b @ ( member1568243296417166973pace_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = bot_bo8414056813613441328pace_b ) ) ) ) ) ).

% vimage_if
thf(fact_963_vimage__if,axiom,
    ! [C: a > b,A2: set_a_b,D: a > b,B2: set_a_5785126655188516188pace_a] :
      ( ( ( member_a_b @ C @ A2 )
       => ( ( ( member_a_b @ D @ A2 )
           => ( ( vimage8456589847784000841_a_a_b
                @ ^ [X2: a > probab4737552673497767871pace_a] : ( if_a_b @ ( member7269867574344811837pace_a @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = top_to4448726976393296908pace_a ) )
          & ( ~ ( member_a_b @ D @ A2 )
           => ( ( vimage8456589847784000841_a_a_b
                @ ^ [X2: a > probab4737552673497767871pace_a] : ( if_a_b @ ( member7269867574344811837pace_a @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = B2 ) ) ) )
      & ( ~ ( member_a_b @ C @ A2 )
       => ( ( ( member_a_b @ D @ A2 )
           => ( ( vimage8456589847784000841_a_a_b
                @ ^ [X2: a > probab4737552673497767871pace_a] : ( if_a_b @ ( member7269867574344811837pace_a @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = ( uminus2441804219072651685pace_a @ B2 ) ) )
          & ( ~ ( member_a_b @ D @ A2 )
           => ( ( vimage8456589847784000841_a_a_b
                @ ^ [X2: a > probab4737552673497767871pace_a] : ( if_a_b @ ( member7269867574344811837pace_a @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = bot_bo5139087513369300976pace_a ) ) ) ) ) ).

% vimage_if
thf(fact_964_vimage__if,axiom,
    ! [C: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,D: a > probab4737552677800996672pace_b,B2: set_a_b] :
      ( ( ( member7340901614391157822pace_b @ C @ A2 )
       => ( ( ( member7340901614391157822pace_b @ D @ A2 )
           => ( ( vimage7369165718344531018pace_b
                @ ^ [X2: a > b] : ( if_a_P5622225504318628705pace_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = top_top_set_a_b ) )
          & ( ~ ( member7340901614391157822pace_b @ D @ A2 )
           => ( ( vimage7369165718344531018pace_b
                @ ^ [X2: a > b] : ( if_a_P5622225504318628705pace_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = B2 ) ) ) )
      & ( ~ ( member7340901614391157822pace_b @ C @ A2 )
       => ( ( ( member7340901614391157822pace_b @ D @ A2 )
           => ( ( vimage7369165718344531018pace_b
                @ ^ [X2: a > b] : ( if_a_P5622225504318628705pace_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = ( uminus6731694806113723621et_a_b @ B2 ) ) )
          & ( ~ ( member7340901614391157822pace_b @ D @ A2 )
           => ( ( vimage7369165718344531018pace_b
                @ ^ [X2: a > b] : ( if_a_P5622225504318628705pace_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = bot_bot_set_a_b ) ) ) ) ) ).

% vimage_if
thf(fact_965_vimage__if,axiom,
    ! [C: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,D: probab4737552673497767871pace_a > b,B2: set_a_b] :
      ( ( ( member5008716543664893436ce_a_b @ C @ A2 )
       => ( ( ( member5008716543664893436ce_a_b @ D @ A2 )
           => ( ( vimage5036980647618266632ce_a_b
                @ ^ [X2: a > b] : ( if_Pro3290040433592364319ce_a_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = top_top_set_a_b ) )
          & ( ~ ( member5008716543664893436ce_a_b @ D @ A2 )
           => ( ( vimage5036980647618266632ce_a_b
                @ ^ [X2: a > b] : ( if_Pro3290040433592364319ce_a_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = B2 ) ) ) )
      & ( ~ ( member5008716543664893436ce_a_b @ C @ A2 )
       => ( ( ( member5008716543664893436ce_a_b @ D @ A2 )
           => ( ( vimage5036980647618266632ce_a_b
                @ ^ [X2: a > b] : ( if_Pro3290040433592364319ce_a_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = ( uminus6731694806113723621et_a_b @ B2 ) ) )
          & ( ~ ( member5008716543664893436ce_a_b @ D @ A2 )
           => ( ( vimage5036980647618266632ce_a_b
                @ ^ [X2: a > b] : ( if_Pro3290040433592364319ce_a_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = bot_bot_set_a_b ) ) ) ) ) ).

% vimage_if
thf(fact_966_vimage__if,axiom,
    ! [C: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,D: b > probab4737552677800996672pace_b,B2: set_a_b] :
      ( ( ( member1568243296417166973pace_b @ C @ A2 )
       => ( ( ( member1568243296417166973pace_b @ D @ A2 )
           => ( ( vimage1596507400370540169pace_b
                @ ^ [X2: a > b] : ( if_b_P9072939223199413664pace_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = top_top_set_a_b ) )
          & ( ~ ( member1568243296417166973pace_b @ D @ A2 )
           => ( ( vimage1596507400370540169pace_b
                @ ^ [X2: a > b] : ( if_b_P9072939223199413664pace_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = B2 ) ) ) )
      & ( ~ ( member1568243296417166973pace_b @ C @ A2 )
       => ( ( ( member1568243296417166973pace_b @ D @ A2 )
           => ( ( vimage1596507400370540169pace_b
                @ ^ [X2: a > b] : ( if_b_P9072939223199413664pace_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = ( uminus6731694806113723621et_a_b @ B2 ) ) )
          & ( ~ ( member1568243296417166973pace_b @ D @ A2 )
           => ( ( vimage1596507400370540169pace_b
                @ ^ [X2: a > b] : ( if_b_P9072939223199413664pace_b @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = bot_bot_set_a_b ) ) ) ) ) ).

% vimage_if
thf(fact_967_vimage__if,axiom,
    ! [C: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,D: a > probab4737552673497767871pace_a,B2: set_a_b] :
      ( ( ( member7269867574344811837pace_a @ C @ A2 )
       => ( ( ( member7269867574344811837pace_a @ D @ A2 )
           => ( ( vimage7298131678298185033pace_a
                @ ^ [X2: a > b] : ( if_a_P5551191464272282720pace_a @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = top_top_set_a_b ) )
          & ( ~ ( member7269867574344811837pace_a @ D @ A2 )
           => ( ( vimage7298131678298185033pace_a
                @ ^ [X2: a > b] : ( if_a_P5551191464272282720pace_a @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = B2 ) ) ) )
      & ( ~ ( member7269867574344811837pace_a @ C @ A2 )
       => ( ( ( member7269867574344811837pace_a @ D @ A2 )
           => ( ( vimage7298131678298185033pace_a
                @ ^ [X2: a > b] : ( if_a_P5551191464272282720pace_a @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = ( uminus6731694806113723621et_a_b @ B2 ) ) )
          & ( ~ ( member7269867574344811837pace_a @ D @ A2 )
           => ( ( vimage7298131678298185033pace_a
                @ ^ [X2: a > b] : ( if_a_P5551191464272282720pace_a @ ( member_a_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = bot_bot_set_a_b ) ) ) ) ) ).

% vimage_if
thf(fact_968_vimage__if,axiom,
    ! [C: a > b,A2: set_a_b,D: a > b,B2: set_Pr7742364250814120412pace_b] :
      ( ( ( member_a_b @ C @ A2 )
       => ( ( ( member_a_b @ D @ A2 )
           => ( ( vimage7679194320585949641_b_a_b
                @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( if_a_b @ ( member6667749562321684925pace_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = top_to5580905317348245644pace_b ) )
          & ( ~ ( member_a_b @ D @ A2 )
           => ( ( vimage7679194320585949641_b_a_b
                @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( if_a_b @ ( member6667749562321684925pace_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = B2 ) ) ) )
      & ( ~ ( member_a_b @ C @ A2 )
       => ( ( ( member_a_b @ D @ A2 )
           => ( ( vimage7679194320585949641_b_a_b
                @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( if_a_b @ ( member6667749562321684925pace_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = ( uminus2224264783410452005pace_b @ B2 ) ) )
          & ( ~ ( member_a_b @ D @ A2 )
           => ( ( vimage7679194320585949641_b_a_b
                @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( if_a_b @ ( member6667749562321684925pace_b @ X2 @ B2 ) @ C @ D )
                @ A2 )
              = bot_bo5050001829711205488pace_b ) ) ) ) ) ).

% vimage_if
thf(fact_969_vimageI2,axiom,
    ! [F: ( a > b ) > a > b,A: a > b,A2: set_a_b] :
      ( ( member_a_b @ ( F @ A ) @ A2 )
     => ( member_a_b @ A @ ( vimage_a_b_a_b @ F @ A2 ) ) ) ).

% vimageI2
thf(fact_970_vimageI2,axiom,
    ! [F: ( a > b ) > a > probab4737552677800996672pace_b,A: a > b,A2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ ( F @ A ) @ A2 )
     => ( member_a_b @ A @ ( vimage7369165718344531018pace_b @ F @ A2 ) ) ) ).

% vimageI2
thf(fact_971_vimageI2,axiom,
    ! [F: ( a > b ) > probab4737552673497767871pace_a > b,A: a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ ( F @ A ) @ A2 )
     => ( member_a_b @ A @ ( vimage5036980647618266632ce_a_b @ F @ A2 ) ) ) ).

% vimageI2
thf(fact_972_vimageI2,axiom,
    ! [F: ( a > b ) > b > probab4737552677800996672pace_b,A: a > b,A2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ ( F @ A ) @ A2 )
     => ( member_a_b @ A @ ( vimage1596507400370540169pace_b @ F @ A2 ) ) ) ).

% vimageI2
thf(fact_973_vimageI2,axiom,
    ! [F: ( a > b ) > a > probab4737552673497767871pace_a,A: a > b,A2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ ( F @ A ) @ A2 )
     => ( member_a_b @ A @ ( vimage7298131678298185033pace_a @ F @ A2 ) ) ) ).

% vimageI2
thf(fact_974_vimageI2,axiom,
    ! [F: ( a > probab4737552677800996672pace_b ) > a > b,A: a > probab4737552677800996672pace_b,A2: set_a_b] :
      ( ( member_a_b @ ( F @ A ) @ A2 )
     => ( member7340901614391157822pace_b @ A @ ( vimage6332008315180197450_b_a_b @ F @ A2 ) ) ) ).

% vimageI2
thf(fact_975_vimageI2,axiom,
    ! [F: ( probab4737552673497767871pace_a > b ) > a > b,A: probab4737552673497767871pace_a > b,A2: set_a_b] :
      ( ( member_a_b @ ( F @ A ) @ A2 )
     => ( member5008716543664893436ce_a_b @ A @ ( vimage3640110617408961544_b_a_b @ F @ A2 ) ) ) ).

% vimageI2
thf(fact_976_vimageI2,axiom,
    ! [F: ( b > probab4737552677800996672pace_b ) > a > b,A: b > probab4737552677800996672pace_b,A2: set_a_b] :
      ( ( member_a_b @ ( F @ A ) @ A2 )
     => ( member1568243296417166973pace_b @ A @ ( vimage9190574721758969481_b_a_b @ F @ A2 ) ) ) ).

% vimageI2
thf(fact_977_vimageI2,axiom,
    ! [F: ( a > probab4737552673497767871pace_a ) > a > b,A: a > probab4737552673497767871pace_a,A2: set_a_b] :
      ( ( member_a_b @ ( F @ A ) @ A2 )
     => ( member7269867574344811837pace_a @ A @ ( vimage8456589847784000841_a_a_b @ F @ A2 ) ) ) ).

% vimageI2
thf(fact_978_vimageI2,axiom,
    ! [F: ( a > b ) > probab4737552673497767871pace_a > probab4737552677800996672pace_b,A: a > b,A2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ ( F @ A ) @ A2 )
     => ( member_a_b @ A @ ( vimage6033027822411555273pace_b @ F @ A2 ) ) ) ).

% vimageI2
thf(fact_979_vimageE,axiom,
    ! [A: a > b,F: ( a > b ) > a > b,B2: set_a_b] :
      ( ( member_a_b @ A @ ( vimage_a_b_a_b @ F @ B2 ) )
     => ( member_a_b @ ( F @ A ) @ B2 ) ) ).

% vimageE
thf(fact_980_vimageE,axiom,
    ! [A: a > probab4737552677800996672pace_b,F: ( a > probab4737552677800996672pace_b ) > a > b,B2: set_a_b] :
      ( ( member7340901614391157822pace_b @ A @ ( vimage6332008315180197450_b_a_b @ F @ B2 ) )
     => ( member_a_b @ ( F @ A ) @ B2 ) ) ).

% vimageE
thf(fact_981_vimageE,axiom,
    ! [A: probab4737552673497767871pace_a > b,F: ( probab4737552673497767871pace_a > b ) > a > b,B2: set_a_b] :
      ( ( member5008716543664893436ce_a_b @ A @ ( vimage3640110617408961544_b_a_b @ F @ B2 ) )
     => ( member_a_b @ ( F @ A ) @ B2 ) ) ).

% vimageE
thf(fact_982_vimageE,axiom,
    ! [A: b > probab4737552677800996672pace_b,F: ( b > probab4737552677800996672pace_b ) > a > b,B2: set_a_b] :
      ( ( member1568243296417166973pace_b @ A @ ( vimage9190574721758969481_b_a_b @ F @ B2 ) )
     => ( member_a_b @ ( F @ A ) @ B2 ) ) ).

% vimageE
thf(fact_983_vimageE,axiom,
    ! [A: a > probab4737552673497767871pace_a,F: ( a > probab4737552673497767871pace_a ) > a > b,B2: set_a_b] :
      ( ( member7269867574344811837pace_a @ A @ ( vimage8456589847784000841_a_a_b @ F @ B2 ) )
     => ( member_a_b @ ( F @ A ) @ B2 ) ) ).

% vimageE
thf(fact_984_vimageE,axiom,
    ! [A: a > b,F: ( a > b ) > a > probab4737552677800996672pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( member_a_b @ A @ ( vimage7369165718344531018pace_b @ F @ B2 ) )
     => ( member7340901614391157822pace_b @ ( F @ A ) @ B2 ) ) ).

% vimageE
thf(fact_985_vimageE,axiom,
    ! [A: a > b,F: ( a > b ) > probab4737552673497767871pace_a > b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( member_a_b @ A @ ( vimage5036980647618266632ce_a_b @ F @ B2 ) )
     => ( member5008716543664893436ce_a_b @ ( F @ A ) @ B2 ) ) ).

% vimageE
thf(fact_986_vimageE,axiom,
    ! [A: a > b,F: ( a > b ) > b > probab4737552677800996672pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( member_a_b @ A @ ( vimage1596507400370540169pace_b @ F @ B2 ) )
     => ( member1568243296417166973pace_b @ ( F @ A ) @ B2 ) ) ).

% vimageE
thf(fact_987_vimageE,axiom,
    ! [A: a > b,F: ( a > b ) > a > probab4737552673497767871pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( member_a_b @ A @ ( vimage7298131678298185033pace_a @ F @ B2 ) )
     => ( member7269867574344811837pace_a @ ( F @ A ) @ B2 ) ) ).

% vimageE
thf(fact_988_vimageE,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,F: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > a > b,B2: set_a_b] :
      ( ( member6667749562321684925pace_b @ A @ ( vimage7679194320585949641_b_a_b @ F @ B2 ) )
     => ( member_a_b @ ( F @ A ) @ B2 ) ) ).

% vimageE
thf(fact_989_vimageD,axiom,
    ! [A: a > b,F: ( a > b ) > a > b,A2: set_a_b] :
      ( ( member_a_b @ A @ ( vimage_a_b_a_b @ F @ A2 ) )
     => ( member_a_b @ ( F @ A ) @ A2 ) ) ).

% vimageD
thf(fact_990_vimageD,axiom,
    ! [A: a > probab4737552677800996672pace_b,F: ( a > probab4737552677800996672pace_b ) > a > b,A2: set_a_b] :
      ( ( member7340901614391157822pace_b @ A @ ( vimage6332008315180197450_b_a_b @ F @ A2 ) )
     => ( member_a_b @ ( F @ A ) @ A2 ) ) ).

% vimageD
thf(fact_991_vimageD,axiom,
    ! [A: probab4737552673497767871pace_a > b,F: ( probab4737552673497767871pace_a > b ) > a > b,A2: set_a_b] :
      ( ( member5008716543664893436ce_a_b @ A @ ( vimage3640110617408961544_b_a_b @ F @ A2 ) )
     => ( member_a_b @ ( F @ A ) @ A2 ) ) ).

% vimageD
thf(fact_992_vimageD,axiom,
    ! [A: b > probab4737552677800996672pace_b,F: ( b > probab4737552677800996672pace_b ) > a > b,A2: set_a_b] :
      ( ( member1568243296417166973pace_b @ A @ ( vimage9190574721758969481_b_a_b @ F @ A2 ) )
     => ( member_a_b @ ( F @ A ) @ A2 ) ) ).

% vimageD
thf(fact_993_vimageD,axiom,
    ! [A: a > probab4737552673497767871pace_a,F: ( a > probab4737552673497767871pace_a ) > a > b,A2: set_a_b] :
      ( ( member7269867574344811837pace_a @ A @ ( vimage8456589847784000841_a_a_b @ F @ A2 ) )
     => ( member_a_b @ ( F @ A ) @ A2 ) ) ).

% vimageD
thf(fact_994_vimageD,axiom,
    ! [A: a > b,F: ( a > b ) > a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ( member_a_b @ A @ ( vimage7369165718344531018pace_b @ F @ A2 ) )
     => ( member7340901614391157822pace_b @ ( F @ A ) @ A2 ) ) ).

% vimageD
thf(fact_995_vimageD,axiom,
    ! [A: a > b,F: ( a > b ) > probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( member_a_b @ A @ ( vimage5036980647618266632ce_a_b @ F @ A2 ) )
     => ( member5008716543664893436ce_a_b @ ( F @ A ) @ A2 ) ) ).

% vimageD
thf(fact_996_vimageD,axiom,
    ! [A: a > b,F: ( a > b ) > b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ( member_a_b @ A @ ( vimage1596507400370540169pace_b @ F @ A2 ) )
     => ( member1568243296417166973pace_b @ ( F @ A ) @ A2 ) ) ).

% vimageD
thf(fact_997_vimageD,axiom,
    ! [A: a > b,F: ( a > b ) > a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ( member_a_b @ A @ ( vimage7298131678298185033pace_a @ F @ A2 ) )
     => ( member7269867574344811837pace_a @ ( F @ A ) @ A2 ) ) ).

% vimageD
thf(fact_998_vimageD,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,F: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > a > b,A2: set_a_b] :
      ( ( member6667749562321684925pace_b @ A @ ( vimage7679194320585949641_b_a_b @ F @ A2 ) )
     => ( member_a_b @ ( F @ A ) @ A2 ) ) ).

% vimageD
thf(fact_999_insertCI,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: set_Pr7742364250814120412pace_b,B: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ( ( ~ ( member6667749562321684925pace_b @ A @ B2 )
       => ( A = B ) )
     => ( member6667749562321684925pace_b @ A @ ( insert3418856332534486358pace_b @ B @ B2 ) ) ) ).

% insertCI
thf(fact_1000_insertCI,axiom,
    ! [A: a > probab4737552677800996672pace_b,B2: set_a_3263942136899480541pace_b,B: a > probab4737552677800996672pace_b] :
      ( ( ~ ( member7340901614391157822pace_b @ A @ B2 )
       => ( A = B ) )
     => ( member7340901614391157822pace_b @ A @ ( insert8265437699098853335pace_b @ B @ B2 ) ) ) ).

% insertCI
thf(fact_1001_insertCI,axiom,
    ! [A: probab4737552673497767871pace_a > b,B2: set_Pr8041968334489646747ce_a_b,B: probab4737552673497767871pace_a > b] :
      ( ( ~ ( member5008716543664893436ce_a_b @ A @ B2 )
       => ( A = B ) )
     => ( member5008716543664893436ce_a_b @ A @ ( insert5933252628372588949ce_a_b @ B @ B2 ) ) ) ).

% insertCI
thf(fact_1002_insertCI,axiom,
    ! [A: b > probab4737552677800996672pace_b,B2: set_b_9060095955432656540pace_b,B: b > probab4737552677800996672pace_b] :
      ( ( ~ ( member1568243296417166973pace_b @ A @ B2 )
       => ( A = B ) )
     => ( member1568243296417166973pace_b @ A @ ( insert2492779381124862486pace_b @ B @ B2 ) ) ) ).

% insertCI
thf(fact_1003_insertCI,axiom,
    ! [A: a > probab8624551251471354625pace_b,B2: set_a_5989463605624649374pace_b,B: a > probab8624551251471354625pace_b] :
      ( ( ~ ( member41169580844105599pace_b @ A @ B2 )
       => ( A = B ) )
     => ( member41169580844105599pace_b @ A @ ( insert6015648387911682840pace_b @ B @ B2 ) ) ) ).

% insertCI
thf(fact_1004_insertCI,axiom,
    ! [A: a > probab4737552673497767871pace_a,B2: set_a_5785126655188516188pace_a,B: a > probab4737552673497767871pace_a] :
      ( ( ~ ( member7269867574344811837pace_a @ A @ B2 )
       => ( A = B ) )
     => ( member7269867574344811837pace_a @ A @ ( insert8194403659052507350pace_a @ B @ B2 ) ) ) ).

% insertCI
thf(fact_1005_insertCI,axiom,
    ! [A: a > b,B2: set_a_b,B: a > b] :
      ( ( ~ ( member_a_b @ A @ B2 )
       => ( A = B ) )
     => ( member_a_b @ A @ ( insert_a_b @ B @ B2 ) ) ) ).

% insertCI
thf(fact_1006_insert__iff,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ A @ ( insert3418856332534486358pace_b @ B @ A2 ) )
      = ( ( A = B )
        | ( member6667749562321684925pace_b @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_1007_insert__iff,axiom,
    ! [A: a > probab4737552677800996672pace_b,B: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ A @ ( insert8265437699098853335pace_b @ B @ A2 ) )
      = ( ( A = B )
        | ( member7340901614391157822pace_b @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_1008_insert__iff,axiom,
    ! [A: probab4737552673497767871pace_a > b,B: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ A @ ( insert5933252628372588949ce_a_b @ B @ A2 ) )
      = ( ( A = B )
        | ( member5008716543664893436ce_a_b @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_1009_insert__iff,axiom,
    ! [A: b > probab4737552677800996672pace_b,B: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ A @ ( insert2492779381124862486pace_b @ B @ A2 ) )
      = ( ( A = B )
        | ( member1568243296417166973pace_b @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_1010_insert__iff,axiom,
    ! [A: a > probab8624551251471354625pace_b,B: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ A @ ( insert6015648387911682840pace_b @ B @ A2 ) )
      = ( ( A = B )
        | ( member41169580844105599pace_b @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_1011_insert__iff,axiom,
    ! [A: a > probab4737552673497767871pace_a,B: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ A @ ( insert8194403659052507350pace_a @ B @ A2 ) )
      = ( ( A = B )
        | ( member7269867574344811837pace_a @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_1012_insert__iff,axiom,
    ! [A: a > b,B: a > b,A2: set_a_b] :
      ( ( member_a_b @ A @ ( insert_a_b @ B @ A2 ) )
      = ( ( A = B )
        | ( member_a_b @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_1013_singletonI,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b] : ( member6667749562321684925pace_b @ A @ ( insert3418856332534486358pace_b @ A @ bot_bo5050001829711205488pace_b ) ) ).

% singletonI
thf(fact_1014_singletonI,axiom,
    ! [A: a > probab4737552677800996672pace_b] : ( member7340901614391157822pace_b @ A @ ( insert8265437699098853335pace_b @ A @ bot_bo2617902995080265329pace_b ) ) ).

% singletonI
thf(fact_1015_singletonI,axiom,
    ! [A: probab4737552673497767871pace_a > b] : ( member5008716543664893436ce_a_b @ A @ ( insert5933252628372588949ce_a_b @ A @ bot_bo7395929192670431535ce_a_b ) ) ).

% singletonI
thf(fact_1016_singletonI,axiom,
    ! [A: b > probab4737552677800996672pace_b] : ( member1568243296417166973pace_b @ A @ ( insert2492779381124862486pace_b @ A @ bot_bo8414056813613441328pace_b ) ) ).

% singletonI
thf(fact_1017_singletonI,axiom,
    ! [A: a > probab8624551251471354625pace_b] : ( member41169580844105599pace_b @ A @ ( insert6015648387911682840pace_b @ A @ bot_bo3297101184521734450pace_b ) ) ).

% singletonI
thf(fact_1018_singletonI,axiom,
    ! [A: a > probab4737552673497767871pace_a] : ( member7269867574344811837pace_a @ A @ ( insert8194403659052507350pace_a @ A @ bot_bo5139087513369300976pace_a ) ) ).

% singletonI
thf(fact_1019_singletonI,axiom,
    ! [A: a > b] : ( member_a_b @ A @ ( insert_a_b @ A @ bot_bot_set_a_b ) ) ).

% singletonI
thf(fact_1020_insert__subset,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( ord_le1280929228223758908pace_b @ ( insert3418856332534486358pace_b @ X3 @ A2 ) @ B2 )
      = ( ( member6667749562321684925pace_b @ X3 @ B2 )
        & ( ord_le1280929228223758908pace_b @ A2 @ B2 ) ) ) ).

% insert_subset
thf(fact_1021_insert__subset,axiom,
    ! [X3: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( ord_le130150003083865149pace_b @ ( insert8265437699098853335pace_b @ X3 @ A2 ) @ B2 )
      = ( ( member7340901614391157822pace_b @ X3 @ B2 )
        & ( ord_le130150003083865149pace_b @ A2 @ B2 ) ) ) ).

% insert_subset
thf(fact_1022_insert__subset,axiom,
    ! [X3: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( ord_le4908176200674031355ce_a_b @ ( insert5933252628372588949ce_a_b @ X3 @ A2 ) @ B2 )
      = ( ( member5008716543664893436ce_a_b @ X3 @ B2 )
        & ( ord_le4908176200674031355ce_a_b @ A2 @ B2 ) ) ) ).

% insert_subset
thf(fact_1023_insert__subset,axiom,
    ! [X3: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( ord_le5926303821617041148pace_b @ ( insert2492779381124862486pace_b @ X3 @ A2 ) @ B2 )
      = ( ( member1568243296417166973pace_b @ X3 @ B2 )
        & ( ord_le5926303821617041148pace_b @ A2 @ B2 ) ) ) ).

% insert_subset
thf(fact_1024_insert__subset,axiom,
    ! [X3: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( ord_le8751400619889063678pace_b @ ( insert6015648387911682840pace_b @ X3 @ A2 ) @ B2 )
      = ( ( member41169580844105599pace_b @ X3 @ B2 )
        & ( ord_le8751400619889063678pace_b @ A2 @ B2 ) ) ) ).

% insert_subset
thf(fact_1025_insert__subset,axiom,
    ! [X3: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( ord_le2651334521372900796pace_a @ ( insert8194403659052507350pace_a @ X3 @ A2 ) @ B2 )
      = ( ( member7269867574344811837pace_a @ X3 @ B2 )
        & ( ord_le2651334521372900796pace_a @ A2 @ B2 ) ) ) ).

% insert_subset
thf(fact_1026_insert__subset,axiom,
    ! [X3: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( ord_less_eq_set_a_b @ ( insert_a_b @ X3 @ A2 ) @ B2 )
      = ( ( member_a_b @ X3 @ B2 )
        & ( ord_less_eq_set_a_b @ A2 @ B2 ) ) ) ).

% insert_subset
thf(fact_1027_Int__insert__right__if1,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ A @ A2 )
     => ( ( inf_in8598470101551243374pace_b @ A2 @ ( insert3418856332534486358pace_b @ A @ B2 ) )
        = ( insert3418856332534486358pace_b @ A @ ( inf_in8598470101551243374pace_b @ A2 @ B2 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_1028_Int__insert__right__if1,axiom,
    ! [A: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ A @ A2 )
     => ( ( inf_in3860511187648227951pace_b @ A2 @ ( insert8265437699098853335pace_b @ A @ B2 ) )
        = ( insert8265437699098853335pace_b @ A @ ( inf_in3860511187648227951pace_b @ A2 @ B2 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_1029_Int__insert__right__if1,axiom,
    ! [A: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ A @ A2 )
     => ( ( inf_in8638537385238394157ce_a_b @ A2 @ ( insert5933252628372588949ce_a_b @ A @ B2 ) )
        = ( insert5933252628372588949ce_a_b @ A @ ( inf_in8638537385238394157ce_a_b @ A2 @ B2 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_1030_Int__insert__right__if1,axiom,
    ! [A: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ A @ A2 )
     => ( ( inf_in433292969326628142pace_b @ A2 @ ( insert2492779381124862486pace_b @ A @ B2 ) )
        = ( insert2492779381124862486pace_b @ A @ ( inf_in433292969326628142pace_b @ A2 @ B2 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_1031_Int__insert__right__if1,axiom,
    ! [A: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ A @ A2 )
     => ( ( inf_in6845569456361772336pace_b @ A2 @ ( insert6015648387911682840pace_b @ A @ B2 ) )
        = ( insert6015648387911682840pace_b @ A @ ( inf_in6845569456361772336pace_b @ A2 @ B2 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_1032_Int__insert__right__if1,axiom,
    ! [A: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ A @ A2 )
     => ( ( inf_in6381695705937263598pace_a @ A2 @ ( insert8194403659052507350pace_a @ A @ B2 ) )
        = ( insert8194403659052507350pace_a @ A @ ( inf_in6381695705937263598pace_a @ A2 @ B2 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_1033_Int__insert__right__if1,axiom,
    ! [A: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( member_a_b @ A @ A2 )
     => ( ( inf_inf_set_a_b @ A2 @ ( insert_a_b @ A @ B2 ) )
        = ( insert_a_b @ A @ ( inf_inf_set_a_b @ A2 @ B2 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_1034_Int__insert__right__if0,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ~ ( member6667749562321684925pace_b @ A @ A2 )
     => ( ( inf_in8598470101551243374pace_b @ A2 @ ( insert3418856332534486358pace_b @ A @ B2 ) )
        = ( inf_in8598470101551243374pace_b @ A2 @ B2 ) ) ) ).

% Int_insert_right_if0
thf(fact_1035_Int__insert__right__if0,axiom,
    ! [A: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ~ ( member7340901614391157822pace_b @ A @ A2 )
     => ( ( inf_in3860511187648227951pace_b @ A2 @ ( insert8265437699098853335pace_b @ A @ B2 ) )
        = ( inf_in3860511187648227951pace_b @ A2 @ B2 ) ) ) ).

% Int_insert_right_if0
thf(fact_1036_Int__insert__right__if0,axiom,
    ! [A: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ~ ( member5008716543664893436ce_a_b @ A @ A2 )
     => ( ( inf_in8638537385238394157ce_a_b @ A2 @ ( insert5933252628372588949ce_a_b @ A @ B2 ) )
        = ( inf_in8638537385238394157ce_a_b @ A2 @ B2 ) ) ) ).

% Int_insert_right_if0
thf(fact_1037_Int__insert__right__if0,axiom,
    ! [A: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ~ ( member1568243296417166973pace_b @ A @ A2 )
     => ( ( inf_in433292969326628142pace_b @ A2 @ ( insert2492779381124862486pace_b @ A @ B2 ) )
        = ( inf_in433292969326628142pace_b @ A2 @ B2 ) ) ) ).

% Int_insert_right_if0
thf(fact_1038_Int__insert__right__if0,axiom,
    ! [A: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ~ ( member41169580844105599pace_b @ A @ A2 )
     => ( ( inf_in6845569456361772336pace_b @ A2 @ ( insert6015648387911682840pace_b @ A @ B2 ) )
        = ( inf_in6845569456361772336pace_b @ A2 @ B2 ) ) ) ).

% Int_insert_right_if0
thf(fact_1039_Int__insert__right__if0,axiom,
    ! [A: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ~ ( member7269867574344811837pace_a @ A @ A2 )
     => ( ( inf_in6381695705937263598pace_a @ A2 @ ( insert8194403659052507350pace_a @ A @ B2 ) )
        = ( inf_in6381695705937263598pace_a @ A2 @ B2 ) ) ) ).

% Int_insert_right_if0
thf(fact_1040_Int__insert__right__if0,axiom,
    ! [A: a > b,A2: set_a_b,B2: set_a_b] :
      ( ~ ( member_a_b @ A @ A2 )
     => ( ( inf_inf_set_a_b @ A2 @ ( insert_a_b @ A @ B2 ) )
        = ( inf_inf_set_a_b @ A2 @ B2 ) ) ) ).

% Int_insert_right_if0
thf(fact_1041_Int__insert__left__if1,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,C2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ A @ C2 )
     => ( ( inf_in8598470101551243374pace_b @ ( insert3418856332534486358pace_b @ A @ B2 ) @ C2 )
        = ( insert3418856332534486358pace_b @ A @ ( inf_in8598470101551243374pace_b @ B2 @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_1042_Int__insert__left__if1,axiom,
    ! [A: a > probab4737552677800996672pace_b,C2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ A @ C2 )
     => ( ( inf_in3860511187648227951pace_b @ ( insert8265437699098853335pace_b @ A @ B2 ) @ C2 )
        = ( insert8265437699098853335pace_b @ A @ ( inf_in3860511187648227951pace_b @ B2 @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_1043_Int__insert__left__if1,axiom,
    ! [A: probab4737552673497767871pace_a > b,C2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ A @ C2 )
     => ( ( inf_in8638537385238394157ce_a_b @ ( insert5933252628372588949ce_a_b @ A @ B2 ) @ C2 )
        = ( insert5933252628372588949ce_a_b @ A @ ( inf_in8638537385238394157ce_a_b @ B2 @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_1044_Int__insert__left__if1,axiom,
    ! [A: b > probab4737552677800996672pace_b,C2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ A @ C2 )
     => ( ( inf_in433292969326628142pace_b @ ( insert2492779381124862486pace_b @ A @ B2 ) @ C2 )
        = ( insert2492779381124862486pace_b @ A @ ( inf_in433292969326628142pace_b @ B2 @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_1045_Int__insert__left__if1,axiom,
    ! [A: a > probab8624551251471354625pace_b,C2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ A @ C2 )
     => ( ( inf_in6845569456361772336pace_b @ ( insert6015648387911682840pace_b @ A @ B2 ) @ C2 )
        = ( insert6015648387911682840pace_b @ A @ ( inf_in6845569456361772336pace_b @ B2 @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_1046_Int__insert__left__if1,axiom,
    ! [A: a > probab4737552673497767871pace_a,C2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ A @ C2 )
     => ( ( inf_in6381695705937263598pace_a @ ( insert8194403659052507350pace_a @ A @ B2 ) @ C2 )
        = ( insert8194403659052507350pace_a @ A @ ( inf_in6381695705937263598pace_a @ B2 @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_1047_Int__insert__left__if1,axiom,
    ! [A: a > b,C2: set_a_b,B2: set_a_b] :
      ( ( member_a_b @ A @ C2 )
     => ( ( inf_inf_set_a_b @ ( insert_a_b @ A @ B2 ) @ C2 )
        = ( insert_a_b @ A @ ( inf_inf_set_a_b @ B2 @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_1048_Int__insert__left__if0,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,C2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ~ ( member6667749562321684925pace_b @ A @ C2 )
     => ( ( inf_in8598470101551243374pace_b @ ( insert3418856332534486358pace_b @ A @ B2 ) @ C2 )
        = ( inf_in8598470101551243374pace_b @ B2 @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_1049_Int__insert__left__if0,axiom,
    ! [A: a > probab4737552677800996672pace_b,C2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ~ ( member7340901614391157822pace_b @ A @ C2 )
     => ( ( inf_in3860511187648227951pace_b @ ( insert8265437699098853335pace_b @ A @ B2 ) @ C2 )
        = ( inf_in3860511187648227951pace_b @ B2 @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_1050_Int__insert__left__if0,axiom,
    ! [A: probab4737552673497767871pace_a > b,C2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ~ ( member5008716543664893436ce_a_b @ A @ C2 )
     => ( ( inf_in8638537385238394157ce_a_b @ ( insert5933252628372588949ce_a_b @ A @ B2 ) @ C2 )
        = ( inf_in8638537385238394157ce_a_b @ B2 @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_1051_Int__insert__left__if0,axiom,
    ! [A: b > probab4737552677800996672pace_b,C2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ~ ( member1568243296417166973pace_b @ A @ C2 )
     => ( ( inf_in433292969326628142pace_b @ ( insert2492779381124862486pace_b @ A @ B2 ) @ C2 )
        = ( inf_in433292969326628142pace_b @ B2 @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_1052_Int__insert__left__if0,axiom,
    ! [A: a > probab8624551251471354625pace_b,C2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ~ ( member41169580844105599pace_b @ A @ C2 )
     => ( ( inf_in6845569456361772336pace_b @ ( insert6015648387911682840pace_b @ A @ B2 ) @ C2 )
        = ( inf_in6845569456361772336pace_b @ B2 @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_1053_Int__insert__left__if0,axiom,
    ! [A: a > probab4737552673497767871pace_a,C2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ~ ( member7269867574344811837pace_a @ A @ C2 )
     => ( ( inf_in6381695705937263598pace_a @ ( insert8194403659052507350pace_a @ A @ B2 ) @ C2 )
        = ( inf_in6381695705937263598pace_a @ B2 @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_1054_Int__insert__left__if0,axiom,
    ! [A: a > b,C2: set_a_b,B2: set_a_b] :
      ( ~ ( member_a_b @ A @ C2 )
     => ( ( inf_inf_set_a_b @ ( insert_a_b @ A @ B2 ) @ C2 )
        = ( inf_inf_set_a_b @ B2 @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_1055_Pi__split__insert__domain,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,I3: probab4737552673497767871pace_a,I2: set_Pr8456636223741192351pace_a,X: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ ( insert8086323747391171983pace_a @ I3 @ I2 ) @ X ) )
      = ( ( member6667749562321684925pace_b @ X3 @ ( pi_Pro4287250843231025420pace_b @ I2 @ X ) )
        & ( member6485455078948787817pace_b @ ( X3 @ I3 ) @ ( X @ I3 ) ) ) ) ).

% Pi_split_insert_domain
thf(fact_1056_Pi__split__insert__domain,axiom,
    ! [X3: a > probab4737552677800996672pace_b,I3: a,I2: set_a,X: a > set_Pr8527670263787538336pace_b] :
      ( ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ ( insert_a @ I3 @ I2 ) @ X ) )
      = ( ( member7340901614391157822pace_b @ X3 @ ( pi_a_P1132609506902963085pace_b @ I2 @ X ) )
        & ( member6485455078948787817pace_b @ ( X3 @ I3 ) @ ( X @ I3 ) ) ) ) ).

% Pi_split_insert_domain
thf(fact_1057_Pi__split__insert__domain,axiom,
    ! [X3: probab4737552673497767871pace_a > b,I3: probab4737552673497767871pace_a,I2: set_Pr8456636223741192351pace_a,X: probab4737552673497767871pace_a > set_b] :
      ( ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ ( insert8086323747391171983pace_a @ I3 @ I2 ) @ X ) )
      = ( ( member5008716543664893436ce_a_b @ X3 @ ( pi_Pro8257876842545441995ce_a_b @ I2 @ X ) )
        & ( member_b @ ( X3 @ I3 ) @ ( X @ I3 ) ) ) ) ).

% Pi_split_insert_domain
thf(fact_1058_Pi__split__insert__domain,axiom,
    ! [X3: b > probab4737552677800996672pace_b,I3: b,I2: set_b,X: b > set_Pr8527670263787538336pace_b] :
      ( ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ ( insert_b @ I3 @ I2 ) @ X ) )
      = ( ( member1568243296417166973pace_b @ X3 @ ( pi_b_P4583323225783748044pace_b @ I2 @ X ) )
        & ( member6485455078948787817pace_b @ ( X3 @ I3 ) @ ( X @ I3 ) ) ) ) ).

% Pi_split_insert_domain
thf(fact_1059_Pi__split__insert__domain,axiom,
    ! [X3: a > probab8624551251471354625pace_b,I3: a,I2: set_a,X: a > set_Pr2974436765678502625pace_b] :
      ( ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ ( insert_a @ I3 @ I2 ) @ X ) )
      = ( ( member41169580844105599pace_b @ X3 @ ( pi_a_P2860934570321248078pace_b @ I2 @ X ) )
        & ( member7462078926031725098pace_b @ ( X3 @ I3 ) @ ( X @ I3 ) ) ) ) ).

% Pi_split_insert_domain
thf(fact_1060_Pi__split__insert__domain,axiom,
    ! [X3: a > probab4737552673497767871pace_a,I3: a,I2: set_a,X: a > set_Pr8456636223741192351pace_a] :
      ( ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ ( insert_a @ I3 @ I2 ) @ X ) )
      = ( ( member7269867574344811837pace_a @ X3 @ ( pi_a_P1132609502599734284pace_a @ I2 @ X ) )
        & ( member6485455074645559016pace_a @ ( X3 @ I3 ) @ ( X @ I3 ) ) ) ) ).

% Pi_split_insert_domain
thf(fact_1061_Pi__split__insert__domain,axiom,
    ! [X3: a > b,I3: a,I2: set_a,X: a > set_b] :
      ( ( member_a_b @ X3 @ ( pi_a_b @ ( insert_a @ I3 @ I2 ) @ X ) )
      = ( ( member_a_b @ X3 @ ( pi_a_b @ I2 @ X ) )
        & ( member_b @ ( X3 @ I3 ) @ ( X @ I3 ) ) ) ) ).

% Pi_split_insert_domain
thf(fact_1062_insert__disjoint_I1_J,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( ( inf_in8598470101551243374pace_b @ ( insert3418856332534486358pace_b @ A @ A2 ) @ B2 )
        = bot_bo5050001829711205488pace_b )
      = ( ~ ( member6667749562321684925pace_b @ A @ B2 )
        & ( ( inf_in8598470101551243374pace_b @ A2 @ B2 )
          = bot_bo5050001829711205488pace_b ) ) ) ).

% insert_disjoint(1)
thf(fact_1063_insert__disjoint_I1_J,axiom,
    ! [A: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( ( inf_in3860511187648227951pace_b @ ( insert8265437699098853335pace_b @ A @ A2 ) @ B2 )
        = bot_bo2617902995080265329pace_b )
      = ( ~ ( member7340901614391157822pace_b @ A @ B2 )
        & ( ( inf_in3860511187648227951pace_b @ A2 @ B2 )
          = bot_bo2617902995080265329pace_b ) ) ) ).

% insert_disjoint(1)
thf(fact_1064_insert__disjoint_I1_J,axiom,
    ! [A: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( ( inf_in8638537385238394157ce_a_b @ ( insert5933252628372588949ce_a_b @ A @ A2 ) @ B2 )
        = bot_bo7395929192670431535ce_a_b )
      = ( ~ ( member5008716543664893436ce_a_b @ A @ B2 )
        & ( ( inf_in8638537385238394157ce_a_b @ A2 @ B2 )
          = bot_bo7395929192670431535ce_a_b ) ) ) ).

% insert_disjoint(1)
thf(fact_1065_insert__disjoint_I1_J,axiom,
    ! [A: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( ( inf_in433292969326628142pace_b @ ( insert2492779381124862486pace_b @ A @ A2 ) @ B2 )
        = bot_bo8414056813613441328pace_b )
      = ( ~ ( member1568243296417166973pace_b @ A @ B2 )
        & ( ( inf_in433292969326628142pace_b @ A2 @ B2 )
          = bot_bo8414056813613441328pace_b ) ) ) ).

% insert_disjoint(1)
thf(fact_1066_insert__disjoint_I1_J,axiom,
    ! [A: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( ( inf_in6845569456361772336pace_b @ ( insert6015648387911682840pace_b @ A @ A2 ) @ B2 )
        = bot_bo3297101184521734450pace_b )
      = ( ~ ( member41169580844105599pace_b @ A @ B2 )
        & ( ( inf_in6845569456361772336pace_b @ A2 @ B2 )
          = bot_bo3297101184521734450pace_b ) ) ) ).

% insert_disjoint(1)
thf(fact_1067_insert__disjoint_I1_J,axiom,
    ! [A: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( ( inf_in6381695705937263598pace_a @ ( insert8194403659052507350pace_a @ A @ A2 ) @ B2 )
        = bot_bo5139087513369300976pace_a )
      = ( ~ ( member7269867574344811837pace_a @ A @ B2 )
        & ( ( inf_in6381695705937263598pace_a @ A2 @ B2 )
          = bot_bo5139087513369300976pace_a ) ) ) ).

% insert_disjoint(1)
thf(fact_1068_insert__disjoint_I1_J,axiom,
    ! [A: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( ( inf_inf_set_a_b @ ( insert_a_b @ A @ A2 ) @ B2 )
        = bot_bot_set_a_b )
      = ( ~ ( member_a_b @ A @ B2 )
        & ( ( inf_inf_set_a_b @ A2 @ B2 )
          = bot_bot_set_a_b ) ) ) ).

% insert_disjoint(1)
thf(fact_1069_insert__disjoint_I2_J,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( bot_bo5050001829711205488pace_b
        = ( inf_in8598470101551243374pace_b @ ( insert3418856332534486358pace_b @ A @ A2 ) @ B2 ) )
      = ( ~ ( member6667749562321684925pace_b @ A @ B2 )
        & ( bot_bo5050001829711205488pace_b
          = ( inf_in8598470101551243374pace_b @ A2 @ B2 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_1070_insert__disjoint_I2_J,axiom,
    ! [A: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( bot_bo2617902995080265329pace_b
        = ( inf_in3860511187648227951pace_b @ ( insert8265437699098853335pace_b @ A @ A2 ) @ B2 ) )
      = ( ~ ( member7340901614391157822pace_b @ A @ B2 )
        & ( bot_bo2617902995080265329pace_b
          = ( inf_in3860511187648227951pace_b @ A2 @ B2 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_1071_insert__disjoint_I2_J,axiom,
    ! [A: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( bot_bo7395929192670431535ce_a_b
        = ( inf_in8638537385238394157ce_a_b @ ( insert5933252628372588949ce_a_b @ A @ A2 ) @ B2 ) )
      = ( ~ ( member5008716543664893436ce_a_b @ A @ B2 )
        & ( bot_bo7395929192670431535ce_a_b
          = ( inf_in8638537385238394157ce_a_b @ A2 @ B2 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_1072_insert__disjoint_I2_J,axiom,
    ! [A: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( bot_bo8414056813613441328pace_b
        = ( inf_in433292969326628142pace_b @ ( insert2492779381124862486pace_b @ A @ A2 ) @ B2 ) )
      = ( ~ ( member1568243296417166973pace_b @ A @ B2 )
        & ( bot_bo8414056813613441328pace_b
          = ( inf_in433292969326628142pace_b @ A2 @ B2 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_1073_insert__disjoint_I2_J,axiom,
    ! [A: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( bot_bo3297101184521734450pace_b
        = ( inf_in6845569456361772336pace_b @ ( insert6015648387911682840pace_b @ A @ A2 ) @ B2 ) )
      = ( ~ ( member41169580844105599pace_b @ A @ B2 )
        & ( bot_bo3297101184521734450pace_b
          = ( inf_in6845569456361772336pace_b @ A2 @ B2 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_1074_insert__disjoint_I2_J,axiom,
    ! [A: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( bot_bo5139087513369300976pace_a
        = ( inf_in6381695705937263598pace_a @ ( insert8194403659052507350pace_a @ A @ A2 ) @ B2 ) )
      = ( ~ ( member7269867574344811837pace_a @ A @ B2 )
        & ( bot_bo5139087513369300976pace_a
          = ( inf_in6381695705937263598pace_a @ A2 @ B2 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_1075_insert__disjoint_I2_J,axiom,
    ! [A: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( bot_bot_set_a_b
        = ( inf_inf_set_a_b @ ( insert_a_b @ A @ A2 ) @ B2 ) )
      = ( ~ ( member_a_b @ A @ B2 )
        & ( bot_bot_set_a_b
          = ( inf_inf_set_a_b @ A2 @ B2 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_1076_disjoint__insert_I1_J,axiom,
    ! [B2: set_Pr7742364250814120412pace_b,A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b] :
      ( ( ( inf_in8598470101551243374pace_b @ B2 @ ( insert3418856332534486358pace_b @ A @ A2 ) )
        = bot_bo5050001829711205488pace_b )
      = ( ~ ( member6667749562321684925pace_b @ A @ B2 )
        & ( ( inf_in8598470101551243374pace_b @ B2 @ A2 )
          = bot_bo5050001829711205488pace_b ) ) ) ).

% disjoint_insert(1)
thf(fact_1077_disjoint__insert_I1_J,axiom,
    ! [B2: set_a_3263942136899480541pace_b,A: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ( ( inf_in3860511187648227951pace_b @ B2 @ ( insert8265437699098853335pace_b @ A @ A2 ) )
        = bot_bo2617902995080265329pace_b )
      = ( ~ ( member7340901614391157822pace_b @ A @ B2 )
        & ( ( inf_in3860511187648227951pace_b @ B2 @ A2 )
          = bot_bo2617902995080265329pace_b ) ) ) ).

% disjoint_insert(1)
thf(fact_1078_disjoint__insert_I1_J,axiom,
    ! [B2: set_Pr8041968334489646747ce_a_b,A: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( ( inf_in8638537385238394157ce_a_b @ B2 @ ( insert5933252628372588949ce_a_b @ A @ A2 ) )
        = bot_bo7395929192670431535ce_a_b )
      = ( ~ ( member5008716543664893436ce_a_b @ A @ B2 )
        & ( ( inf_in8638537385238394157ce_a_b @ B2 @ A2 )
          = bot_bo7395929192670431535ce_a_b ) ) ) ).

% disjoint_insert(1)
thf(fact_1079_disjoint__insert_I1_J,axiom,
    ! [B2: set_b_9060095955432656540pace_b,A: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ( ( inf_in433292969326628142pace_b @ B2 @ ( insert2492779381124862486pace_b @ A @ A2 ) )
        = bot_bo8414056813613441328pace_b )
      = ( ~ ( member1568243296417166973pace_b @ A @ B2 )
        & ( ( inf_in433292969326628142pace_b @ B2 @ A2 )
          = bot_bo8414056813613441328pace_b ) ) ) ).

% disjoint_insert(1)
thf(fact_1080_disjoint__insert_I1_J,axiom,
    ! [B2: set_a_5989463605624649374pace_b,A: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b] :
      ( ( ( inf_in6845569456361772336pace_b @ B2 @ ( insert6015648387911682840pace_b @ A @ A2 ) )
        = bot_bo3297101184521734450pace_b )
      = ( ~ ( member41169580844105599pace_b @ A @ B2 )
        & ( ( inf_in6845569456361772336pace_b @ B2 @ A2 )
          = bot_bo3297101184521734450pace_b ) ) ) ).

% disjoint_insert(1)
thf(fact_1081_disjoint__insert_I1_J,axiom,
    ! [B2: set_a_5785126655188516188pace_a,A: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ( ( inf_in6381695705937263598pace_a @ B2 @ ( insert8194403659052507350pace_a @ A @ A2 ) )
        = bot_bo5139087513369300976pace_a )
      = ( ~ ( member7269867574344811837pace_a @ A @ B2 )
        & ( ( inf_in6381695705937263598pace_a @ B2 @ A2 )
          = bot_bo5139087513369300976pace_a ) ) ) ).

% disjoint_insert(1)
thf(fact_1082_disjoint__insert_I1_J,axiom,
    ! [B2: set_a_b,A: a > b,A2: set_a_b] :
      ( ( ( inf_inf_set_a_b @ B2 @ ( insert_a_b @ A @ A2 ) )
        = bot_bot_set_a_b )
      = ( ~ ( member_a_b @ A @ B2 )
        & ( ( inf_inf_set_a_b @ B2 @ A2 )
          = bot_bot_set_a_b ) ) ) ).

% disjoint_insert(1)
thf(fact_1083_disjoint__insert_I2_J,axiom,
    ! [A2: set_Pr7742364250814120412pace_b,B: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( bot_bo5050001829711205488pace_b
        = ( inf_in8598470101551243374pace_b @ A2 @ ( insert3418856332534486358pace_b @ B @ B2 ) ) )
      = ( ~ ( member6667749562321684925pace_b @ B @ A2 )
        & ( bot_bo5050001829711205488pace_b
          = ( inf_in8598470101551243374pace_b @ A2 @ B2 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_1084_disjoint__insert_I2_J,axiom,
    ! [A2: set_a_3263942136899480541pace_b,B: a > probab4737552677800996672pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( bot_bo2617902995080265329pace_b
        = ( inf_in3860511187648227951pace_b @ A2 @ ( insert8265437699098853335pace_b @ B @ B2 ) ) )
      = ( ~ ( member7340901614391157822pace_b @ B @ A2 )
        & ( bot_bo2617902995080265329pace_b
          = ( inf_in3860511187648227951pace_b @ A2 @ B2 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_1085_disjoint__insert_I2_J,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,B: probab4737552673497767871pace_a > b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( bot_bo7395929192670431535ce_a_b
        = ( inf_in8638537385238394157ce_a_b @ A2 @ ( insert5933252628372588949ce_a_b @ B @ B2 ) ) )
      = ( ~ ( member5008716543664893436ce_a_b @ B @ A2 )
        & ( bot_bo7395929192670431535ce_a_b
          = ( inf_in8638537385238394157ce_a_b @ A2 @ B2 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_1086_disjoint__insert_I2_J,axiom,
    ! [A2: set_b_9060095955432656540pace_b,B: b > probab4737552677800996672pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( bot_bo8414056813613441328pace_b
        = ( inf_in433292969326628142pace_b @ A2 @ ( insert2492779381124862486pace_b @ B @ B2 ) ) )
      = ( ~ ( member1568243296417166973pace_b @ B @ A2 )
        & ( bot_bo8414056813613441328pace_b
          = ( inf_in433292969326628142pace_b @ A2 @ B2 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_1087_disjoint__insert_I2_J,axiom,
    ! [A2: set_a_5989463605624649374pace_b,B: a > probab8624551251471354625pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( bot_bo3297101184521734450pace_b
        = ( inf_in6845569456361772336pace_b @ A2 @ ( insert6015648387911682840pace_b @ B @ B2 ) ) )
      = ( ~ ( member41169580844105599pace_b @ B @ A2 )
        & ( bot_bo3297101184521734450pace_b
          = ( inf_in6845569456361772336pace_b @ A2 @ B2 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_1088_disjoint__insert_I2_J,axiom,
    ! [A2: set_a_5785126655188516188pace_a,B: a > probab4737552673497767871pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( bot_bo5139087513369300976pace_a
        = ( inf_in6381695705937263598pace_a @ A2 @ ( insert8194403659052507350pace_a @ B @ B2 ) ) )
      = ( ~ ( member7269867574344811837pace_a @ B @ A2 )
        & ( bot_bo5139087513369300976pace_a
          = ( inf_in6381695705937263598pace_a @ A2 @ B2 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_1089_disjoint__insert_I2_J,axiom,
    ! [A2: set_a_b,B: a > b,B2: set_a_b] :
      ( ( bot_bot_set_a_b
        = ( inf_inf_set_a_b @ A2 @ ( insert_a_b @ B @ B2 ) ) )
      = ( ~ ( member_a_b @ B @ A2 )
        & ( bot_bot_set_a_b
          = ( inf_inf_set_a_b @ A2 @ B2 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_1090_subset__Compl__singleton,axiom,
    ! [A2: set_Pr7742364250814120412pace_b,B: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ( ( ord_le1280929228223758908pace_b @ A2 @ ( uminus2224264783410452005pace_b @ ( insert3418856332534486358pace_b @ B @ bot_bo5050001829711205488pace_b ) ) )
      = ( ~ ( member6667749562321684925pace_b @ B @ A2 ) ) ) ).

% subset_Compl_singleton
thf(fact_1091_subset__Compl__singleton,axiom,
    ! [A2: set_a_3263942136899480541pace_b,B: a > probab4737552677800996672pace_b] :
      ( ( ord_le130150003083865149pace_b @ A2 @ ( uminus9143991737638391846pace_b @ ( insert8265437699098853335pace_b @ B @ bot_bo2617902995080265329pace_b ) ) )
      = ( ~ ( member7340901614391157822pace_b @ B @ A2 ) ) ) ).

% subset_Compl_singleton
thf(fact_1092_subset__Compl__singleton,axiom,
    ! [A2: set_Pr8041968334489646747ce_a_b,B: probab4737552673497767871pace_a > b] :
      ( ( ord_le4908176200674031355ce_a_b @ A2 @ ( uminus4698645898373782244ce_a_b @ ( insert5933252628372588949ce_a_b @ B @ bot_bo7395929192670431535ce_a_b ) ) )
      = ( ~ ( member5008716543664893436ce_a_b @ B @ A2 ) ) ) ).

% subset_Compl_singleton
thf(fact_1093_subset__Compl__singleton,axiom,
    ! [A2: set_b_9060095955432656540pace_b,B: b > probab4737552677800996672pace_b] :
      ( ( ord_le5926303821617041148pace_b @ A2 @ ( uminus5716773519316792037pace_b @ ( insert2492779381124862486pace_b @ B @ bot_bo8414056813613441328pace_b ) ) )
      = ( ~ ( member1568243296417166973pace_b @ B @ A2 ) ) ) ).

% subset_Compl_singleton
thf(fact_1094_subset__Compl__singleton,axiom,
    ! [A2: set_a_5989463605624649374pace_b,B: a > probab8624551251471354625pace_b] :
      ( ( ord_le8751400619889063678pace_b @ A2 @ ( uminus471364138220980967pace_b @ ( insert6015648387911682840pace_b @ B @ bot_bo3297101184521734450pace_b ) ) )
      = ( ~ ( member41169580844105599pace_b @ B @ A2 ) ) ) ).

% subset_Compl_singleton
thf(fact_1095_subset__Compl__singleton,axiom,
    ! [A2: set_a_5785126655188516188pace_a,B: a > probab4737552673497767871pace_a] :
      ( ( ord_le2651334521372900796pace_a @ A2 @ ( uminus2441804219072651685pace_a @ ( insert8194403659052507350pace_a @ B @ bot_bo5139087513369300976pace_a ) ) )
      = ( ~ ( member7269867574344811837pace_a @ B @ A2 ) ) ) ).

% subset_Compl_singleton
thf(fact_1096_subset__Compl__singleton,axiom,
    ! [A2: set_a_b,B: a > b] :
      ( ( ord_less_eq_set_a_b @ A2 @ ( uminus6731694806113723621et_a_b @ ( insert_a_b @ B @ bot_bot_set_a_b ) ) )
      = ( ~ ( member_a_b @ B @ A2 ) ) ) ).

% subset_Compl_singleton
thf(fact_1097_subset__insert,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ~ ( member6667749562321684925pace_b @ X3 @ A2 )
     => ( ( ord_le1280929228223758908pace_b @ A2 @ ( insert3418856332534486358pace_b @ X3 @ B2 ) )
        = ( ord_le1280929228223758908pace_b @ A2 @ B2 ) ) ) ).

% subset_insert
thf(fact_1098_subset__insert,axiom,
    ! [X3: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ~ ( member7340901614391157822pace_b @ X3 @ A2 )
     => ( ( ord_le130150003083865149pace_b @ A2 @ ( insert8265437699098853335pace_b @ X3 @ B2 ) )
        = ( ord_le130150003083865149pace_b @ A2 @ B2 ) ) ) ).

% subset_insert
thf(fact_1099_subset__insert,axiom,
    ! [X3: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ~ ( member5008716543664893436ce_a_b @ X3 @ A2 )
     => ( ( ord_le4908176200674031355ce_a_b @ A2 @ ( insert5933252628372588949ce_a_b @ X3 @ B2 ) )
        = ( ord_le4908176200674031355ce_a_b @ A2 @ B2 ) ) ) ).

% subset_insert
thf(fact_1100_subset__insert,axiom,
    ! [X3: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ~ ( member1568243296417166973pace_b @ X3 @ A2 )
     => ( ( ord_le5926303821617041148pace_b @ A2 @ ( insert2492779381124862486pace_b @ X3 @ B2 ) )
        = ( ord_le5926303821617041148pace_b @ A2 @ B2 ) ) ) ).

% subset_insert
thf(fact_1101_subset__insert,axiom,
    ! [X3: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ~ ( member41169580844105599pace_b @ X3 @ A2 )
     => ( ( ord_le8751400619889063678pace_b @ A2 @ ( insert6015648387911682840pace_b @ X3 @ B2 ) )
        = ( ord_le8751400619889063678pace_b @ A2 @ B2 ) ) ) ).

% subset_insert
thf(fact_1102_subset__insert,axiom,
    ! [X3: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ~ ( member7269867574344811837pace_a @ X3 @ A2 )
     => ( ( ord_le2651334521372900796pace_a @ A2 @ ( insert8194403659052507350pace_a @ X3 @ B2 ) )
        = ( ord_le2651334521372900796pace_a @ A2 @ B2 ) ) ) ).

% subset_insert
thf(fact_1103_subset__insert,axiom,
    ! [X3: a > b,A2: set_a_b,B2: set_a_b] :
      ( ~ ( member_a_b @ X3 @ A2 )
     => ( ( ord_less_eq_set_a_b @ A2 @ ( insert_a_b @ X3 @ B2 ) )
        = ( ord_less_eq_set_a_b @ A2 @ B2 ) ) ) ).

% subset_insert
thf(fact_1104_singleton__iff,axiom,
    ! [B: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ( ( member6667749562321684925pace_b @ B @ ( insert3418856332534486358pace_b @ A @ bot_bo5050001829711205488pace_b ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_1105_singleton__iff,axiom,
    ! [B: a > probab4737552677800996672pace_b,A: a > probab4737552677800996672pace_b] :
      ( ( member7340901614391157822pace_b @ B @ ( insert8265437699098853335pace_b @ A @ bot_bo2617902995080265329pace_b ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_1106_singleton__iff,axiom,
    ! [B: probab4737552673497767871pace_a > b,A: probab4737552673497767871pace_a > b] :
      ( ( member5008716543664893436ce_a_b @ B @ ( insert5933252628372588949ce_a_b @ A @ bot_bo7395929192670431535ce_a_b ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_1107_singleton__iff,axiom,
    ! [B: b > probab4737552677800996672pace_b,A: b > probab4737552677800996672pace_b] :
      ( ( member1568243296417166973pace_b @ B @ ( insert2492779381124862486pace_b @ A @ bot_bo8414056813613441328pace_b ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_1108_singleton__iff,axiom,
    ! [B: a > probab8624551251471354625pace_b,A: a > probab8624551251471354625pace_b] :
      ( ( member41169580844105599pace_b @ B @ ( insert6015648387911682840pace_b @ A @ bot_bo3297101184521734450pace_b ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_1109_singleton__iff,axiom,
    ! [B: a > probab4737552673497767871pace_a,A: a > probab4737552673497767871pace_a] :
      ( ( member7269867574344811837pace_a @ B @ ( insert8194403659052507350pace_a @ A @ bot_bo5139087513369300976pace_a ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_1110_singleton__iff,axiom,
    ! [B: a > b,A: a > b] :
      ( ( member_a_b @ B @ ( insert_a_b @ A @ bot_bot_set_a_b ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_1111_singletonD,axiom,
    ! [B: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ( ( member6667749562321684925pace_b @ B @ ( insert3418856332534486358pace_b @ A @ bot_bo5050001829711205488pace_b ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_1112_singletonD,axiom,
    ! [B: a > probab4737552677800996672pace_b,A: a > probab4737552677800996672pace_b] :
      ( ( member7340901614391157822pace_b @ B @ ( insert8265437699098853335pace_b @ A @ bot_bo2617902995080265329pace_b ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_1113_singletonD,axiom,
    ! [B: probab4737552673497767871pace_a > b,A: probab4737552673497767871pace_a > b] :
      ( ( member5008716543664893436ce_a_b @ B @ ( insert5933252628372588949ce_a_b @ A @ bot_bo7395929192670431535ce_a_b ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_1114_singletonD,axiom,
    ! [B: b > probab4737552677800996672pace_b,A: b > probab4737552677800996672pace_b] :
      ( ( member1568243296417166973pace_b @ B @ ( insert2492779381124862486pace_b @ A @ bot_bo8414056813613441328pace_b ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_1115_singletonD,axiom,
    ! [B: a > probab8624551251471354625pace_b,A: a > probab8624551251471354625pace_b] :
      ( ( member41169580844105599pace_b @ B @ ( insert6015648387911682840pace_b @ A @ bot_bo3297101184521734450pace_b ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_1116_singletonD,axiom,
    ! [B: a > probab4737552673497767871pace_a,A: a > probab4737552673497767871pace_a] :
      ( ( member7269867574344811837pace_a @ B @ ( insert8194403659052507350pace_a @ A @ bot_bo5139087513369300976pace_a ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_1117_singletonD,axiom,
    ! [B: a > b,A: a > b] :
      ( ( member_a_b @ B @ ( insert_a_b @ A @ bot_bot_set_a_b ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_1118_Int__insert__left,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,C2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( ( member6667749562321684925pace_b @ A @ C2 )
       => ( ( inf_in8598470101551243374pace_b @ ( insert3418856332534486358pace_b @ A @ B2 ) @ C2 )
          = ( insert3418856332534486358pace_b @ A @ ( inf_in8598470101551243374pace_b @ B2 @ C2 ) ) ) )
      & ( ~ ( member6667749562321684925pace_b @ A @ C2 )
       => ( ( inf_in8598470101551243374pace_b @ ( insert3418856332534486358pace_b @ A @ B2 ) @ C2 )
          = ( inf_in8598470101551243374pace_b @ B2 @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_1119_Int__insert__left,axiom,
    ! [A: a > probab4737552677800996672pace_b,C2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( ( member7340901614391157822pace_b @ A @ C2 )
       => ( ( inf_in3860511187648227951pace_b @ ( insert8265437699098853335pace_b @ A @ B2 ) @ C2 )
          = ( insert8265437699098853335pace_b @ A @ ( inf_in3860511187648227951pace_b @ B2 @ C2 ) ) ) )
      & ( ~ ( member7340901614391157822pace_b @ A @ C2 )
       => ( ( inf_in3860511187648227951pace_b @ ( insert8265437699098853335pace_b @ A @ B2 ) @ C2 )
          = ( inf_in3860511187648227951pace_b @ B2 @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_1120_Int__insert__left,axiom,
    ! [A: probab4737552673497767871pace_a > b,C2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( ( member5008716543664893436ce_a_b @ A @ C2 )
       => ( ( inf_in8638537385238394157ce_a_b @ ( insert5933252628372588949ce_a_b @ A @ B2 ) @ C2 )
          = ( insert5933252628372588949ce_a_b @ A @ ( inf_in8638537385238394157ce_a_b @ B2 @ C2 ) ) ) )
      & ( ~ ( member5008716543664893436ce_a_b @ A @ C2 )
       => ( ( inf_in8638537385238394157ce_a_b @ ( insert5933252628372588949ce_a_b @ A @ B2 ) @ C2 )
          = ( inf_in8638537385238394157ce_a_b @ B2 @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_1121_Int__insert__left,axiom,
    ! [A: b > probab4737552677800996672pace_b,C2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( ( member1568243296417166973pace_b @ A @ C2 )
       => ( ( inf_in433292969326628142pace_b @ ( insert2492779381124862486pace_b @ A @ B2 ) @ C2 )
          = ( insert2492779381124862486pace_b @ A @ ( inf_in433292969326628142pace_b @ B2 @ C2 ) ) ) )
      & ( ~ ( member1568243296417166973pace_b @ A @ C2 )
       => ( ( inf_in433292969326628142pace_b @ ( insert2492779381124862486pace_b @ A @ B2 ) @ C2 )
          = ( inf_in433292969326628142pace_b @ B2 @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_1122_Int__insert__left,axiom,
    ! [A: a > probab8624551251471354625pace_b,C2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( ( member41169580844105599pace_b @ A @ C2 )
       => ( ( inf_in6845569456361772336pace_b @ ( insert6015648387911682840pace_b @ A @ B2 ) @ C2 )
          = ( insert6015648387911682840pace_b @ A @ ( inf_in6845569456361772336pace_b @ B2 @ C2 ) ) ) )
      & ( ~ ( member41169580844105599pace_b @ A @ C2 )
       => ( ( inf_in6845569456361772336pace_b @ ( insert6015648387911682840pace_b @ A @ B2 ) @ C2 )
          = ( inf_in6845569456361772336pace_b @ B2 @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_1123_Int__insert__left,axiom,
    ! [A: a > probab4737552673497767871pace_a,C2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( ( member7269867574344811837pace_a @ A @ C2 )
       => ( ( inf_in6381695705937263598pace_a @ ( insert8194403659052507350pace_a @ A @ B2 ) @ C2 )
          = ( insert8194403659052507350pace_a @ A @ ( inf_in6381695705937263598pace_a @ B2 @ C2 ) ) ) )
      & ( ~ ( member7269867574344811837pace_a @ A @ C2 )
       => ( ( inf_in6381695705937263598pace_a @ ( insert8194403659052507350pace_a @ A @ B2 ) @ C2 )
          = ( inf_in6381695705937263598pace_a @ B2 @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_1124_Int__insert__left,axiom,
    ! [A: a > b,C2: set_a_b,B2: set_a_b] :
      ( ( ( member_a_b @ A @ C2 )
       => ( ( inf_inf_set_a_b @ ( insert_a_b @ A @ B2 ) @ C2 )
          = ( insert_a_b @ A @ ( inf_inf_set_a_b @ B2 @ C2 ) ) ) )
      & ( ~ ( member_a_b @ A @ C2 )
       => ( ( inf_inf_set_a_b @ ( insert_a_b @ A @ B2 ) @ C2 )
          = ( inf_inf_set_a_b @ B2 @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_1125_Int__insert__right,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ( ( member6667749562321684925pace_b @ A @ A2 )
       => ( ( inf_in8598470101551243374pace_b @ A2 @ ( insert3418856332534486358pace_b @ A @ B2 ) )
          = ( insert3418856332534486358pace_b @ A @ ( inf_in8598470101551243374pace_b @ A2 @ B2 ) ) ) )
      & ( ~ ( member6667749562321684925pace_b @ A @ A2 )
       => ( ( inf_in8598470101551243374pace_b @ A2 @ ( insert3418856332534486358pace_b @ A @ B2 ) )
          = ( inf_in8598470101551243374pace_b @ A2 @ B2 ) ) ) ) ).

% Int_insert_right
thf(fact_1126_Int__insert__right,axiom,
    ! [A: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ( ( member7340901614391157822pace_b @ A @ A2 )
       => ( ( inf_in3860511187648227951pace_b @ A2 @ ( insert8265437699098853335pace_b @ A @ B2 ) )
          = ( insert8265437699098853335pace_b @ A @ ( inf_in3860511187648227951pace_b @ A2 @ B2 ) ) ) )
      & ( ~ ( member7340901614391157822pace_b @ A @ A2 )
       => ( ( inf_in3860511187648227951pace_b @ A2 @ ( insert8265437699098853335pace_b @ A @ B2 ) )
          = ( inf_in3860511187648227951pace_b @ A2 @ B2 ) ) ) ) ).

% Int_insert_right
thf(fact_1127_Int__insert__right,axiom,
    ! [A: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ( ( member5008716543664893436ce_a_b @ A @ A2 )
       => ( ( inf_in8638537385238394157ce_a_b @ A2 @ ( insert5933252628372588949ce_a_b @ A @ B2 ) )
          = ( insert5933252628372588949ce_a_b @ A @ ( inf_in8638537385238394157ce_a_b @ A2 @ B2 ) ) ) )
      & ( ~ ( member5008716543664893436ce_a_b @ A @ A2 )
       => ( ( inf_in8638537385238394157ce_a_b @ A2 @ ( insert5933252628372588949ce_a_b @ A @ B2 ) )
          = ( inf_in8638537385238394157ce_a_b @ A2 @ B2 ) ) ) ) ).

% Int_insert_right
thf(fact_1128_Int__insert__right,axiom,
    ! [A: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ( ( member1568243296417166973pace_b @ A @ A2 )
       => ( ( inf_in433292969326628142pace_b @ A2 @ ( insert2492779381124862486pace_b @ A @ B2 ) )
          = ( insert2492779381124862486pace_b @ A @ ( inf_in433292969326628142pace_b @ A2 @ B2 ) ) ) )
      & ( ~ ( member1568243296417166973pace_b @ A @ A2 )
       => ( ( inf_in433292969326628142pace_b @ A2 @ ( insert2492779381124862486pace_b @ A @ B2 ) )
          = ( inf_in433292969326628142pace_b @ A2 @ B2 ) ) ) ) ).

% Int_insert_right
thf(fact_1129_Int__insert__right,axiom,
    ! [A: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ( ( member41169580844105599pace_b @ A @ A2 )
       => ( ( inf_in6845569456361772336pace_b @ A2 @ ( insert6015648387911682840pace_b @ A @ B2 ) )
          = ( insert6015648387911682840pace_b @ A @ ( inf_in6845569456361772336pace_b @ A2 @ B2 ) ) ) )
      & ( ~ ( member41169580844105599pace_b @ A @ A2 )
       => ( ( inf_in6845569456361772336pace_b @ A2 @ ( insert6015648387911682840pace_b @ A @ B2 ) )
          = ( inf_in6845569456361772336pace_b @ A2 @ B2 ) ) ) ) ).

% Int_insert_right
thf(fact_1130_Int__insert__right,axiom,
    ! [A: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ( ( member7269867574344811837pace_a @ A @ A2 )
       => ( ( inf_in6381695705937263598pace_a @ A2 @ ( insert8194403659052507350pace_a @ A @ B2 ) )
          = ( insert8194403659052507350pace_a @ A @ ( inf_in6381695705937263598pace_a @ A2 @ B2 ) ) ) )
      & ( ~ ( member7269867574344811837pace_a @ A @ A2 )
       => ( ( inf_in6381695705937263598pace_a @ A2 @ ( insert8194403659052507350pace_a @ A @ B2 ) )
          = ( inf_in6381695705937263598pace_a @ A2 @ B2 ) ) ) ) ).

% Int_insert_right
thf(fact_1131_Int__insert__right,axiom,
    ! [A: a > b,A2: set_a_b,B2: set_a_b] :
      ( ( ( member_a_b @ A @ A2 )
       => ( ( inf_inf_set_a_b @ A2 @ ( insert_a_b @ A @ B2 ) )
          = ( insert_a_b @ A @ ( inf_inf_set_a_b @ A2 @ B2 ) ) ) )
      & ( ~ ( member_a_b @ A @ A2 )
       => ( ( inf_inf_set_a_b @ A2 @ ( insert_a_b @ A @ B2 ) )
          = ( inf_inf_set_a_b @ A2 @ B2 ) ) ) ) ).

% Int_insert_right
thf(fact_1132_insert__compr,axiom,
    ( insert3418856332534486358pace_b
    = ( ^ [A4: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B4: set_Pr7742364250814120412pace_b] :
          ( collec7915783404360165627pace_b
          @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
              ( ( X2 = A4 )
              | ( member6667749562321684925pace_b @ X2 @ B4 ) ) ) ) ) ).

% insert_compr
thf(fact_1133_insert__compr,axiom,
    ( insert8265437699098853335pace_b
    = ( ^ [A4: a > probab4737552677800996672pace_b,B4: set_a_3263942136899480541pace_b] :
          ( collec5907158909762593660pace_b
          @ ^ [X2: a > probab4737552677800996672pace_b] :
              ( ( X2 = A4 )
              | ( member7340901614391157822pace_b @ X2 @ B4 ) ) ) ) ) ).

% insert_compr
thf(fact_1134_insert__compr,axiom,
    ( insert5933252628372588949ce_a_b
    = ( ^ [A4: probab4737552673497767871pace_a > b,B4: set_Pr8041968334489646747ce_a_b] :
          ( collec3574973839036329274ce_a_b
          @ ^ [X2: probab4737552673497767871pace_a > b] :
              ( ( X2 = A4 )
              | ( member5008716543664893436ce_a_b @ X2 @ B4 ) ) ) ) ) ).

% insert_compr
thf(fact_1135_insert__compr,axiom,
    ( insert2492779381124862486pace_b
    = ( ^ [A4: b > probab4737552677800996672pace_b,B4: set_b_9060095955432656540pace_b] :
          ( collec134500591788602811pace_b
          @ ^ [X2: b > probab4737552677800996672pace_b] :
              ( ( X2 = A4 )
              | ( member1568243296417166973pace_b @ X2 @ B4 ) ) ) ) ) ).

% insert_compr
thf(fact_1136_insert__compr,axiom,
    ( insert6015648387911682840pace_b
    = ( ^ [A4: a > probab8624551251471354625pace_b,B4: set_a_5989463605624649374pace_b] :
          ( collec1289203422882586301pace_b
          @ ^ [X2: a > probab8624551251471354625pace_b] :
              ( ( X2 = A4 )
              | ( member41169580844105599pace_b @ X2 @ B4 ) ) ) ) ) ).

% insert_compr
thf(fact_1137_insert__compr,axiom,
    ( insert8194403659052507350pace_a
    = ( ^ [A4: a > probab4737552673497767871pace_a,B4: set_a_5785126655188516188pace_a] :
          ( collec5836124869716247675pace_a
          @ ^ [X2: a > probab4737552673497767871pace_a] :
              ( ( X2 = A4 )
              | ( member7269867574344811837pace_a @ X2 @ B4 ) ) ) ) ) ).

% insert_compr
thf(fact_1138_insert__compr,axiom,
    ( insert_a_b
    = ( ^ [A4: a > b,B4: set_a_b] :
          ( collect_a_b
          @ ^ [X2: a > b] :
              ( ( X2 = A4 )
              | ( member_a_b @ X2 @ B4 ) ) ) ) ) ).

% insert_compr
thf(fact_1139_insertE,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ A @ ( insert3418856332534486358pace_b @ B @ A2 ) )
     => ( ( A != B )
       => ( member6667749562321684925pace_b @ A @ A2 ) ) ) ).

% insertE
thf(fact_1140_insertE,axiom,
    ! [A: a > probab4737552677800996672pace_b,B: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ A @ ( insert8265437699098853335pace_b @ B @ A2 ) )
     => ( ( A != B )
       => ( member7340901614391157822pace_b @ A @ A2 ) ) ) ).

% insertE
thf(fact_1141_insertE,axiom,
    ! [A: probab4737552673497767871pace_a > b,B: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ A @ ( insert5933252628372588949ce_a_b @ B @ A2 ) )
     => ( ( A != B )
       => ( member5008716543664893436ce_a_b @ A @ A2 ) ) ) ).

% insertE
thf(fact_1142_insertE,axiom,
    ! [A: b > probab4737552677800996672pace_b,B: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ A @ ( insert2492779381124862486pace_b @ B @ A2 ) )
     => ( ( A != B )
       => ( member1568243296417166973pace_b @ A @ A2 ) ) ) ).

% insertE
thf(fact_1143_insertE,axiom,
    ! [A: a > probab8624551251471354625pace_b,B: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ A @ ( insert6015648387911682840pace_b @ B @ A2 ) )
     => ( ( A != B )
       => ( member41169580844105599pace_b @ A @ A2 ) ) ) ).

% insertE
thf(fact_1144_insertE,axiom,
    ! [A: a > probab4737552673497767871pace_a,B: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ A @ ( insert8194403659052507350pace_a @ B @ A2 ) )
     => ( ( A != B )
       => ( member7269867574344811837pace_a @ A @ A2 ) ) ) ).

% insertE
thf(fact_1145_insertE,axiom,
    ! [A: a > b,B: a > b,A2: set_a_b] :
      ( ( member_a_b @ A @ ( insert_a_b @ B @ A2 ) )
     => ( ( A != B )
       => ( member_a_b @ A @ A2 ) ) ) ).

% insertE
thf(fact_1146_insertI1,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: set_Pr7742364250814120412pace_b] : ( member6667749562321684925pace_b @ A @ ( insert3418856332534486358pace_b @ A @ B2 ) ) ).

% insertI1
thf(fact_1147_insertI1,axiom,
    ! [A: a > probab4737552677800996672pace_b,B2: set_a_3263942136899480541pace_b] : ( member7340901614391157822pace_b @ A @ ( insert8265437699098853335pace_b @ A @ B2 ) ) ).

% insertI1
thf(fact_1148_insertI1,axiom,
    ! [A: probab4737552673497767871pace_a > b,B2: set_Pr8041968334489646747ce_a_b] : ( member5008716543664893436ce_a_b @ A @ ( insert5933252628372588949ce_a_b @ A @ B2 ) ) ).

% insertI1
thf(fact_1149_insertI1,axiom,
    ! [A: b > probab4737552677800996672pace_b,B2: set_b_9060095955432656540pace_b] : ( member1568243296417166973pace_b @ A @ ( insert2492779381124862486pace_b @ A @ B2 ) ) ).

% insertI1
thf(fact_1150_insertI1,axiom,
    ! [A: a > probab8624551251471354625pace_b,B2: set_a_5989463605624649374pace_b] : ( member41169580844105599pace_b @ A @ ( insert6015648387911682840pace_b @ A @ B2 ) ) ).

% insertI1
thf(fact_1151_insertI1,axiom,
    ! [A: a > probab4737552673497767871pace_a,B2: set_a_5785126655188516188pace_a] : ( member7269867574344811837pace_a @ A @ ( insert8194403659052507350pace_a @ A @ B2 ) ) ).

% insertI1
thf(fact_1152_insertI1,axiom,
    ! [A: a > b,B2: set_a_b] : ( member_a_b @ A @ ( insert_a_b @ A @ B2 ) ) ).

% insertI1
thf(fact_1153_insertI2,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: set_Pr7742364250814120412pace_b,B: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ( ( member6667749562321684925pace_b @ A @ B2 )
     => ( member6667749562321684925pace_b @ A @ ( insert3418856332534486358pace_b @ B @ B2 ) ) ) ).

% insertI2
thf(fact_1154_insertI2,axiom,
    ! [A: a > probab4737552677800996672pace_b,B2: set_a_3263942136899480541pace_b,B: a > probab4737552677800996672pace_b] :
      ( ( member7340901614391157822pace_b @ A @ B2 )
     => ( member7340901614391157822pace_b @ A @ ( insert8265437699098853335pace_b @ B @ B2 ) ) ) ).

% insertI2
thf(fact_1155_insertI2,axiom,
    ! [A: probab4737552673497767871pace_a > b,B2: set_Pr8041968334489646747ce_a_b,B: probab4737552673497767871pace_a > b] :
      ( ( member5008716543664893436ce_a_b @ A @ B2 )
     => ( member5008716543664893436ce_a_b @ A @ ( insert5933252628372588949ce_a_b @ B @ B2 ) ) ) ).

% insertI2
thf(fact_1156_insertI2,axiom,
    ! [A: b > probab4737552677800996672pace_b,B2: set_b_9060095955432656540pace_b,B: b > probab4737552677800996672pace_b] :
      ( ( member1568243296417166973pace_b @ A @ B2 )
     => ( member1568243296417166973pace_b @ A @ ( insert2492779381124862486pace_b @ B @ B2 ) ) ) ).

% insertI2
thf(fact_1157_insertI2,axiom,
    ! [A: a > probab8624551251471354625pace_b,B2: set_a_5989463605624649374pace_b,B: a > probab8624551251471354625pace_b] :
      ( ( member41169580844105599pace_b @ A @ B2 )
     => ( member41169580844105599pace_b @ A @ ( insert6015648387911682840pace_b @ B @ B2 ) ) ) ).

% insertI2
thf(fact_1158_insertI2,axiom,
    ! [A: a > probab4737552673497767871pace_a,B2: set_a_5785126655188516188pace_a,B: a > probab4737552673497767871pace_a] :
      ( ( member7269867574344811837pace_a @ A @ B2 )
     => ( member7269867574344811837pace_a @ A @ ( insert8194403659052507350pace_a @ B @ B2 ) ) ) ).

% insertI2
thf(fact_1159_insertI2,axiom,
    ! [A: a > b,B2: set_a_b,B: a > b] :
      ( ( member_a_b @ A @ B2 )
     => ( member_a_b @ A @ ( insert_a_b @ B @ B2 ) ) ) ).

% insertI2
thf(fact_1160_Set_Oset__insert,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ X3 @ A2 )
     => ~ ! [B5: set_Pr7742364250814120412pace_b] :
            ( ( A2
              = ( insert3418856332534486358pace_b @ X3 @ B5 ) )
           => ( member6667749562321684925pace_b @ X3 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_1161_Set_Oset__insert,axiom,
    ! [X3: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ X3 @ A2 )
     => ~ ! [B5: set_a_3263942136899480541pace_b] :
            ( ( A2
              = ( insert8265437699098853335pace_b @ X3 @ B5 ) )
           => ( member7340901614391157822pace_b @ X3 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_1162_Set_Oset__insert,axiom,
    ! [X3: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ X3 @ A2 )
     => ~ ! [B5: set_Pr8041968334489646747ce_a_b] :
            ( ( A2
              = ( insert5933252628372588949ce_a_b @ X3 @ B5 ) )
           => ( member5008716543664893436ce_a_b @ X3 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_1163_Set_Oset__insert,axiom,
    ! [X3: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ X3 @ A2 )
     => ~ ! [B5: set_b_9060095955432656540pace_b] :
            ( ( A2
              = ( insert2492779381124862486pace_b @ X3 @ B5 ) )
           => ( member1568243296417166973pace_b @ X3 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_1164_Set_Oset__insert,axiom,
    ! [X3: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ X3 @ A2 )
     => ~ ! [B5: set_a_5989463605624649374pace_b] :
            ( ( A2
              = ( insert6015648387911682840pace_b @ X3 @ B5 ) )
           => ( member41169580844105599pace_b @ X3 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_1165_Set_Oset__insert,axiom,
    ! [X3: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ X3 @ A2 )
     => ~ ! [B5: set_a_5785126655188516188pace_a] :
            ( ( A2
              = ( insert8194403659052507350pace_a @ X3 @ B5 ) )
           => ( member7269867574344811837pace_a @ X3 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_1166_Set_Oset__insert,axiom,
    ! [X3: a > b,A2: set_a_b] :
      ( ( member_a_b @ X3 @ A2 )
     => ~ ! [B5: set_a_b] :
            ( ( A2
              = ( insert_a_b @ X3 @ B5 ) )
           => ( member_a_b @ X3 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_1167_insert__ident,axiom,
    ! [X3: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ~ ( member6667749562321684925pace_b @ X3 @ A2 )
     => ( ~ ( member6667749562321684925pace_b @ X3 @ B2 )
       => ( ( ( insert3418856332534486358pace_b @ X3 @ A2 )
            = ( insert3418856332534486358pace_b @ X3 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_1168_insert__ident,axiom,
    ! [X3: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ~ ( member7340901614391157822pace_b @ X3 @ A2 )
     => ( ~ ( member7340901614391157822pace_b @ X3 @ B2 )
       => ( ( ( insert8265437699098853335pace_b @ X3 @ A2 )
            = ( insert8265437699098853335pace_b @ X3 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_1169_insert__ident,axiom,
    ! [X3: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ~ ( member5008716543664893436ce_a_b @ X3 @ A2 )
     => ( ~ ( member5008716543664893436ce_a_b @ X3 @ B2 )
       => ( ( ( insert5933252628372588949ce_a_b @ X3 @ A2 )
            = ( insert5933252628372588949ce_a_b @ X3 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_1170_insert__ident,axiom,
    ! [X3: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ~ ( member1568243296417166973pace_b @ X3 @ A2 )
     => ( ~ ( member1568243296417166973pace_b @ X3 @ B2 )
       => ( ( ( insert2492779381124862486pace_b @ X3 @ A2 )
            = ( insert2492779381124862486pace_b @ X3 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_1171_insert__ident,axiom,
    ! [X3: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ~ ( member41169580844105599pace_b @ X3 @ A2 )
     => ( ~ ( member41169580844105599pace_b @ X3 @ B2 )
       => ( ( ( insert6015648387911682840pace_b @ X3 @ A2 )
            = ( insert6015648387911682840pace_b @ X3 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_1172_insert__ident,axiom,
    ! [X3: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ~ ( member7269867574344811837pace_a @ X3 @ A2 )
     => ( ~ ( member7269867574344811837pace_a @ X3 @ B2 )
       => ( ( ( insert8194403659052507350pace_a @ X3 @ A2 )
            = ( insert8194403659052507350pace_a @ X3 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_1173_insert__ident,axiom,
    ! [X3: a > b,A2: set_a_b,B2: set_a_b] :
      ( ~ ( member_a_b @ X3 @ A2 )
     => ( ~ ( member_a_b @ X3 @ B2 )
       => ( ( ( insert_a_b @ X3 @ A2 )
            = ( insert_a_b @ X3 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_1174_insert__absorb,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ A @ A2 )
     => ( ( insert3418856332534486358pace_b @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1175_insert__absorb,axiom,
    ! [A: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ A @ A2 )
     => ( ( insert8265437699098853335pace_b @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1176_insert__absorb,axiom,
    ! [A: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ A @ A2 )
     => ( ( insert5933252628372588949ce_a_b @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1177_insert__absorb,axiom,
    ! [A: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ A @ A2 )
     => ( ( insert2492779381124862486pace_b @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1178_insert__absorb,axiom,
    ! [A: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ A @ A2 )
     => ( ( insert6015648387911682840pace_b @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1179_insert__absorb,axiom,
    ! [A: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ A @ A2 )
     => ( ( insert8194403659052507350pace_a @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1180_insert__absorb,axiom,
    ! [A: a > b,A2: set_a_b] :
      ( ( member_a_b @ A @ A2 )
     => ( ( insert_a_b @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1181_insert__eq__iff,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: set_Pr7742364250814120412pace_b] :
      ( ~ ( member6667749562321684925pace_b @ A @ A2 )
     => ( ~ ( member6667749562321684925pace_b @ B @ B2 )
       => ( ( ( insert3418856332534486358pace_b @ A @ A2 )
            = ( insert3418856332534486358pace_b @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C3: set_Pr7742364250814120412pace_b] :
                  ( ( A2
                    = ( insert3418856332534486358pace_b @ B @ C3 ) )
                  & ~ ( member6667749562321684925pace_b @ B @ C3 )
                  & ( B2
                    = ( insert3418856332534486358pace_b @ A @ C3 ) )
                  & ~ ( member6667749562321684925pace_b @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1182_insert__eq__iff,axiom,
    ! [A: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B: a > probab4737552677800996672pace_b,B2: set_a_3263942136899480541pace_b] :
      ( ~ ( member7340901614391157822pace_b @ A @ A2 )
     => ( ~ ( member7340901614391157822pace_b @ B @ B2 )
       => ( ( ( insert8265437699098853335pace_b @ A @ A2 )
            = ( insert8265437699098853335pace_b @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C3: set_a_3263942136899480541pace_b] :
                  ( ( A2
                    = ( insert8265437699098853335pace_b @ B @ C3 ) )
                  & ~ ( member7340901614391157822pace_b @ B @ C3 )
                  & ( B2
                    = ( insert8265437699098853335pace_b @ A @ C3 ) )
                  & ~ ( member7340901614391157822pace_b @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1183_insert__eq__iff,axiom,
    ! [A: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B: probab4737552673497767871pace_a > b,B2: set_Pr8041968334489646747ce_a_b] :
      ( ~ ( member5008716543664893436ce_a_b @ A @ A2 )
     => ( ~ ( member5008716543664893436ce_a_b @ B @ B2 )
       => ( ( ( insert5933252628372588949ce_a_b @ A @ A2 )
            = ( insert5933252628372588949ce_a_b @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C3: set_Pr8041968334489646747ce_a_b] :
                  ( ( A2
                    = ( insert5933252628372588949ce_a_b @ B @ C3 ) )
                  & ~ ( member5008716543664893436ce_a_b @ B @ C3 )
                  & ( B2
                    = ( insert5933252628372588949ce_a_b @ A @ C3 ) )
                  & ~ ( member5008716543664893436ce_a_b @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1184_insert__eq__iff,axiom,
    ! [A: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B: b > probab4737552677800996672pace_b,B2: set_b_9060095955432656540pace_b] :
      ( ~ ( member1568243296417166973pace_b @ A @ A2 )
     => ( ~ ( member1568243296417166973pace_b @ B @ B2 )
       => ( ( ( insert2492779381124862486pace_b @ A @ A2 )
            = ( insert2492779381124862486pace_b @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C3: set_b_9060095955432656540pace_b] :
                  ( ( A2
                    = ( insert2492779381124862486pace_b @ B @ C3 ) )
                  & ~ ( member1568243296417166973pace_b @ B @ C3 )
                  & ( B2
                    = ( insert2492779381124862486pace_b @ A @ C3 ) )
                  & ~ ( member1568243296417166973pace_b @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1185_insert__eq__iff,axiom,
    ! [A: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b,B: a > probab8624551251471354625pace_b,B2: set_a_5989463605624649374pace_b] :
      ( ~ ( member41169580844105599pace_b @ A @ A2 )
     => ( ~ ( member41169580844105599pace_b @ B @ B2 )
       => ( ( ( insert6015648387911682840pace_b @ A @ A2 )
            = ( insert6015648387911682840pace_b @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C3: set_a_5989463605624649374pace_b] :
                  ( ( A2
                    = ( insert6015648387911682840pace_b @ B @ C3 ) )
                  & ~ ( member41169580844105599pace_b @ B @ C3 )
                  & ( B2
                    = ( insert6015648387911682840pace_b @ A @ C3 ) )
                  & ~ ( member41169580844105599pace_b @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1186_insert__eq__iff,axiom,
    ! [A: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B: a > probab4737552673497767871pace_a,B2: set_a_5785126655188516188pace_a] :
      ( ~ ( member7269867574344811837pace_a @ A @ A2 )
     => ( ~ ( member7269867574344811837pace_a @ B @ B2 )
       => ( ( ( insert8194403659052507350pace_a @ A @ A2 )
            = ( insert8194403659052507350pace_a @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C3: set_a_5785126655188516188pace_a] :
                  ( ( A2
                    = ( insert8194403659052507350pace_a @ B @ C3 ) )
                  & ~ ( member7269867574344811837pace_a @ B @ C3 )
                  & ( B2
                    = ( insert8194403659052507350pace_a @ A @ C3 ) )
                  & ~ ( member7269867574344811837pace_a @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1187_insert__eq__iff,axiom,
    ! [A: a > b,A2: set_a_b,B: a > b,B2: set_a_b] :
      ( ~ ( member_a_b @ A @ A2 )
     => ( ~ ( member_a_b @ B @ B2 )
       => ( ( ( insert_a_b @ A @ A2 )
            = ( insert_a_b @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C3: set_a_b] :
                  ( ( A2
                    = ( insert_a_b @ B @ C3 ) )
                  & ~ ( member_a_b @ B @ C3 )
                  & ( B2
                    = ( insert_a_b @ A @ C3 ) )
                  & ~ ( member_a_b @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1188_mk__disjoint__insert,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b] :
      ( ( member6667749562321684925pace_b @ A @ A2 )
     => ? [B5: set_Pr7742364250814120412pace_b] :
          ( ( A2
            = ( insert3418856332534486358pace_b @ A @ B5 ) )
          & ~ ( member6667749562321684925pace_b @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_1189_mk__disjoint__insert,axiom,
    ! [A: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b] :
      ( ( member7340901614391157822pace_b @ A @ A2 )
     => ? [B5: set_a_3263942136899480541pace_b] :
          ( ( A2
            = ( insert8265437699098853335pace_b @ A @ B5 ) )
          & ~ ( member7340901614391157822pace_b @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_1190_mk__disjoint__insert,axiom,
    ! [A: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( member5008716543664893436ce_a_b @ A @ A2 )
     => ? [B5: set_Pr8041968334489646747ce_a_b] :
          ( ( A2
            = ( insert5933252628372588949ce_a_b @ A @ B5 ) )
          & ~ ( member5008716543664893436ce_a_b @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_1191_mk__disjoint__insert,axiom,
    ! [A: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b] :
      ( ( member1568243296417166973pace_b @ A @ A2 )
     => ? [B5: set_b_9060095955432656540pace_b] :
          ( ( A2
            = ( insert2492779381124862486pace_b @ A @ B5 ) )
          & ~ ( member1568243296417166973pace_b @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_1192_mk__disjoint__insert,axiom,
    ! [A: a > probab8624551251471354625pace_b,A2: set_a_5989463605624649374pace_b] :
      ( ( member41169580844105599pace_b @ A @ A2 )
     => ? [B5: set_a_5989463605624649374pace_b] :
          ( ( A2
            = ( insert6015648387911682840pace_b @ A @ B5 ) )
          & ~ ( member41169580844105599pace_b @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_1193_mk__disjoint__insert,axiom,
    ! [A: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a] :
      ( ( member7269867574344811837pace_a @ A @ A2 )
     => ? [B5: set_a_5785126655188516188pace_a] :
          ( ( A2
            = ( insert8194403659052507350pace_a @ A @ B5 ) )
          & ~ ( member7269867574344811837pace_a @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_1194_mk__disjoint__insert,axiom,
    ! [A: a > b,A2: set_a_b] :
      ( ( member_a_b @ A @ A2 )
     => ? [B5: set_a_b] :
          ( ( A2
            = ( insert_a_b @ A @ B5 ) )
          & ~ ( member_a_b @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_1195_PiE__singleton,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr8456636223741192351pace_a] :
      ( ( member6667749562321684925pace_b @ F @ ( extens3782360123960272121pace_b @ A2 ) )
     => ( ( piE_Pr1548282726383880571pace_b @ A2
          @ ^ [X2: probab4737552673497767871pace_a] : ( insert8086323751694400784pace_b @ ( F @ X2 ) @ bot_bo2869796269454395916pace_b ) )
        = ( insert3418856332534486358pace_b @ F @ bot_bo5050001829711205488pace_b ) ) ) ).

% PiE_singleton
thf(fact_1196_PiE__singleton,axiom,
    ! [F: a > probab4737552677800996672pace_b,A2: set_a] :
      ( ( member7340901614391157822pace_b @ F @ ( extens3470472542307807098pace_b @ A2 ) )
     => ( ( piE_a_4194508618861114364pace_b @ A2
          @ ^ [X2: a] : ( insert8086323751694400784pace_b @ ( F @ X2 ) @ bot_bo2869796269454395916pace_b ) )
        = ( insert8265437699098853335pace_b @ F @ bot_bo2617902995080265329pace_b ) ) ) ).

% PiE_singleton
thf(fact_1197_PiE__singleton,axiom,
    ! [F: probab4737552673497767871pace_a > b,A2: set_Pr8456636223741192351pace_a] :
      ( ( member5008716543664893436ce_a_b @ F @ ( extens1372367841095510200ce_a_b @ A2 ) )
     => ( ( piE_Pr2096403917648817466ce_a_b @ A2
          @ ^ [X2: probab4737552673497767871pace_a] : ( insert_b @ ( F @ X2 ) @ bot_bot_set_b ) )
        = ( insert5933252628372588949ce_a_b @ F @ bot_bo7395929192670431535ce_a_b ) ) ) ).

% PiE_singleton
thf(fact_1198_PiE__singleton,axiom,
    ! [F: b > probab4737552677800996672pace_b,A2: set_b] :
      ( ( member1568243296417166973pace_b @ F @ ( extens6921186261188592057pace_b @ A2 ) )
     => ( ( piE_b_7645222337741899323pace_b @ A2
          @ ^ [X2: b] : ( insert8086323751694400784pace_b @ ( F @ X2 ) @ bot_bo2869796269454395916pace_b ) )
        = ( insert2492779381124862486pace_b @ F @ bot_bo8414056813613441328pace_b ) ) ) ).

% PiE_singleton
thf(fact_1199_PiE__singleton,axiom,
    ! [F: a > probab8624551251471354625pace_b,A2: set_a] :
      ( ( member41169580844105599pace_b @ F @ ( extens2356043851050494779pace_b @ A2 ) )
     => ( ( piE_a_121966453474103229pace_b @ A2
          @ ^ [X2: a] : ( insert821530756347189457pace_b @ ( F @ X2 ) @ bot_bo5310430670759953741pace_b ) )
        = ( insert6015648387911682840pace_b @ F @ bot_bo3297101184521734450pace_b ) ) ) ).

% PiE_singleton
thf(fact_1200_PiE__singleton,axiom,
    ! [F: a > probab4737552673497767871pace_a,A2: set_a] :
      ( ( member7269867574344811837pace_a @ F @ ( extens3470472538004578297pace_a @ A2 ) )
     => ( ( piE_a_4194508614557885563pace_a @ A2
          @ ^ [X2: a] : ( insert8086323747391171983pace_a @ ( F @ X2 ) @ bot_bo2798762229408049931pace_a ) )
        = ( insert8194403659052507350pace_a @ F @ bot_bo5139087513369300976pace_a ) ) ) ).

% PiE_singleton
thf(fact_1201_PiE__singleton,axiom,
    ! [F: a > b,A2: set_a] :
      ( ( member_a_b @ F @ ( extensional_a_b @ A2 ) )
     => ( ( piE_a_b @ A2
          @ ^ [X2: a] : ( insert_b @ ( F @ X2 ) @ bot_bot_set_b ) )
        = ( insert_a_b @ F @ bot_bot_set_a_b ) ) ) ).

% PiE_singleton
thf(fact_1202_extensional__insert__cancel,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,I2: set_Pr8456636223741192351pace_a,I3: probab4737552673497767871pace_a] :
      ( ( member6667749562321684925pace_b @ A @ ( extens3782360123960272121pace_b @ I2 ) )
     => ( member6667749562321684925pace_b @ A @ ( extens3782360123960272121pace_b @ ( insert8086323747391171983pace_a @ I3 @ I2 ) ) ) ) ).

% extensional_insert_cancel
thf(fact_1203_extensional__insert__cancel,axiom,
    ! [A: a > probab4737552677800996672pace_b,I2: set_a,I3: a] :
      ( ( member7340901614391157822pace_b @ A @ ( extens3470472542307807098pace_b @ I2 ) )
     => ( member7340901614391157822pace_b @ A @ ( extens3470472542307807098pace_b @ ( insert_a @ I3 @ I2 ) ) ) ) ).

% extensional_insert_cancel
thf(fact_1204_extensional__insert__cancel,axiom,
    ! [A: probab4737552673497767871pace_a > b,I2: set_Pr8456636223741192351pace_a,I3: probab4737552673497767871pace_a] :
      ( ( member5008716543664893436ce_a_b @ A @ ( extens1372367841095510200ce_a_b @ I2 ) )
     => ( member5008716543664893436ce_a_b @ A @ ( extens1372367841095510200ce_a_b @ ( insert8086323747391171983pace_a @ I3 @ I2 ) ) ) ) ).

% extensional_insert_cancel
thf(fact_1205_extensional__insert__cancel,axiom,
    ! [A: b > probab4737552677800996672pace_b,I2: set_b,I3: b] :
      ( ( member1568243296417166973pace_b @ A @ ( extens6921186261188592057pace_b @ I2 ) )
     => ( member1568243296417166973pace_b @ A @ ( extens6921186261188592057pace_b @ ( insert_b @ I3 @ I2 ) ) ) ) ).

% extensional_insert_cancel
thf(fact_1206_extensional__insert__cancel,axiom,
    ! [A: a > probab8624551251471354625pace_b,I2: set_a,I3: a] :
      ( ( member41169580844105599pace_b @ A @ ( extens2356043851050494779pace_b @ I2 ) )
     => ( member41169580844105599pace_b @ A @ ( extens2356043851050494779pace_b @ ( insert_a @ I3 @ I2 ) ) ) ) ).

% extensional_insert_cancel
thf(fact_1207_extensional__insert__cancel,axiom,
    ! [A: a > probab4737552673497767871pace_a,I2: set_a,I3: a] :
      ( ( member7269867574344811837pace_a @ A @ ( extens3470472538004578297pace_a @ I2 ) )
     => ( member7269867574344811837pace_a @ A @ ( extens3470472538004578297pace_a @ ( insert_a @ I3 @ I2 ) ) ) ) ).

% extensional_insert_cancel
thf(fact_1208_extensional__insert__cancel,axiom,
    ! [A: a > b,I2: set_a,I3: a] :
      ( ( member_a_b @ A @ ( extensional_a_b @ I2 ) )
     => ( member_a_b @ A @ ( extensional_a_b @ ( insert_a @ I3 @ I2 ) ) ) ) ).

% extensional_insert_cancel
thf(fact_1209_UN__I,axiom,
    ! [A: a > b,A2: set_a_b,B: a > b,B2: ( a > b ) > set_a_b] :
      ( ( member_a_b @ A @ A2 )
     => ( ( member_a_b @ B @ ( B2 @ A ) )
       => ( member_a_b @ B @ ( comple6589653751571696623et_a_b @ ( image_a_b_set_a_b @ B2 @ A2 ) ) ) ) ) ).

% UN_I
thf(fact_1210_UN__I,axiom,
    ! [A: a > probab4737552677800996672pace_b,A2: set_a_3263942136899480541pace_b,B: a > b,B2: ( a > probab4737552677800996672pace_b ) > set_a_b] :
      ( ( member7340901614391157822pace_b @ A @ A2 )
     => ( ( member_a_b @ B @ ( B2 @ A ) )
       => ( member_a_b @ B @ ( comple6589653751571696623et_a_b @ ( image_3320987880458065994et_a_b @ B2 @ A2 ) ) ) ) ) ).

% UN_I
thf(fact_1211_UN__I,axiom,
    ! [A: probab4737552673497767871pace_a > b,A2: set_Pr8041968334489646747ce_a_b,B: a > b,B2: ( probab4737552673497767871pace_a > b ) > set_a_b] :
      ( ( member5008716543664893436ce_a_b @ A @ A2 )
     => ( ( member_a_b @ B @ ( B2 @ A ) )
       => ( member_a_b @ B @ ( comple6589653751571696623et_a_b @ ( image_8419905865881351688et_a_b @ B2 @ A2 ) ) ) ) ) ).

% UN_I
thf(fact_1212_UN__I,axiom,
    ! [A: b > probab4737552677800996672pace_b,A2: set_b_9060095955432656540pace_b,B: a > b,B2: ( b > probab4737552677800996672pace_b ) > set_a_b] :
      ( ( member1568243296417166973pace_b @ A @ A2 )
     => ( ( member_a_b @ B @ ( B2 @ A ) )
       => ( member_a_b @ B @ ( comple6589653751571696623et_a_b @ ( image_6723652579854267529et_a_b @ B2 @ A2 ) ) ) ) ) ).

% UN_I
thf(fact_1213_UN__I,axiom,
    ! [A: a > probab4737552673497767871pace_a,A2: set_a_5785126655188516188pace_a,B: a > b,B2: ( a > probab4737552673497767871pace_a ) > set_a_b] :
      ( ( member7269867574344811837pace_a @ A @ A2 )
     => ( ( member_a_b @ B @ ( B2 @ A ) )
       => ( member_a_b @ B @ ( comple6589653751571696623et_a_b @ ( image_1059268598997287753et_a_b @ B2 @ A2 ) ) ) ) ) ).

% UN_I
thf(fact_1214_UN__I,axiom,
    ! [A: a > b,A2: set_a_b,B: a > probab4737552677800996672pace_b,B2: ( a > b ) > set_a_3263942136899480541pace_b] :
      ( ( member_a_b @ A @ A2 )
     => ( ( member7340901614391157822pace_b @ B @ ( B2 @ A ) )
       => ( member7340901614391157822pace_b @ B @ ( comple6646451451432703792pace_b @ ( image_2483489791776158154pace_b @ B2 @ A2 ) ) ) ) ) ).

% UN_I
thf(fact_1215_UN__I,axiom,
    ! [A: a > b,A2: set_a_b,B: probab4737552673497767871pace_a > b,B2: ( a > b ) > set_Pr8041968334489646747ce_a_b] :
      ( ( member_a_b @ A @ A2 )
     => ( ( member5008716543664893436ce_a_b @ B @ ( B2 @ A ) )
       => ( member5008716543664893436ce_a_b @ B @ ( comple2201105612168094190ce_a_b @ ( image_7261515989366324360ce_a_b @ B2 @ A2 ) ) ) ) ) ).

% UN_I
thf(fact_1216_UN__I,axiom,
    ! [A: a > b,A2: set_a_b,B: b > probab4737552677800996672pace_b,B2: ( a > b ) > set_b_9060095955432656540pace_b] :
      ( ( member_a_b @ A @ A2 )
     => ( ( member1568243296417166973pace_b @ B @ ( B2 @ A ) )
       => ( member1568243296417166973pace_b @ B @ ( comple3219233233111103983pace_b @ ( image_8279643610309334153pace_b @ B2 @ A2 ) ) ) ) ) ).

% UN_I
thf(fact_1217_UN__I,axiom,
    ! [A: a > b,A2: set_a_b,B: a > probab4737552673497767871pace_a,B2: ( a > b ) > set_a_5785126655188516188pace_a] :
      ( ( member_a_b @ A @ A2 )
     => ( ( member7269867574344811837pace_a @ B @ ( B2 @ A ) )
       => ( member7269867574344811837pace_a @ B @ ( comple9167635969721739439pace_a @ ( image_5004674310065193801pace_a @ B2 @ A2 ) ) ) ) ) ).

% UN_I
thf(fact_1218_UN__I,axiom,
    ! [A: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr7742364250814120412pace_b,B: a > b,B2: ( probab4737552673497767871pace_a > probab4737552677800996672pace_b ) > set_a_b] :
      ( ( member6667749562321684925pace_b @ A @ A2 )
     => ( ( member_a_b @ B @ ( B2 @ A ) )
       => ( member_a_b @ B @ ( comple6589653751571696623et_a_b @ ( image_3665357532286474185et_a_b @ B2 @ A2 ) ) ) ) ) ).

% UN_I
thf(fact_1219_restrict__extensional__sub,axiom,
    ! [A2: set_Pr8456636223741192351pace_a,B2: set_Pr8456636223741192351pace_a,F: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ( ( ord_le6763996948946501695pace_a @ A2 @ B2 )
     => ( member6667749562321684925pace_b @ ( restri5846393312276451823pace_b @ F @ A2 ) @ ( extens3782360123960272121pace_b @ B2 ) ) ) ).

% restrict_extensional_sub
thf(fact_1220_restrict__extensional__sub,axiom,
    ! [A2: set_a,B2: set_a,F: a > probab4737552677800996672pace_b] :
      ( ( ord_less_eq_set_a @ A2 @ B2 )
     => ( member7340901614391157822pace_b @ ( restri4927025876843904112pace_b @ F @ A2 ) @ ( extens3470472542307807098pace_b @ B2 ) ) ) ).

% restrict_extensional_sub
thf(fact_1221_restrict__extensional__sub,axiom,
    ! [A2: set_Pr8456636223741192351pace_a,B2: set_Pr8456636223741192351pace_a,F: probab4737552673497767871pace_a > b] :
      ( ( ord_le6763996948946501695pace_a @ A2 @ B2 )
     => ( member5008716543664893436ce_a_b @ ( restri2828921175631607214ce_a_b @ F @ A2 ) @ ( extens1372367841095510200ce_a_b @ B2 ) ) ) ).

% restrict_extensional_sub
thf(fact_1222_restrict__extensional__sub,axiom,
    ! [A2: set_b,B2: set_b,F: b > probab4737552677800996672pace_b] :
      ( ( ord_less_eq_set_b @ A2 @ B2 )
     => ( member1568243296417166973pace_b @ ( restri8377739595724689071pace_b @ F @ A2 ) @ ( extens6921186261188592057pace_b @ B2 ) ) ) ).

% restrict_extensional_sub
thf(fact_1223_restrict__extensional__sub,axiom,
    ! [A2: set_a,B2: set_a,F: a > probab8624551251471354625pace_b] :
      ( ( ord_less_eq_set_a @ A2 @ B2 )
     => ( member41169580844105599pace_b @ ( restri4420077039366674481pace_b @ F @ A2 ) @ ( extens2356043851050494779pace_b @ B2 ) ) ) ).

% restrict_extensional_sub
thf(fact_1224_restrict__extensional__sub,axiom,
    ! [A2: set_a,B2: set_a,F: a > probab4737552673497767871pace_a] :
      ( ( ord_less_eq_set_a @ A2 @ B2 )
     => ( member7269867574344811837pace_a @ ( restri4927025872540675311pace_a @ F @ A2 ) @ ( extens3470472538004578297pace_a @ B2 ) ) ) ).

% restrict_extensional_sub
thf(fact_1225_restrict__extensional__sub,axiom,
    ! [A2: set_a,B2: set_a,F: a > b] :
      ( ( ord_less_eq_set_a @ A2 @ B2 )
     => ( member_a_b @ ( restrict_a_b @ F @ A2 ) @ ( extensional_a_b @ B2 ) ) ) ).

% restrict_extensional_sub
thf(fact_1226_extensional__subset,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr8456636223741192351pace_a,B2: set_Pr8456636223741192351pace_a] :
      ( ( member6667749562321684925pace_b @ F @ ( extens3782360123960272121pace_b @ A2 ) )
     => ( ( ord_le6763996948946501695pace_a @ A2 @ B2 )
       => ( member6667749562321684925pace_b @ F @ ( extens3782360123960272121pace_b @ B2 ) ) ) ) ).

% extensional_subset
thf(fact_1227_extensional__subset,axiom,
    ! [F: a > probab4737552677800996672pace_b,A2: set_a,B2: set_a] :
      ( ( member7340901614391157822pace_b @ F @ ( extens3470472542307807098pace_b @ A2 ) )
     => ( ( ord_less_eq_set_a @ A2 @ B2 )
       => ( member7340901614391157822pace_b @ F @ ( extens3470472542307807098pace_b @ B2 ) ) ) ) ).

% extensional_subset
thf(fact_1228_extensional__subset,axiom,
    ! [F: probab4737552673497767871pace_a > b,A2: set_Pr8456636223741192351pace_a,B2: set_Pr8456636223741192351pace_a] :
      ( ( member5008716543664893436ce_a_b @ F @ ( extens1372367841095510200ce_a_b @ A2 ) )
     => ( ( ord_le6763996948946501695pace_a @ A2 @ B2 )
       => ( member5008716543664893436ce_a_b @ F @ ( extens1372367841095510200ce_a_b @ B2 ) ) ) ) ).

% extensional_subset
thf(fact_1229_extensional__subset,axiom,
    ! [F: b > probab4737552677800996672pace_b,A2: set_b,B2: set_b] :
      ( ( member1568243296417166973pace_b @ F @ ( extens6921186261188592057pace_b @ A2 ) )
     => ( ( ord_less_eq_set_b @ A2 @ B2 )
       => ( member1568243296417166973pace_b @ F @ ( extens6921186261188592057pace_b @ B2 ) ) ) ) ).

% extensional_subset
thf(fact_1230_extensional__subset,axiom,
    ! [F: a > probab8624551251471354625pace_b,A2: set_a,B2: set_a] :
      ( ( member41169580844105599pace_b @ F @ ( extens2356043851050494779pace_b @ A2 ) )
     => ( ( ord_less_eq_set_a @ A2 @ B2 )
       => ( member41169580844105599pace_b @ F @ ( extens2356043851050494779pace_b @ B2 ) ) ) ) ).

% extensional_subset
thf(fact_1231_extensional__subset,axiom,
    ! [F: a > probab4737552673497767871pace_a,A2: set_a,B2: set_a] :
      ( ( member7269867574344811837pace_a @ F @ ( extens3470472538004578297pace_a @ A2 ) )
     => ( ( ord_less_eq_set_a @ A2 @ B2 )
       => ( member7269867574344811837pace_a @ F @ ( extens3470472538004578297pace_a @ B2 ) ) ) ) ).

% extensional_subset
thf(fact_1232_extensional__subset,axiom,
    ! [F: a > b,A2: set_a,B2: set_a] :
      ( ( member_a_b @ F @ ( extensional_a_b @ A2 ) )
     => ( ( ord_less_eq_set_a @ A2 @ B2 )
       => ( member_a_b @ F @ ( extensional_a_b @ B2 ) ) ) ) ).

% extensional_subset
thf(fact_1233_PiE__iff,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,I2: set_Pr8456636223741192351pace_a,X: probab4737552673497767871pace_a > set_Pr8527670263787538336pace_b] :
      ( ( member6667749562321684925pace_b @ F @ ( piE_Pr1548282726383880571pace_b @ I2 @ X ) )
      = ( ! [X2: probab4737552673497767871pace_a] :
            ( ( member6485455074645559016pace_a @ X2 @ I2 )
           => ( member6485455078948787817pace_b @ ( F @ X2 ) @ ( X @ X2 ) ) )
        & ( member6667749562321684925pace_b @ F @ ( extens3782360123960272121pace_b @ I2 ) ) ) ) ).

% PiE_iff
thf(fact_1234_PiE__iff,axiom,
    ! [F: a > probab4737552677800996672pace_b,I2: set_a,X: a > set_Pr8527670263787538336pace_b] :
      ( ( member7340901614391157822pace_b @ F @ ( piE_a_4194508618861114364pace_b @ I2 @ X ) )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ I2 )
           => ( member6485455078948787817pace_b @ ( F @ X2 ) @ ( X @ X2 ) ) )
        & ( member7340901614391157822pace_b @ F @ ( extens3470472542307807098pace_b @ I2 ) ) ) ) ).

% PiE_iff
thf(fact_1235_PiE__iff,axiom,
    ! [F: probab4737552673497767871pace_a > b,I2: set_Pr8456636223741192351pace_a,X: probab4737552673497767871pace_a > set_b] :
      ( ( member5008716543664893436ce_a_b @ F @ ( piE_Pr2096403917648817466ce_a_b @ I2 @ X ) )
      = ( ! [X2: probab4737552673497767871pace_a] :
            ( ( member6485455074645559016pace_a @ X2 @ I2 )
           => ( member_b @ ( F @ X2 ) @ ( X @ X2 ) ) )
        & ( member5008716543664893436ce_a_b @ F @ ( extens1372367841095510200ce_a_b @ I2 ) ) ) ) ).

% PiE_iff
thf(fact_1236_PiE__iff,axiom,
    ! [F: b > probab4737552677800996672pace_b,I2: set_b,X: b > set_Pr8527670263787538336pace_b] :
      ( ( member1568243296417166973pace_b @ F @ ( piE_b_7645222337741899323pace_b @ I2 @ X ) )
      = ( ! [X2: b] :
            ( ( member_b @ X2 @ I2 )
           => ( member6485455078948787817pace_b @ ( F @ X2 ) @ ( X @ X2 ) ) )
        & ( member1568243296417166973pace_b @ F @ ( extens6921186261188592057pace_b @ I2 ) ) ) ) ).

% PiE_iff
thf(fact_1237_PiE__iff,axiom,
    ! [F: a > probab8624551251471354625pace_b,I2: set_a,X: a > set_Pr2974436765678502625pace_b] :
      ( ( member41169580844105599pace_b @ F @ ( piE_a_121966453474103229pace_b @ I2 @ X ) )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ I2 )
           => ( member7462078926031725098pace_b @ ( F @ X2 ) @ ( X @ X2 ) ) )
        & ( member41169580844105599pace_b @ F @ ( extens2356043851050494779pace_b @ I2 ) ) ) ) ).

% PiE_iff
thf(fact_1238_PiE__iff,axiom,
    ! [F: a > probab4737552673497767871pace_a,I2: set_a,X: a > set_Pr8456636223741192351pace_a] :
      ( ( member7269867574344811837pace_a @ F @ ( piE_a_4194508614557885563pace_a @ I2 @ X ) )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ I2 )
           => ( member6485455074645559016pace_a @ ( F @ X2 ) @ ( X @ X2 ) ) )
        & ( member7269867574344811837pace_a @ F @ ( extens3470472538004578297pace_a @ I2 ) ) ) ) ).

% PiE_iff
thf(fact_1239_PiE__iff,axiom,
    ! [F: a > b,I2: set_a,X: a > set_b] :
      ( ( member_a_b @ F @ ( piE_a_b @ I2 @ X ) )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ I2 )
           => ( member_b @ ( F @ X2 ) @ ( X @ X2 ) ) )
        & ( member_a_b @ F @ ( extensional_a_b @ I2 ) ) ) ) ).

% PiE_iff
thf(fact_1240_extensionalityI,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr8456636223741192351pace_a,G: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
      ( ( member6667749562321684925pace_b @ F @ ( extens3782360123960272121pace_b @ A2 ) )
     => ( ( member6667749562321684925pace_b @ G @ ( extens3782360123960272121pace_b @ A2 ) )
       => ( ! [X4: probab4737552673497767871pace_a] :
              ( ( member6485455074645559016pace_a @ X4 @ A2 )
             => ( ( F @ X4 )
                = ( G @ X4 ) ) )
         => ( F = G ) ) ) ) ).

% extensionalityI
thf(fact_1241_extensionalityI,axiom,
    ! [F: a > probab4737552677800996672pace_b,A2: set_a,G: a > probab4737552677800996672pace_b] :
      ( ( member7340901614391157822pace_b @ F @ ( extens3470472542307807098pace_b @ A2 ) )
     => ( ( member7340901614391157822pace_b @ G @ ( extens3470472542307807098pace_b @ A2 ) )
       => ( ! [X4: a] :
              ( ( member_a @ X4 @ A2 )
             => ( ( F @ X4 )
                = ( G @ X4 ) ) )
         => ( F = G ) ) ) ) ).

% extensionalityI
thf(fact_1242_extensionalityI,axiom,
    ! [F: probab4737552673497767871pace_a > b,A2: set_Pr8456636223741192351pace_a,G: probab4737552673497767871pace_a > b] :
      ( ( member5008716543664893436ce_a_b @ F @ ( extens1372367841095510200ce_a_b @ A2 ) )
     => ( ( member5008716543664893436ce_a_b @ G @ ( extens1372367841095510200ce_a_b @ A2 ) )
       => ( ! [X4: probab4737552673497767871pace_a] :
              ( ( member6485455074645559016pace_a @ X4 @ A2 )
             => ( ( F @ X4 )
                = ( G @ X4 ) ) )
         => ( F = G ) ) ) ) ).

% extensionalityI
thf(fact_1243_extensionalityI,axiom,
    ! [F: b > probab4737552677800996672pace_b,A2: set_b,G: b > probab4737552677800996672pace_b] :
      ( ( member1568243296417166973pace_b @ F @ ( extens6921186261188592057pace_b @ A2 ) )
     => ( ( member1568243296417166973pace_b @ G @ ( extens6921186261188592057pace_b @ A2 ) )
       => ( ! [X4: b] :
              ( ( member_b @ X4 @ A2 )
             => ( ( F @ X4 )
                = ( G @ X4 ) ) )
         => ( F = G ) ) ) ) ).

% extensionalityI
thf(fact_1244_extensionalityI,axiom,
    ! [F: a > probab8624551251471354625pace_b,A2: set_a,G: a > probab8624551251471354625pace_b] :
      ( ( member41169580844105599pace_b @ F @ ( extens2356043851050494779pace_b @ A2 ) )
     => ( ( member41169580844105599pace_b @ G @ ( extens2356043851050494779pace_b @ A2 ) )
       => ( ! [X4: a] :
              ( ( member_a @ X4 @ A2 )
             => ( ( F @ X4 )
                = ( G @ X4 ) ) )
         => ( F = G ) ) ) ) ).

% extensionalityI
thf(fact_1245_extensionalityI,axiom,
    ! [F: a > probab4737552673497767871pace_a,A2: set_a,G: a > probab4737552673497767871pace_a] :
      ( ( member7269867574344811837pace_a @ F @ ( extens3470472538004578297pace_a @ A2 ) )
     => ( ( member7269867574344811837pace_a @ G @ ( extens3470472538004578297pace_a @ A2 ) )
       => ( ! [X4: a] :
              ( ( member_a @ X4 @ A2 )
             => ( ( F @ X4 )
                = ( G @ X4 ) ) )
         => ( F = G ) ) ) ) ).

% extensionalityI
thf(fact_1246_extensionalityI,axiom,
    ! [F: a > b,A2: set_a,G: a > b] :
      ( ( member_a_b @ F @ ( extensional_a_b @ A2 ) )
     => ( ( member_a_b @ G @ ( extensional_a_b @ A2 ) )
       => ( ! [X4: a] :
              ( ( member_a @ X4 @ A2 )
             => ( ( F @ X4 )
                = ( G @ X4 ) ) )
         => ( F = G ) ) ) ) ).

% extensionalityI
thf(fact_1247_Union__eq,axiom,
    ( comple3236514525185195311pace_b
    = ( ^ [A3: set_se4320058886960055698pace_b] :
          ( collec7915783404360165627pace_b
          @ ^ [X2: probab4737552673497767871pace_a > probab4737552677800996672pace_b] :
            ? [Y6: set_Pr7742364250814120412pace_b] :
              ( ( member3909763555603355763pace_b @ Y6 @ A3 )
              & ( member6667749562321684925pace_b @ X2 @ Y6 ) ) ) ) ) ).

% Union_eq
thf(fact_1248_Union__eq,axiom,
    ( comple6646451451432703792pace_b
    = ( ^ [A3: set_se5848838506614550291pace_b] :
          ( collec5907158909762593660pace_b
          @ ^ [X2: a > probab4737552677800996672pace_b] :
            ? [Y6: set_a_3263942136899480541pace_b] :
              ( ( member1517563714087563892pace_b @ Y6 @ A3 )
              & ( member7340901614391157822pace_b @ X2 @ Y6 ) ) ) ) ) ).

% Union_eq
thf(fact_1249_Union__eq,axiom,
    ( comple2201105612168094190ce_a_b
    = ( ^ [A3: set_se3219625108814215889ce_a_b] :
          ( collec3574973839036329274ce_a_b
          @ ^ [X2: probab4737552673497767871pace_a > b] :
            ? [Y6: set_Pr8041968334489646747ce_a_b] :
              ( ( member6295589911677730098ce_a_b @ Y6 @ A3 )
              & ( member5008716543664893436ce_a_b @ X2 @ Y6 ) ) ) ) ) ).

% Union_eq
thf(fact_1250_Union__eq,axiom,
    ( comple3219233233111103983pace_b
    = ( ^ [A3: set_se2718600146793341522pace_b] :
          ( collec134500591788602811pace_b
          @ ^ [X2: b > probab4737552677800996672pace_b] :
            ? [Y6: set_b_9060095955432656540pace_b] :
              ( ( member7313717532620739891pace_b @ Y6 @ A3 )
              & ( member1568243296417166973pace_b @ X2 @ Y6 ) ) ) ) ) ).

% Union_eq
thf(fact_1251_Union__eq,axiom,
    ( comple1483613879995724273pace_b
    = ( ^ [A3: set_se5218783146767645012pace_b] :
          ( collec1289203422882586301pace_b
          @ ^ [X2: a > probab8624551251471354625pace_b] :
            ? [Y6: set_a_5989463605624649374pace_b] :
              ( ( member2156862910413884725pace_b @ Y6 @ A3 )
              & ( member41169580844105599pace_b @ X2 @ Y6 ) ) ) ) ) ).

% Union_eq
thf(fact_1252_Union__eq,axiom,
    ( comple9167635969721739439pace_a
    = ( ^ [A3: set_se6007621025939403026pace_a] :
          ( collec5836124869716247675pace_a
          @ ^ [X2: a > probab4737552673497767871pace_a] :
            ? [Y6: set_a_5785126655188516188pace_a] :
              ( ( member4038748232376599539pace_a @ Y6 @ A3 )
              & ( member7269867574344811837pace_a @ X2 @ Y6 ) ) ) ) ) ).

% Union_eq
thf(fact_1253_Union__eq,axiom,
    ( comple6589653751571696623et_a_b
    = ( ^ [A3: set_set_a_b] :
          ( collect_a_b
          @ ^ [X2: a > b] :
            ? [Y6: set_a_b] :
              ( ( member_set_a_b @ Y6 @ A3 )
              & ( member_a_b @ X2 @ Y6 ) ) ) ) ) ).

% Union_eq
thf(fact_1254_restrict__extensional,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr8456636223741192351pace_a] : ( member6667749562321684925pace_b @ ( restri5846393312276451823pace_b @ F @ A2 ) @ ( extens3782360123960272121pace_b @ A2 ) ) ).

% restrict_extensional
thf(fact_1255_restrict__extensional,axiom,
    ! [F: a > probab4737552677800996672pace_b,A2: set_a] : ( member7340901614391157822pace_b @ ( restri4927025876843904112pace_b @ F @ A2 ) @ ( extens3470472542307807098pace_b @ A2 ) ) ).

% restrict_extensional
thf(fact_1256_restrict__extensional,axiom,
    ! [F: probab4737552673497767871pace_a > b,A2: set_Pr8456636223741192351pace_a] : ( member5008716543664893436ce_a_b @ ( restri2828921175631607214ce_a_b @ F @ A2 ) @ ( extens1372367841095510200ce_a_b @ A2 ) ) ).

% restrict_extensional
thf(fact_1257_restrict__extensional,axiom,
    ! [F: b > probab4737552677800996672pace_b,A2: set_b] : ( member1568243296417166973pace_b @ ( restri8377739595724689071pace_b @ F @ A2 ) @ ( extens6921186261188592057pace_b @ A2 ) ) ).

% restrict_extensional
thf(fact_1258_restrict__extensional,axiom,
    ! [F: a > probab8624551251471354625pace_b,A2: set_a] : ( member41169580844105599pace_b @ ( restri4420077039366674481pace_b @ F @ A2 ) @ ( extens2356043851050494779pace_b @ A2 ) ) ).

% restrict_extensional
thf(fact_1259_restrict__extensional,axiom,
    ! [F: a > probab4737552673497767871pace_a,A2: set_a] : ( member7269867574344811837pace_a @ ( restri4927025872540675311pace_a @ F @ A2 ) @ ( extens3470472538004578297pace_a @ A2 ) ) ).

% restrict_extensional
thf(fact_1260_restrict__extensional,axiom,
    ! [F: a > b,A2: set_a] : ( member_a_b @ ( restrict_a_b @ F @ A2 ) @ ( extensional_a_b @ A2 ) ) ).

% restrict_extensional
thf(fact_1261_extensional__restrict,axiom,
    ! [F: probab4737552673497767871pace_a > probab4737552677800996672pace_b,A2: set_Pr8456636223741192351pace_a] :
      ( ( member6667749562321684925pace_b @ F @ ( extens3782360123960272121pace_b @ A2 ) )
     => ( ( restri5846393312276451823pace_b @ F @ A2 )
        = F ) ) ).

% extensional_restrict
thf(fact_1262_extensional__restrict,axiom,
    ! [F: a > probab4737552677800996672pace_b,A2: set_a] :
      ( ( member7340901614391157822pace_b @ F @ ( extens3470472542307807098pace_b @ A2 ) )
     => ( ( restri4927025876843904112pace_b @ F @ A2 )
        = F ) ) ).

% extensional_restrict
thf(fact_1263_extensional__restrict,axiom,
    ! [F: probab4737552673497767871pace_a > b,A2: set_Pr8456636223741192351pace_a] :
      ( ( member5008716543664893436ce_a_b @ F @ ( extens1372367841095510200ce_a_b @ A2 ) )
     => ( ( restri2828921175631607214ce_a_b @ F @ A2 )
        = F ) ) ).

% extensional_restrict
thf(fact_1264_extensional__restrict,axiom,
    ! [F: b > probab4737552677800996672pace_b,A2: set_b] :
      ( ( member1568243296417166973pace_b @ F @ ( extens6921186261188592057pace_b @ A2 ) )
     => ( ( restri8377739595724689071pace_b @ F @ A2 )
        = F ) ) ).

% extensional_restrict
thf(fact_1265_extensional__restrict,axiom,
    ! [F: a > probab8624551251471354625pace_b,A2: set_a] :
      ( ( member41169580844105599pace_b @ F @ ( extens2356043851050494779pace_b @ A2 ) )
     => ( ( restri4420077039366674481pace_b @ F @ A2 )
        = F ) ) ).

% extensional_restrict
thf(fact_1266_extensional__restrict,axiom,
    ! [F: a > probab4737552673497767871pace_a,A2: set_a] :
      ( ( member7269867574344811837pace_a @ F @ ( extens3470472538004578297pace_a @ A2 ) )
     => ( ( restri4927025872540675311pace_a @ F @ A2 )
        = F ) ) ).

% extensional_restrict
thf(fact_1267_extensional__restrict,axiom,
    ! [F: a > b,A2: set_a] :
      ( ( member_a_b @ F @ ( extensional_a_b @ A2 ) )
     => ( ( restrict_a_b @ F @ A2 )
        = F ) ) ).

% extensional_restrict
thf(fact_1268_UN__E,axiom,
    ! [B: a > b,B2: ( a > b ) > set_a_b,A2: set_a_b] :
      ( ( member_a_b @ B @ ( comple6589653751571696623et_a_b @ ( image_a_b_set_a_b @ B2 @ A2 ) ) )
     => ~ ! [X4: a > b] :
            ( ( member_a_b @ X4 @ A2 )
           => ~ ( member_a_b @ B @ ( B2 @ X4 ) ) ) ) ).

% UN_E
thf(fact_1269_UN__E,axiom,
    ! [B: a > probab4737552677800996672pace_b,B2: ( a > b ) > set_a_3263942136899480541pace_b,A2: set_a_b] :
      ( ( member7340901614391157822pace_b @ B @ ( comple6646451451432703792pace_b @ ( image_2483489791776158154pace_b @ B2 @ A2 ) ) )
     => ~ ! [X4: a > b] :
            ( ( member_a_b @ X4 @ A2 )
           => ~ ( member7340901614391157822pace_b @ B @ ( B2 @ X4 ) ) ) ) ).

% UN_E
thf(fact_1270_UN__E,axiom,
    ! [B: probab4737552673497767871pace_a > b,B2: ( a > b ) > set_Pr8041968334489646747ce_a_b,A2: set_a_b] :
      ( ( member5008716543664893436ce_a_b @ B @ ( comple2201105612168094190ce_a_b @ ( image_7261515989366324360ce_a_b @ B2 @ A2 ) ) )
     => ~ ! [X4: a > b] :
            ( ( member_a_b @ X4 @ A2 )
           => ~ ( member5008716543664893436ce_a_b @ B @ ( B2 @ X4 ) ) ) ) ).

% UN_E
thf(fact_1271_UN__E,axiom,
    ! [B: b > probab4737552677800996672pace_b,B2: ( a > b ) > set_b_9060095955432656540pace_b,A2: set_a_b] :
      ( ( member1568243296417166973pace_b @ B @ ( comple3219233233111103983pace_b @ ( image_8279643610309334153pace_b @ B2 @ A2 ) ) )
     => ~ ! [X4: a > b] :
            ( ( member_a_b @ X4 @ A2 )
           => ~ ( member1568243296417166973pace_b @ B @ ( B2 @ X4 ) ) ) ) ).

% UN_E
thf(fact_1272_UN__E,axiom,
    ! [B: a > probab4737552673497767871pace_a,B2: ( a > b ) > set_a_5785126655188516188pace_a,A2: set_a_b] :
      ( ( member7269867574344811837pace_a @ B @ ( comple9167635969721739439pace_a @ ( image_5004674310065193801pace_a @ B2 @ A2 ) ) )
     => ~ ! [X4: a > b] :
            ( ( member_a_b @ X4 @ A2 )
           => ~ ( member7269867574344811837pace_a @ B @ ( B2 @ X4 ) ) ) ) ).

% UN_E
thf(fact_1273_UN__E,axiom,
    ! [B: a > b,B2: ( a > probab4737552677800996672pace_b ) > set_a_b,A2: set_a_3263942136899480541pace_b] :
      ( ( member_a_b @ B @ ( comple6589653751571696623et_a_b @ ( image_3320987880458065994et_a_b @ B2 @ A2 ) ) )
     => ~ ! [X4: a > probab4737552677800996672pace_b] :
            ( ( member7340901614391157822pace_b @ X4 @ A2 )
           => ~ ( member_a_b @ B @ ( B2 @ X4 ) ) ) ) ).

% UN_E
thf(fact_1274_UN__E,axiom,
    ! [B: a > b,B2: ( probab4737552673497767871pace_a > b ) > set_a_b,A2: set_Pr8041968334489646747ce_a_b] :
      ( ( member_a_b @ B @ ( comple6589653751571696623et_a_b @ ( image_8419905865881351688et_a_b @ B2 @ A2 ) ) )
     => ~ ! [X4: probab4737552673497767871pace_a > b] :
            ( ( member5008716543664893436ce_a_b @ X4 @ A2 )
           => ~ ( member_a_b @ B @ ( B2 @ X4 ) ) ) ) ).

% UN_E
thf(fact_1275_UN__E,axiom,
    ! [B: a > b,B2: ( b > probab4737552677800996672pace_b ) > set_a_b,A2: set_b_9060095955432656540pace_b] :
      ( ( member_a_b @ B @ ( comple6589653751571696623et_a_b @ ( image_6723652579854267529et_a_b @ B2 @ A2 ) ) )
     => ~ ! [X4: b > probab4737552677800996672pace_b] :
            ( ( member1568243296417166973pace_b @ X4 @ A2 )
           => ~ ( member_a_b @ B @ ( B2 @ X4 ) ) ) ) ).

% UN_E
thf(fact_1276_UN__E,axiom,
    ! [B: a > b,B2: ( a > probab4737552673497767871pace_a ) > set_a_b,A2: set_a_5785126655188516188pace_a] :
      ( ( member_a_b @ B @ ( comple6589653751571696623et_a_b @ ( image_1059268598997287753et_a_b @ B2 @ A2 ) ) )
     => ~ ! [X4: a > probab4737552673497767871pace_a] :
            ( ( member7269867574344811837pace_a @ X4 @ A2 )
           => ~ ( member_a_b @ B @ ( B2 @ X4 ) ) ) ) ).

% UN_E
thf(fact_1277_UN__E,axiom,
    ! [B: probab4737552673497767871pace_a > probab4737552677800996672pace_b,B2: ( a > b ) > set_Pr7742364250814120412pace_b,A2: set_a_b] :
      ( ( member6667749562321684925pace_b @ B @ ( comple3236514525185195311pace_b @ ( image_1600672952583092169pace_b @ B2 @ A2 ) ) )
     => ~ ! [X4: a > b] :
            ( ( member_a_b @ X4 @ A2 )
           => ~ ( member6667749562321684925pace_b @ B @ ( B2 @ X4 ) ) ) ) ).

% UN_E

% Helper facts (15)
thf(help_If_2_1_If_001_062_Itf__a_Mtf__b_J_T,axiom,
    ! [X3: a > b,Y2: a > b] :
      ( ( if_a_b @ $false @ X3 @ Y2 )
      = Y2 ) ).

thf(help_If_1_1_If_001_062_Itf__a_Mtf__b_J_T,axiom,
    ! [X3: a > b,Y2: a > b] :
      ( ( if_a_b @ $true @ X3 @ Y2 )
      = X3 ) ).

thf(help_If_2_1_If_001_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mtf__b_J_T,axiom,
    ! [X3: probab4737552673497767871pace_a > b,Y2: probab4737552673497767871pace_a > b] :
      ( ( if_Pro3290040433592364319ce_a_b @ $false @ X3 @ Y2 )
      = Y2 ) ).

thf(help_If_1_1_If_001_062_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_Mtf__b_J_T,axiom,
    ! [X3: probab4737552673497767871pace_a > b,Y2: probab4737552673497767871pace_a > b] :
      ( ( if_Pro3290040433592364319ce_a_b @ $true @ X3 @ Y2 )
      = X3 ) ).

thf(help_If_2_1_If_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_T,axiom,
    ! [X3: a > probab4737552673497767871pace_a,Y2: a > probab4737552673497767871pace_a] :
      ( ( if_a_P5551191464272282720pace_a @ $false @ X3 @ Y2 )
      = Y2 ) ).

thf(help_If_1_1_If_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_T,axiom,
    ! [X3: a > probab4737552673497767871pace_a,Y2: a > probab4737552673497767871pace_a] :
      ( ( if_a_P5551191464272282720pace_a @ $true @ X3 @ Y2 )
      = X3 ) ).

thf(help_If_2_1_If_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_T,axiom,
    ! [X3: a > probab4737552677800996672pace_b,Y2: a > probab4737552677800996672pace_b] :
      ( ( if_a_P5622225504318628705pace_b @ $false @ X3 @ Y2 )
      = Y2 ) ).

thf(help_If_1_1_If_001_062_Itf__a_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_T,axiom,
    ! [X3: a > probab4737552677800996672pace_b,Y2: a > probab4737552677800996672pace_b] :
      ( ( if_a_P5622225504318628705pace_b @ $true @ X3 @ Y2 )
      = X3 ) ).

thf(help_If_2_1_If_001_062_Itf__b_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_T,axiom,
    ! [X3: b > probab4737552677800996672pace_b,Y2: b > probab4737552677800996672pace_b] :
      ( ( if_b_P9072939223199413664pace_b @ $false @ X3 @ Y2 )
      = Y2 ) ).

thf(help_If_1_1_If_001_062_Itf__b_Mt__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_T,axiom,
    ! [X3: b > probab4737552677800996672pace_b,Y2: b > probab4737552677800996672pace_b] :
      ( ( if_b_P9072939223199413664pace_b @ $true @ X3 @ Y2 )
      = X3 ) ).

thf(help_If_2_1_If_001t__QuasiBorel__Oquasi____borel_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_T,axiom,
    ! [X3: quasi_3360289866124776421pace_a,Y2: quasi_3360289866124776421pace_a] :
      ( ( if_qua2296460398793721259pace_a @ $false @ X3 @ Y2 )
      = Y2 ) ).

thf(help_If_1_1_If_001t__QuasiBorel__Oquasi____borel_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__a_J_J_T,axiom,
    ! [X3: quasi_3360289866124776421pace_a,Y2: quasi_3360289866124776421pace_a] :
      ( ( if_qua2296460398793721259pace_a @ $true @ X3 @ Y2 )
      = X3 ) ).

thf(help_If_3_1_If_001t__QuasiBorel__Oquasi____borel_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__QuasiBorel__Oquasi____borel_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_T,axiom,
    ! [X3: quasi_3431323906171122406pace_b,Y2: quasi_3431323906171122406pace_b] :
      ( ( if_qua2367494438840067244pace_b @ $false @ X3 @ Y2 )
      = Y2 ) ).

thf(help_If_1_1_If_001t__QuasiBorel__Oquasi____borel_It__Probability____Space____QuasiBorel__Oqbs____prob____space_Itf__b_J_J_T,axiom,
    ! [X3: quasi_3431323906171122406pace_b,Y2: quasi_3431323906171122406pace_b] :
      ( ( if_qua2367494438840067244pace_b @ $true @ X3 @ Y2 )
      = X3 ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ( member6667749562321684925pace_b
    @ ^ [X2: probab4737552673497767871pace_a] : ( monad_qbs_bind_a_b @ X2 @ f )
    @ ( qbs_mo9092548148132419897pace_b @ ( monad_monadP_qbs_a @ x ) @ ( monad_monadP_qbs_b @ y ) ) ) ).

%------------------------------------------------------------------------------