%------------------------------------------------------------------------------
% 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/0007_Exponent_QuasiBorel/prob_00171_006302__15304892_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 2729 ( 712 unt;1456 typ;   0 def)
%            Number of atoms       : 2465 (1175 equ;   0 cnn)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives : 11209 ( 113   ~;   0   |;  80   &;10062   @)
%                                         (   0 <=>; 954  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Number of types       :  352 ( 351 usr)
%            Number of type conns  : 5148 (5148   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1106 (1105 usr;  18 con; 0-5 aty)
%            Number of variables   : 3976 ( 637   ^;3297   !;  42   ?;3976   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 14:09:55.817
%------------------------------------------------------------------------------
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thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_062_It__Real__Oreal_M_Eo_J_J_J,type,
    set_real_real_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_062_I_Eo_Mt__Real__Oreal_J_J_J,type,
    set_real_o_real: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Real__Oreal_J_J,type,
    set_Pr4180788328258511119a_real: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_J,type,
    set_Pr6589227744151929853real_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__b_M_062_Itf__a_M_062_Itf__b_Mtf__c_J_J_J_J,type,
    set_b_a_b_c: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_Eo_M_062_Itf__a_M_062_Itf__b_Mtf__c_J_J_J_J,type,
    set_o_a_b_c: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_062_It__Real__Oreal_M_Eo_J_J,type,
    quasi_borel_real_o: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_062_I_Eo_Mt__Real__Oreal_J_J,type,
    quasi_borel_o_real: $tType ).

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

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_062_Itf__b_Mtf__c_J_J_J,type,
    set_real_b_c: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_M_062_Itf__a_Mtf__c_J_J_J,type,
    set_real_a_c: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
    produc2422161461964618553l_real: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_M_062_Itf__b_Mtf__c_J_J_J,type,
    set_nat_b_c: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_M_062_Itf__a_Mtf__c_J_J_J,type,
    set_nat_a_c: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    set_Product_prod_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Nat__Onat_J,type,
    produc3741383161447143261al_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Real__Oreal_J,type,
    produc7716430852924023517t_real: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_Itf__b_Mtf__c_J_Mtf__b_J,type,
    product_prod_b_c_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    product_prod_nat_nat: $tType ).

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

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_062_Itf__b_Mtf__c_J_J,type,
    quasi_borel_b_c: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_062_Itf__a_Mtf__c_J_J,type,
    quasi_borel_a_c: $tType ).

thf(ty_n_t__Sigma____Algebra__Omeasure_I_062_Itf__b_Mtf__c_J_J,type,
    sigma_measure_b_c: $tType ).

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

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

thf(ty_n_t__Set__Oset_I_062_Itf__a_M_062_Itf__b_Mtf__c_J_J_J,type,
    set_a_b_c: $tType ).

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

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mt__Real__Oreal_J,type,
    product_prod_b_real: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__Real__Oreal_J,type,
    product_prod_a_real: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mtf__b_J,type,
    product_prod_real_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J,type,
    product_prod_real_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_Eo_M_062_Itf__b_Mtf__c_J_J_J,type,
    set_o_b_c: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_Eo_M_062_Itf__a_Mtf__c_J_J_J,type,
    set_o_a_c: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_It__Real__Oreal_J,type,
    quasi_borel_real: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_M_Eo_J,type,
    product_prod_real_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mtf__b_J,type,
    product_prod_nat_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mtf__a_J,type,
    product_prod_nat_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Real__Oreal_J,type,
    product_prod_o_real: $tType ).

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

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

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

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
    product_prod_nat_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
    product_prod_o_nat: $tType ).

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

thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mtf__c_J_J,type,
    set_real_c: $tType ).

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

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

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

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

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

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

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

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

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
    product_prod_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__a_J,type,
    product_prod_b_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    product_prod_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
    product_prod_a_a: $tType ).

thf(ty_n_t__QuasiBorel__Oquasi____borel_Itf__c_J,type,
    quasi_borel_c: $tType ).

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

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

thf(ty_n_t__Sigma____Algebra__Omeasure_Itf__c_J,type,
    sigma_measure_c: $tType ).

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

thf(ty_n_t__QuasiBorel__Oquasi____borel_I_Eo_J,type,
    quasi_borel_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    product_prod_o_o: $tType ).

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

thf(ty_n_t__Set__Oset_I_062_Itf__b_Mtf__c_J_J,type,
    set_b_c: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__a_Mtf__c_J_J,type,
    set_a_c: $tType ).

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

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

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

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

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

thf(ty_n_t__Set__Oset_Itf__c_J,type,
    set_c: $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__Set__Oset_I_Eo_J,type,
    set_o: $tType ).

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

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

thf(ty_n_tf__c,type,
    c: $tType ).

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

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

% Explicit typings (1105)
thf(sy_c_BNF__Def_Oconvol_001_062_Itf__a_M_062_Itf__b_Mtf__c_J_J_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mtf__c_J_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mtf__c_J,type,
    bNF_co2532616626889521512_a_b_c: ( ( a > b > c ) > product_prod_a_b > c ) > ( ( a > b > c ) > product_prod_a_b > c ) > ( a > b > c ) > produc1454182667395973467_a_b_c ).

thf(sy_c_BNF__Def_Oconvol_001_Eo_001_Eo_001_Eo,type,
    bNF_convol_o_o_o: ( $o > $o ) > ( $o > $o ) > $o > product_prod_o_o ).

thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_co805650143699787099at_nat: ( nat > nat ) > ( nat > nat ) > nat > product_prod_nat_nat ).

thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Real__Oreal_J_001t__Nat__Onat_001t__Real__Oreal,type,
    bNF_co3215693860977014834t_real: ( produc7716430852924023517t_real > nat ) > ( produc7716430852924023517t_real > real ) > produc7716430852924023517t_real > produc7716430852924023517t_real ).

thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Real__Oreal_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Real__Oreal_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Real__Oreal_J,type,
    bNF_co2828654319395810420t_real: ( produc7716430852924023517t_real > produc7716430852924023517t_real ) > ( produc7716430852924023517t_real > produc7716430852924023517t_real ) > produc7716430852924023517t_real > produc2059033415072754535t_real ).

thf(sy_c_BNF__Def_Oconvol_001t__Real__Oreal_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mtf__c_J_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mtf__c_J,type,
    bNF_co3546090298090268817_a_b_c: ( real > product_prod_a_b > c ) > ( real > product_prod_a_b > c ) > real > produc1454182667395973467_a_b_c ).

thf(sy_c_BNF__Def_Oconvol_001t__Real__Oreal_001_Eo_001_Eo,type,
    bNF_convol_real_o_o: ( real > $o ) > ( real > $o ) > real > product_prod_o_o ).

thf(sy_c_BNF__Def_Oconvol_001t__Real__Oreal_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_co2503443643428117431at_nat: ( real > nat ) > ( real > nat ) > real > product_prod_nat_nat ).

thf(sy_c_BNF__Def_Oconvol_001t__Real__Oreal_001t__Nat__Onat_001t__Real__Oreal,type,
    bNF_co3869861653827910419t_real: ( real > nat ) > ( real > real ) > real > produc7716430852924023517t_real ).

thf(sy_c_BNF__Def_Oconvol_001t__Real__Oreal_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Real__Oreal_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Real__Oreal_J,type,
    bNF_co3113411965631273301t_real: ( real > produc7716430852924023517t_real ) > ( real > produc7716430852924023517t_real ) > real > produc2059033415072754535t_real ).

thf(sy_c_BNF__Def_Oconvol_001t__Real__Oreal_001t__Real__Oreal_001t__Real__Oreal,type,
    bNF_co7388595451723801839l_real: ( real > real ) > ( real > real ) > real > produc2422161461964618553l_real ).

thf(sy_c_BNF__Def_OfstOp_001t__Nat__Onat_001t__Real__Oreal_001t__Real__Oreal,type,
    bNF_fs3113317720638777948l_real: ( nat > real > $o ) > ( real > real > $o ) > produc7716430852924023517t_real > produc7716430852924023517t_real ).

thf(sy_c_BNF__Def_OfstOp_001t__Real__Oreal_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Real__Oreal,type,
    bNF_fs4413835580006596598b_real: ( real > product_prod_a_b > $o ) > ( product_prod_a_b > real > $o ) > produc2422161461964618553l_real > produc1405624045518934769od_a_b ).

thf(sy_c_BNF__Def_OfstOp_001t__Real__Oreal_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001tf__a,type,
    bNF_fs1099215190774911796_a_b_a: ( real > product_prod_a_b > $o ) > ( product_prod_a_b > a > $o ) > product_prod_real_a > produc1405624045518934769od_a_b ).

thf(sy_c_BNF__Def_OfstOp_001t__Real__Oreal_001t__Real__Oreal_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    bNF_fs1652773232771623964od_a_b: ( real > real > $o ) > ( real > product_prod_a_b > $o ) > produc1405624045518934769od_a_b > produc2422161461964618553l_real ).

thf(sy_c_BNF__Def_OfstOp_001t__Real__Oreal_001t__Real__Oreal_001t__Real__Oreal,type,
    bNF_fs3847565544535062584l_real: ( real > real > $o ) > ( real > real > $o ) > produc2422161461964618553l_real > produc2422161461964618553l_real ).

thf(sy_c_BNF__Def_OfstOp_001t__Real__Oreal_001t__Real__Oreal_001tf__a,type,
    bNF_fs6109789071227381362real_a: ( real > real > $o ) > ( real > a > $o ) > product_prod_real_a > produc2422161461964618553l_real ).

thf(sy_c_BNF__Def_OfstOp_001t__Real__Oreal_001tf__a_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    bNF_fs5697544725373665032od_a_b: ( real > a > $o ) > ( a > product_prod_a_b > $o ) > produc1405624045518934769od_a_b > product_prod_real_a ).

thf(sy_c_BNF__Def_OfstOp_001t__Real__Oreal_001tf__a_001t__Real__Oreal,type,
    bNF_fs5479770303754431564a_real: ( real > a > $o ) > ( a > real > $o ) > produc2422161461964618553l_real > product_prod_real_a ).

thf(sy_c_BNF__Def_OfstOp_001t__Real__Oreal_001tf__a_001tf__a,type,
    bNF_fstOp_real_a_a: ( real > a > $o ) > ( a > a > $o ) > product_prod_real_a > product_prod_real_a ).

thf(sy_c_BNF__Def_OfstOp_001t__Real__Oreal_001tf__b_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    bNF_fs5058104425041848903od_a_b: ( real > b > $o ) > ( b > product_prod_a_b > $o ) > produc1405624045518934769od_a_b > product_prod_real_b ).

thf(sy_c_BNF__Def_OfstOp_001t__Real__Oreal_001tf__b_001t__Real__Oreal,type,
    bNF_fs1852616882087786445b_real: ( real > b > $o ) > ( b > real > $o ) > produc2422161461964618553l_real > product_prod_real_b ).

thf(sy_c_BNF__Def_OfstOp_001t__Real__Oreal_001tf__b_001tf__a,type,
    bNF_fstOp_real_b_a: ( real > b > $o ) > ( b > a > $o ) > product_prod_real_a > product_prod_real_b ).

thf(sy_c_BNF__Def_OfstOp_001tf__a_001t__Real__Oreal_001tf__b,type,
    bNF_fstOp_a_real_b: ( a > real > $o ) > ( real > b > $o ) > product_prod_a_b > product_prod_a_real ).

thf(sy_c_BNF__Def_OfstOp_001tf__a_001tf__b_001tf__b,type,
    bNF_fstOp_a_b_b: ( a > b > $o ) > ( b > b > $o ) > product_prod_a_b > product_prod_a_b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Nat__Onat_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Real__Oreal,type,
    bNF_pi3352055721067236384b_real: ( nat > product_prod_a_b > $o ) > ( product_prod_a_b > real > $o ) > nat > real > product_prod_a_b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Nat__Onat_001tf__a_001t__Real__Oreal,type,
    bNF_pi4581077271498945142a_real: ( nat > a > $o ) > ( a > real > $o ) > nat > real > a ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Nat__Onat_001tf__b_001t__Real__Oreal,type,
    bNF_pi953923849832300023b_real: ( nat > b > $o ) > ( b > real > $o ) > nat > real > b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Real__Oreal_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Real__Oreal,type,
    bNF_pi353393763585934404b_real: ( real > product_prod_a_b > $o ) > ( product_prod_a_b > real > $o ) > real > real > product_prod_a_b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Real__Oreal_001t__Real__Oreal_001tf__a,type,
    bNF_pi8761527169845995712real_a: ( real > real > $o ) > ( real > a > $o ) > real > a > real ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Real__Oreal_001tf__a_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    bNF_pi215755999452490554od_a_b: ( real > a > $o ) > ( a > product_prod_a_b > $o ) > real > product_prod_a_b > a ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Real__Oreal_001tf__a_001t__Real__Oreal,type,
    bNF_pi8131508402373045914a_real: ( real > a > $o ) > ( a > real > $o ) > real > real > a ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Real__Oreal_001tf__a_001tf__a,type,
    bNF_pi8219073671537963920al_a_a: ( real > a > $o ) > ( a > a > $o ) > real > a > a ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Real__Oreal_001tf__b_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    bNF_pi8799687735975450233od_a_b: ( real > b > $o ) > ( b > product_prod_a_b > $o ) > real > product_prod_a_b > b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Real__Oreal_001tf__b_001t__Real__Oreal,type,
    bNF_pi4504354980706400795b_real: ( real > b > $o ) > ( b > real > $o ) > real > real > b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Real__Oreal_001tf__b_001tf__a,type,
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    comp_P7740967659496281733od_a_b: ( produc7929879615859924995b_real > real ) > ( produc1405624045518934769od_a_b > produc7929879615859924995b_real ) > produc1405624045518934769od_a_b > real ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_M_Eo_J_001_Eo_001t__Real__Oreal,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Nat__Onat_J_001_Eo_001t__Real__Oreal,type,
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    comp_P6248124061026825784t_real: ( produc3741383161447143261al_nat > nat ) > ( real > produc3741383161447143261al_nat ) > real > nat ).

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    comp_P8173869841510096599b_real: ( produc1405624045518934769od_a_b > product_prod_a_b ) > ( produc7929879615859924995b_real > produc1405624045518934769od_a_b ) > produc7929879615859924995b_real > product_prod_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    comp_P1649614271169106373od_a_b: ( produc1405624045518934769od_a_b > product_prod_a_b ) > ( produc1405624045518934769od_a_b > produc1405624045518934769od_a_b ) > produc1405624045518934769od_a_b > product_prod_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Real__Oreal_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Real__Oreal_J,type,
    comp_P7154842541956054149b_real: ( produc1405624045518934769od_a_b > real ) > ( produc7929879615859924995b_real > produc1405624045518934769od_a_b ) > produc7929879615859924995b_real > real ).

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    comp_P630586971615063923od_a_b: ( produc1405624045518934769od_a_b > real ) > ( produc1405624045518934769od_a_b > produc1405624045518934769od_a_b ) > produc1405624045518934769od_a_b > real ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Real__Oreal_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
    comp_P5152745405570707767l_real: ( produc1405624045518934769od_a_b > real ) > ( produc2422161461964618553l_real > produc1405624045518934769od_a_b ) > produc2422161461964618553l_real > real ).

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    comp_P6767852656780618441real_a: ( produc1405624045518934769od_a_b > real ) > ( product_prod_real_a > produc1405624045518934769od_a_b ) > product_prod_real_a > real ).

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    comp_P5065359899111419289t_real: ( produc2422161461964618553l_real > real ) > ( produc7716430852924023517t_real > produc2422161461964618553l_real ) > produc7716430852924023517t_real > real ).

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    comp_P544700997026044725od_a_b: ( produc2422161461964618553l_real > real ) > ( produc1405624045518934769od_a_b > produc2422161461964618553l_real ) > produc1405624045518934769od_a_b > real ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_001t__Real__Oreal_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
    comp_P3276979369905350645l_real: ( produc2422161461964618553l_real > real ) > ( produc2422161461964618553l_real > produc2422161461964618553l_real ) > produc2422161461964618553l_real > real ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_001t__Real__Oreal_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J,type,
    comp_P1589298742348195979real_a: ( produc2422161461964618553l_real > real ) > ( product_prod_real_a > produc2422161461964618553l_real ) > product_prod_real_a > real ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_001t__Real__Oreal_001t__Real__Oreal,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_001t__Real__Oreal_001_Eo,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_001t__Real__Oreal_001t__Nat__Onat,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_001t__Real__Oreal_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    comp_P7339791398657499593od_a_b: ( product_prod_real_a > real ) > ( produc1405624045518934769od_a_b > product_prod_real_a ) > produc1405624045518934769od_a_b > real ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_001t__Real__Oreal_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
    comp_P549788833721629281l_real: ( product_prod_real_a > real ) > ( produc2422161461964618553l_real > product_prod_real_a ) > produc2422161461964618553l_real > real ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_001t__Real__Oreal_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J,type,
    comp_P62423180901884703real_a: ( product_prod_real_a > real ) > ( product_prod_real_a > product_prod_real_a ) > product_prod_real_a > real ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_001t__Real__Oreal_001t__Product____Type__Oprod_Itf__a_Mt__Real__Oreal_J,type,
    comp_P8768528715489323313a_real: ( product_prod_real_a > real ) > ( product_prod_a_real > product_prod_real_a ) > product_prod_a_real > real ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_001t__Real__Oreal_001t__Real__Oreal,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_001tf__a_001_Eo,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_001tf__a_001t__Nat__Onat,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_001tf__a_001t__Product____Type__Oprod_Itf__a_Mt__Real__Oreal_J,type,
    comp_P8403000611219577773a_real: ( product_prod_real_a > a ) > ( product_prod_a_real > product_prod_real_a ) > product_prod_a_real > a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_001tf__a_001t__Real__Oreal,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_001tf__c_001t__Real__Oreal,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__b_J_001t__Real__Oreal_001t__Product____Type__Oprod_Itf__b_Mt__Real__Oreal_J,type,
    comp_P8514091664527323699b_real: ( product_prod_real_b > real ) > ( product_prod_b_real > product_prod_real_b ) > product_prod_b_real > real ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__b_J_001tf__b_001t__Product____Type__Oprod_Itf__b_Mt__Real__Oreal_J,type,
    comp_P488263325884094958b_real: ( product_prod_real_b > b ) > ( product_prod_b_real > product_prod_real_b ) > product_prod_b_real > b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__b_J_001tf__c_001t__Real__Oreal,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mt__Real__Oreal_J_001t__Real__Oreal_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J,type,
    comp_P3982218943028520241real_a: ( product_prod_a_real > real ) > ( product_prod_real_a > product_prod_a_real ) > product_prod_real_a > real ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mt__Real__Oreal_J_001tf__a_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J,type,
    comp_P3994435691685055241real_a: ( product_prod_a_real > a ) > ( product_prod_real_a > product_prod_a_real ) > product_prod_real_a > a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001tf__a_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    comp_P1447306808648735059od_a_b: ( product_prod_a_b > produc2233330766403592615od_a_b ) > ( produc1405624045518934769od_a_b > product_prod_a_b ) > produc1405624045518934769od_a_b > produc2233330766403592615od_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    comp_P8432976128825459156od_a_b: ( product_prod_a_b > product_prod_a_b ) > ( produc1405624045518934769od_a_b > product_prod_a_b ) > produc1405624045518934769od_a_b > product_prod_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001tf__a_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001tf__a_001t__Product____Type__Oprod_Itf__b_Mtf__a_J,type,
    comp_P9084872743345139181od_b_a: ( product_prod_a_b > a ) > ( product_prod_b_a > product_prod_a_b ) > product_prod_b_a > a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001tf__b_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001tf__b_001t__Product____Type__Oprod_Itf__b_Mtf__a_J,type,
    comp_P8445432443013323052od_b_a: ( product_prod_a_b > b ) > ( product_prod_b_a > product_prod_a_b ) > product_prod_b_a > b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001tf__c_001t__Real__Oreal,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mt__Real__Oreal_J_001t__Real__Oreal_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__b_J,type,
    comp_P6914732054928830003real_b: ( product_prod_b_real > real ) > ( product_prod_real_b > product_prod_b_real ) > product_prod_real_b > real ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mt__Real__Oreal_J_001tf__b_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__b_J,type,
    comp_P3883066875231310154real_b: ( product_prod_b_real > b ) > ( product_prod_real_b > product_prod_b_real ) > product_prod_real_b > b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mtf__a_J_001tf__a_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mtf__a_J_001tf__b_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
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thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mtf__b_J_001tf__b_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
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thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001_062_Itf__a_M_062_Itf__b_Mtf__c_J_J_001t__Real__Oreal,type,
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thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001_062_Itf__a_Mtf__c_J_001t__Real__Oreal,type,
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thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001_062_Itf__b_Mtf__c_J_001t__Real__Oreal,type,
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thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Extended____Nonnegative____Real__Oennreal_001t__Extended____Nonnegative____Real__Oennreal,type,
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thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Nat__Onat_001_Eo,type,
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thf(sy_c_member_001_062_It__Real__Oreal_M_062_Itf__b_Mtf__c_J_J,type,
    member_real_b_c: ( real > b > c ) > set_real_b_c > $o ).

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

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

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

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    member8624048055576332635od_o_o: ( real > product_prod_o_o ) > set_re107118480509647250od_o_o > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
    member7334495436961965817_o_nat: ( real > product_prod_o_nat ) > set_re4428436886758594328_o_nat > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_I_Eo_Mt__Real__Oreal_J_J,type,
    member8223553389164786773o_real: ( real > product_prod_o_real ) > set_re6310451797962030196o_real > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
    member8382098559140269471_nat_o: ( real > product_prod_nat_o ) > set_re8292840631325018814_nat_o > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    member278708040391457717at_nat: ( real > product_prod_nat_nat ) > set_re3218616107942652140at_nat > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Real__Oreal_J_J,type,
    member969486235890772753t_real: ( real > produc7716430852924023517t_real ) > set_re7361189984880485448t_real > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Real__Oreal_J_J,type,
    member7738959517937940581b_real: ( real > produc7929879615859924995b_real ) > set_re4638290270145833604b_real > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_It__Real__Oreal_M_Eo_J_J,type,
    member6586820919158520515real_o: ( real > product_prod_real_o ) > set_re2415389523565734882real_o > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_It__Real__Oreal_Mt__Extended____Nonnegative____Real__Oennreal_J_J,type,
    member4263462704469908217nnreal: ( real > produc1565745902094061253nnreal ) > set_re6219555973709217840nnreal > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_It__Real__Oreal_Mt__Nat__Onat_J_J,type,
    member4159480375084375953al_nat: ( real > produc3741383161447143261al_nat ) > set_re940251665846180040al_nat > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    member798328933530555475od_a_b: ( real > produc1405624045518934769od_a_b ) > set_re6443464594289979250od_a_b > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    member9086635009091248365l_real: ( real > produc2422161461964618553l_real ) > set_re3939601646622484004l_real > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_J,type,
    member1006887528422719913real_a: ( real > product_prod_real_a ) > set_re3364297189494924744real_a > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_It__Real__Oreal_Mtf__b_J_J,type,
    member1077921568469065898real_b: ( real > product_prod_real_b ) > set_re843112671205889097real_b > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_Itf__a_Mt__Real__Oreal_J_J,type,
    member7821820149384076987a_real: ( real > product_prod_a_real ) > set_re2326067922770778586a_real > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    member4641211897452655452od_a_b: ( real > product_prod_a_b ) > set_re1895575558621013779od_a_b > $o ).

thf(sy_c_member_001_062_It__Real__Oreal_Mt__Product____Type__Oprod_Itf__b_Mt__Real__Oreal_J_J,type,
    member5043115841524054460b_real: ( real > product_prod_b_real ) > set_re3618862337447380059b_real > $o ).

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

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

thf(sy_c_member_001_062_It__Real__Oreal_Mtf__c_J,type,
    member_real_c: ( real > c ) > set_real_c > $o ).

thf(sy_c_member_001_062_Itf__a_M_062_It__Real__Oreal_M_062_Itf__b_Mtf__c_J_J_J,type,
    member_a_real_b_c: ( a > real > b > c ) > set_a_real_b_c > $o ).

thf(sy_c_member_001_062_Itf__a_M_062_Itf__b_Mtf__c_J_J,type,
    member_a_b_c: ( a > b > c ) > set_a_b_c > $o ).

thf(sy_c_member_001_062_Itf__a_Mt__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J_J,type,
    member1097457462631741663real_a: ( a > product_prod_real_a ) > set_a_1226877085566163734real_a > $o ).

thf(sy_c_member_001_062_Itf__a_Mt__Product____Type__Oprod_Itf__a_Mt__Real__Oreal_J_J,type,
    member7912390083593098737a_real: ( a > product_prod_a_real ) > set_a_188647818842017576a_real > $o ).

thf(sy_c_member_001_062_Itf__a_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    member2028809742453662374od_a_b: ( a > product_prod_a_b ) > set_a_4308501811888595525od_a_b > $o ).

thf(sy_c_member_001_062_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__a_J_J,type,
    member1322126701802329700od_b_a: ( a > product_prod_b_a ) > set_a_256984723821451011od_b_a > $o ).

thf(sy_c_member_001_062_Itf__a_Mtf__c_J,type,
    member_a_c: ( a > c ) > set_a_c > $o ).

thf(sy_c_member_001_062_Itf__b_M_062_Itf__a_M_062_Itf__b_Mtf__c_J_J_J,type,
    member_b_a_b_c: ( b > a > b > c ) > set_b_a_b_c > $o ).

thf(sy_c_member_001_062_Itf__b_Mt__Product____Type__Oprod_It__Real__Oreal_Mtf__b_J_J,type,
    member5108440089302923873real_b: ( b > product_prod_real_b ) > set_b_3685635715425631128real_b > $o ).

thf(sy_c_member_001_062_Itf__b_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    member1389369442121846245od_a_b: ( b > product_prod_a_b ) > set_b_2972451191935901188od_a_b > $o ).

thf(sy_c_member_001_062_Itf__b_Mt__Product____Type__Oprod_Itf__b_Mt__Real__Oreal_J_J,type,
    member9073634362357912435b_real: ( b > product_prod_b_real ) > set_b_6461385381667122090b_real > $o ).

thf(sy_c_member_001_062_Itf__b_Mt__Product____Type__Oprod_Itf__b_Mtf__a_J_J,type,
    member682686401470513571od_b_a: ( b > product_prod_b_a ) > set_b_8144306140723532482od_b_a > $o ).

thf(sy_c_member_001_062_Itf__b_Mtf__c_J,type,
    member_b_c: ( b > c ) > set_b_c > $o ).

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

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

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

thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Real__Oreal_J,type,
    member557208447399453958t_real: produc7716430852924023517t_real > set_Pr320017278500174781t_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    member8825075204131838472od_a_b: produc1405624045518934769od_a_b > set_Pr8440535549847184039od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
    member7849222048561428706l_real: produc2422161461964618553l_real > set_Pr6218003697084177305l_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Real__Oreal_Mtf__a_J,type,
    member7555082150335017566real_a: product_prod_real_a > set_Pr6589227744151929853real_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Real__Oreal_J,type,
    member7037815648067680368a_real: product_prod_a_real > set_Pr4180788328258511119a_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    member1426531481828664017od_a_b: product_prod_a_b > set_Product_prod_a_b > $o ).

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

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Real__Oreal_J_J,type,
    member6599792433088240102t_real: set_Pr320017278500174781t_real > set_se5221187972681207965t_real > $o ).

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    member6767226683953100098l_real: set_Pr6218003697084177305l_real > set_se4295722930022447097l_real > $o ).

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

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

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

thf(sy_c_member_001tf__c,type,
    member_c: c > set_c > $o ).

thf(sy_v_X,type,
    x: quasi_borel_a ).

thf(sy_v_Y,type,
    y: quasi_borel_b ).

thf(sy_v_Z,type,
    z: quasi_borel_c ).

thf(sy_v__092_060alpha_062____,type,
    alpha: real > produc1405624045518934769od_a_b ).

thf(sy_v_k____,type,
    k: real > a > b > c ).

% Relevant facts (1272)
thf(fact_0_h_I1_J,axiom,
    member6939723154228711331_a_b_c @ ( produc8409101302566321868_a_b_c @ k ) @ ( qbs_mo8653977514671865831_a_b_c @ ( binary5762279046363823267real_a @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ x ) @ ( exponent_exp_qbs_b_c @ y @ z ) ) ).

% h(1)
thf(fact_1_exp__qbs__Mx__def,axiom,
    ( expone7022597896679715718Mx_a_c
    = ( ^ [X: quasi_borel_a,Y: quasi_borel_c] :
          ( collect_real_a_c
          @ ^ [G: real > a > c] : ( member6092897591332320217al_a_c @ ( produc5622917954539892058al_a_c @ G ) @ ( qbs_mo5379295239341213439al_a_c @ ( binary5762279046363823267real_a @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ X ) @ Y ) ) ) ) ) ).

% exp_qbs_Mx_def
thf(fact_2_exp__qbs__Mx__def,axiom,
    ( expone95873867685489500_a_b_c
    = ( ^ [X: quasi_8309430206217406798od_a_b,Y: quasi_borel_c] :
          ( collec9182426333961588829_a_b_c
          @ ^ [G: real > product_prod_a_b > c] : ( member8926022639343475119_a_b_c @ ( produc8366947261062197552_a_b_c @ G ) @ ( qbs_mo2372680880966528981_a_b_c @ ( binary7782493704384473421od_a_b @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ X ) @ Y ) ) ) ) ) ).

% exp_qbs_Mx_def
thf(fact_3_exp__qbs__Mx__def,axiom,
    ( expone4235142314707039685Mx_b_c
    = ( ^ [X: quasi_borel_b,Y: quasi_borel_c] :
          ( collect_real_b_c
          @ ^ [G: real > b > c] : ( member5457248590727333528al_b_c @ ( produc2835462372567216025al_b_c @ G ) @ ( qbs_mo4743646238736226750al_b_c @ ( binary5762279046363823268real_b @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ X ) @ Y ) ) ) ) ) ).

% exp_qbs_Mx_def
thf(fact_4_exp__qbs__Mx__def,axiom,
    ( expone5572123575668448672_a_b_c
    = ( ^ [X: quasi_borel_a,Y: quasi_borel_b_c] :
          ( collect_real_a_b_c
          @ ^ [G: real > a > b > c] : ( member6939723154228711331_a_b_c @ ( produc8409101302566321868_a_b_c @ G ) @ ( qbs_mo8653977514671865831_a_b_c @ ( binary5762279046363823267real_a @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ X ) @ Y ) ) ) ) ) ).

% exp_qbs_Mx_def
thf(fact_5_case__prod__app,axiom,
    ( produc7198824580026001574al_b_c
    = ( ^ [F: a > real > b > c,X2: product_prod_a_real,Y2: b] :
          ( produc1233131502984679936real_c
          @ ^ [L: a,R: real] : ( F @ L @ R @ Y2 )
          @ X2 ) ) ) ).

% case_prod_app
thf(fact_6_case__prod__app,axiom,
    ( produc8409101302566321868_a_b_c
    = ( ^ [F: real > a > b > c,X2: product_prod_real_a,Y2: b] :
          ( produc5622917954539892058al_a_c
          @ ^ [L: real,R: a] : ( F @ L @ R @ Y2 )
          @ X2 ) ) ) ).

% case_prod_app
thf(fact_7_h_I2_J,axiom,
    member798328933530555475od_a_b @ alpha @ ( binary1851749123906691170od_a_b @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( binary3918968219557196014bs_a_b @ x @ y ) ) ).

% h(2)
thf(fact_8_curry__preserves__morphisms,axiom,
    ! [F2: produc6065541746132100699real_b > c,X3: quasi_5298506126099802441a_real,Y3: quasi_borel_b,Z: quasi_borel_c] :
      ( ( member97807679366788293al_b_c @ F2 @ ( qbs_mo2767837957844617963al_b_c @ ( binary8791970442794005559real_b @ X3 @ Y3 ) @ Z ) )
     => ( member2979925738865732021al_b_c @ ( produc4827883403600754789al_b_c @ F2 ) @ ( qbs_mo4694180099308886521al_b_c @ X3 @ ( exponent_exp_qbs_b_c @ Y3 @ Z ) ) ) ) ).

% curry_preserves_morphisms
thf(fact_9_curry__preserves__morphisms,axiom,
    ! [F2: product_prod_real_b > c,X3: quasi_borel_real,Y3: quasi_borel_b,Z: quasi_borel_c] :
      ( ( member5457248590727333528al_b_c @ F2 @ ( qbs_mo4743646238736226750al_b_c @ ( binary5762279046363823268real_b @ X3 @ Y3 ) @ Z ) )
     => ( member_real_b_c @ ( produc7369401904616417848al_b_c @ F2 ) @ ( qbs_mo6398413456135019852al_b_c @ X3 @ ( exponent_exp_qbs_b_c @ Y3 @ Z ) ) ) ) ).

% curry_preserves_morphisms
thf(fact_10_curry__preserves__morphisms,axiom,
    ! [F2: product_prod_b_a > b > c,X3: quasi_borel_b,Y3: quasi_borel_a,Z: quasi_borel_b_c] :
      ( ( member7636239244871725222_a_b_c @ F2 @ ( qbs_mo938896878422149652_a_b_c @ ( binary1131512637584519980bs_b_a @ X3 @ Y3 ) @ Z ) )
     => ( member_b_a_b_c @ ( produc2762368449492327216_a_b_c @ F2 ) @ ( qbs_morphism_b_a_b_c @ X3 @ ( expone6081388564108922123_a_b_c @ Y3 @ Z ) ) ) ) ).

% curry_preserves_morphisms
thf(fact_11_curry__preserves__morphisms,axiom,
    ! [F2: product_prod_a_real > b > c,X3: quasi_borel_a,Y3: quasi_borel_real,Z: quasi_borel_b_c] :
      ( ( member2979925738865732021al_b_c @ F2 @ ( qbs_mo4694180099308886521al_b_c @ ( binary5132260278890873469a_real @ X3 @ Y3 ) @ Z ) )
     => ( member_a_real_b_c @ ( produc2621439639359427143al_b_c @ F2 ) @ ( qbs_mo737023097252057719al_b_c @ X3 @ ( expone5053526631941837485al_b_c @ Y3 @ Z ) ) ) ) ).

% curry_preserves_morphisms
thf(fact_12_curry__preserves__morphisms,axiom,
    ! [F2: produc2857309735095370733al_a_b > c,X3: quasi_7706945541993221175real_a,Y3: quasi_borel_b,Z: quasi_borel_c] :
      ( ( member5833231890863366067_a_b_c @ F2 @ ( qbs_mo8503262169341195737_a_b_c @ ( binary5583738431757275593al_a_b @ X3 @ Y3 ) @ Z ) )
     => ( member6939723154228711331_a_b_c @ ( produc1339935578242556755_a_b_c @ F2 ) @ ( qbs_mo8653977514671865831_a_b_c @ X3 @ ( exponent_exp_qbs_b_c @ Y3 @ Z ) ) ) ) ).

% curry_preserves_morphisms
thf(fact_13_curry__preserves__morphisms,axiom,
    ! [F2: product_prod_real_a > b > c,X3: quasi_borel_real,Y3: quasi_borel_a,Z: quasi_borel_b_c] :
      ( ( member6939723154228711331_a_b_c @ F2 @ ( qbs_mo8653977514671865831_a_b_c @ ( binary5762279046363823267real_a @ X3 @ Y3 ) @ Z ) )
     => ( member_real_a_b_c @ ( produc3831716361899747437_a_b_c @ F2 ) @ ( qbs_mo534596117765811055_a_b_c @ X3 @ ( expone6081388564108922123_a_b_c @ Y3 @ Z ) ) ) ) ).

% curry_preserves_morphisms
thf(fact_14_curry__preserves__morphisms,axiom,
    ! [F2: product_prod_a_b > c,X3: quasi_borel_a,Y3: quasi_borel_b,Z: quasi_borel_c] :
      ( ( member1080921174361771732_a_b_c @ F2 @ ( qbs_mo2296058654870477648_a_b_c @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) @ Z ) )
     => ( member_a_b_c @ ( product_curry_a_b_c @ F2 ) @ ( qbs_morphism_a_b_c @ X3 @ ( exponent_exp_qbs_b_c @ Y3 @ Z ) ) ) ) ).

% curry_preserves_morphisms
thf(fact_15_qbs__morphism__ident_H,axiom,
    ! [X3: quasi_borel_real] :
      ( member_real_real
      @ ^ [X2: real] : X2
      @ ( qbs_mo5229770564518008146l_real @ X3 @ X3 ) ) ).

% qbs_morphism_ident'
thf(fact_16_prod_Ocase__distrib,axiom,
    ! [H: ( b > c ) > c,F2: real > a > b > c,Prod: product_prod_real_a] :
      ( ( H @ ( produc8409101302566321868_a_b_c @ F2 @ Prod ) )
      = ( produc5622917954539892058al_a_c
        @ ^ [X1: real,X22: a] : ( H @ ( F2 @ X1 @ X22 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_17_prod_Ocase__distrib,axiom,
    ! [H: c > b > c,F2: real > a > c,Prod: product_prod_real_a] :
      ( ( H @ ( produc5622917954539892058al_a_c @ F2 @ Prod ) )
      = ( produc8409101302566321868_a_b_c
        @ ^ [X1: real,X22: a] : ( H @ ( F2 @ X1 @ X22 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_18_prod_Ocase__distrib,axiom,
    ! [H: c > c,F2: real > a > c,Prod: product_prod_real_a] :
      ( ( H @ ( produc5622917954539892058al_a_c @ F2 @ Prod ) )
      = ( produc5622917954539892058al_a_c
        @ ^ [X1: real,X22: a] : ( H @ ( F2 @ X1 @ X22 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_19_prod_Ocase__distrib,axiom,
    ! [H: ( b > c ) > b > c,F2: a > real > b > c,Prod: product_prod_a_real] :
      ( ( H @ ( produc7198824580026001574al_b_c @ F2 @ Prod ) )
      = ( produc7198824580026001574al_b_c
        @ ^ [X1: a,X22: real] : ( H @ ( F2 @ X1 @ X22 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_20_prod_Ocase__distrib,axiom,
    ! [H: ( b > c ) > b > c,F2: real > a > b > c,Prod: product_prod_real_a] :
      ( ( H @ ( produc8409101302566321868_a_b_c @ F2 @ Prod ) )
      = ( produc8409101302566321868_a_b_c
        @ ^ [X1: real,X22: a] : ( H @ ( F2 @ X1 @ X22 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_21_prod_Ocase__distrib,axiom,
    ! [H: c > c,F2: real > product_prod_a_b > c,Prod: produc1405624045518934769od_a_b] :
      ( ( H @ ( produc8366947261062197552_a_b_c @ F2 @ Prod ) )
      = ( produc8366947261062197552_a_b_c
        @ ^ [X1: real,X22: product_prod_a_b] : ( H @ ( F2 @ X1 @ X22 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_22_prod_Ocase__distrib,axiom,
    ! [H: c > c,F2: a > b > c,Prod: product_prod_a_b] :
      ( ( H @ ( produc6028431345588019475_a_b_c @ F2 @ Prod ) )
      = ( produc6028431345588019475_a_b_c
        @ ^ [X1: a,X22: b] : ( H @ ( F2 @ X1 @ X22 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_23_prod_Ocase__distrib,axiom,
    ! [H: c > c,F2: real > b > c,Prod: product_prod_real_b] :
      ( ( H @ ( produc2835462372567216025al_b_c @ F2 @ Prod ) )
      = ( produc2835462372567216025al_b_c
        @ ^ [X1: real,X22: b] : ( H @ ( F2 @ X1 @ X22 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_24_case__prod__const,axiom,
    ! [C: c] :
      ( ( produc5622917954539892058al_a_c
        @ ^ [I: real,J: a] : C )
      = ( ^ [Uu: product_prod_real_a] : C ) ) ).

% case_prod_const
thf(fact_25_case__prod__const,axiom,
    ! [C: b > c] :
      ( ( produc7198824580026001574al_b_c
        @ ^ [I: a,J: real] : C )
      = ( ^ [Uu: product_prod_a_real] : C ) ) ).

% case_prod_const
thf(fact_26_case__prod__const,axiom,
    ! [C: b > c] :
      ( ( produc8409101302566321868_a_b_c
        @ ^ [I: real,J: a] : C )
      = ( ^ [Uu: product_prod_real_a] : C ) ) ).

% case_prod_const
thf(fact_27_case__prod__const,axiom,
    ! [C: c] :
      ( ( produc8366947261062197552_a_b_c
        @ ^ [I: real,J: product_prod_a_b] : C )
      = ( ^ [Uu: produc1405624045518934769od_a_b] : C ) ) ).

% case_prod_const
thf(fact_28_case__prod__const,axiom,
    ! [C: c] :
      ( ( produc6028431345588019475_a_b_c
        @ ^ [I: a,J: b] : C )
      = ( ^ [Uu: product_prod_a_b] : C ) ) ).

% case_prod_const
thf(fact_29_case__prod__const,axiom,
    ! [C: c] :
      ( ( produc2835462372567216025al_b_c
        @ ^ [I: real,J: b] : C )
      = ( ^ [Uu: product_prod_real_b] : C ) ) ).

% case_prod_const
thf(fact_30_qbs__morphism__fst_H_H,axiom,
    ! [F2: real > real,X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_a] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
     => ( member7939111694857414313a_real
        @ ^ [K: product_prod_real_a] : ( F2 @ ( product_fst_real_a @ K ) )
        @ ( qbs_mo704561573410066541a_real @ ( binary5762279046363823267real_a @ X3 @ Z ) @ Y3 ) ) ) ).

% qbs_morphism_fst''
thf(fact_31_qbs__morphism__fst_H_H,axiom,
    ! [F2: real > $o,X3: quasi_borel_real,Y3: quasi_borel_o,Z: quasi_borel_a] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
     => ( member346752906940258161al_a_o
        @ ^ [K: product_prod_real_a] : ( F2 @ ( product_fst_real_a @ K ) )
        @ ( qbs_mo8821471276632854295al_a_o @ ( binary5762279046363823267real_a @ X3 @ Z ) @ Y3 ) ) ) ).

% qbs_morphism_fst''
thf(fact_32_qbs__morphism__fst_H_H,axiom,
    ! [F2: real > nat,X3: quasi_borel_real,Y3: quasi_borel_nat,Z: quasi_borel_a] :
      ( ( member_real_nat @ F2 @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) )
     => ( member5377495750445857485_a_nat
        @ ^ [K: product_prod_real_a] : ( F2 @ ( product_fst_real_a @ K ) )
        @ ( qbs_mo4561836765000465937_a_nat @ ( binary5762279046363823267real_a @ X3 @ Z ) @ Y3 ) ) ) ).

% qbs_morphism_fst''
thf(fact_33_qbs__morphism__fst_H_H,axiom,
    ! [F2: nat > real,X3: quasi_borel_nat,Y3: quasi_borel_real,Z: quasi_borel_real] :
      ( ( member_nat_real @ F2 @ ( qbs_mo2000642995705457910t_real @ X3 @ Y3 ) )
     => ( member4539693599630147619l_real
        @ ^ [K: produc7716430852924023517t_real] : ( F2 @ ( product_fst_nat_real @ K ) )
        @ ( qbs_mo8506632985670901265l_real @ ( binary2938201662863479403t_real @ X3 @ Z ) @ Y3 ) ) ) ).

% qbs_morphism_fst''
thf(fact_34_qbs__morphism__fst_H_H,axiom,
    ! [F2: real > real,X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_real] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
     => ( member6699615393305559423l_real
        @ ^ [K: produc2422161461964618553l_real] : ( F2 @ ( produc5828954698716094813l_real @ K ) )
        @ ( qbs_mo6849673928694174957l_real @ ( binary210465342804807751l_real @ X3 @ Z ) @ Y3 ) ) ) ).

% qbs_morphism_fst''
thf(fact_35_qbs__morphism__fst_H_H,axiom,
    ! [F2: real > $o,X3: quasi_borel_real,Y3: quasi_borel_o,Z: quasi_borel_real] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
     => ( member9025505449285005339real_o
        @ ^ [K: produc2422161461964618553l_real] : ( F2 @ ( produc5828954698716094813l_real @ K ) )
        @ ( qbs_mo7803983300892306071real_o @ ( binary210465342804807751l_real @ X3 @ Z ) @ Y3 ) ) ) ).

% qbs_morphism_fst''
thf(fact_36_qbs__morphism__fst_H_H,axiom,
    ! [F2: real > nat,X3: quasi_borel_real,Y3: quasi_borel_nat,Z: quasi_borel_real] :
      ( ( member_real_nat @ F2 @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) )
     => ( member6756320954723885219al_nat
        @ ^ [K: produc2422161461964618553l_real] : ( F2 @ ( produc5828954698716094813l_real @ K ) )
        @ ( qbs_mo818872531660866193al_nat @ ( binary210465342804807751l_real @ X3 @ Z ) @ Y3 ) ) ) ).

% qbs_morphism_fst''
thf(fact_37_qbs__morphism__fst_H_H,axiom,
    ! [F2: real > real,X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_8309430206217406798od_a_b] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
     => ( member6209306361823650387b_real
        @ ^ [K: produc1405624045518934769od_a_b] : ( F2 @ ( produc4505306568083885239od_a_b @ K ) )
        @ ( qbs_mo1721096491341367575b_real @ ( binary7782493704384473421od_a_b @ X3 @ Z ) @ Y3 ) ) ) ).

% qbs_morphism_fst''
thf(fact_38_qbs__morphism__fst_H_H,axiom,
    ! [F2: real > $o,X3: quasi_borel_real,Y3: quasi_borel_o,Z: quasi_8309430206217406798od_a_b] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
     => ( member3321580722020452423_a_b_o
        @ ^ [K: produc1405624045518934769od_a_b] : ( F2 @ ( produc4505306568083885239od_a_b @ K ) )
        @ ( qbs_mo1053261323999691501_a_b_o @ ( binary7782493704384473421od_a_b @ X3 @ Z ) @ Y3 ) ) ) ).

% qbs_morphism_fst''
thf(fact_39_qbs__morphism__fst_H_H,axiom,
    ! [F2: real > nat,X3: quasi_borel_real,Y3: quasi_borel_nat,Z: quasi_8309430206217406798od_a_b] :
      ( ( member_real_nat @ F2 @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) )
     => ( member4965947250304052087_b_nat
        @ ^ [K: produc1405624045518934769od_a_b] : ( F2 @ ( produc4505306568083885239od_a_b @ K ) )
        @ ( qbs_mo2771881436390566843_b_nat @ ( binary7782493704384473421od_a_b @ X3 @ Z ) @ Y3 ) ) ) ).

% qbs_morphism_fst''
thf(fact_40_qbs__morphism__pair__swap,axiom,
    ! [F2: product_prod_a_b > c,X3: quasi_borel_a,Y3: quasi_borel_b,Z: quasi_borel_c] :
      ( ( member1080921174361771732_a_b_c @ F2 @ ( qbs_mo2296058654870477648_a_b_c @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) @ Z ) )
     => ( member7312788790154889110_b_a_c
        @ ( produc5188733505894050389_b_a_c
          @ ^ [X2: b,Y2: a] : ( F2 @ ( product_Pair_a_b @ Y2 @ X2 ) ) )
        @ ( qbs_mo8527926270663595026_b_a_c @ ( binary1131512637584519980bs_b_a @ Y3 @ X3 ) @ Z ) ) ) ).

% qbs_morphism_pair_swap
thf(fact_41_qbs__morphism__pair__swap,axiom,
    ! [F2: product_prod_a_real > c,X3: quasi_borel_a,Y3: quasi_borel_real,Z: quasi_borel_c] :
      ( ( member77757565514274375real_c @ F2 @ ( qbs_mo8587527250377943405real_c @ ( binary5132260278890873469a_real @ X3 @ Y3 ) @ Z ) )
     => ( member6092897591332320217al_a_c
        @ ( produc5622917954539892058al_a_c
          @ ^ [X2: real,Y2: a] : ( F2 @ ( product_Pair_a_real @ Y2 @ X2 ) ) )
        @ ( qbs_mo5379295239341213439al_a_c @ ( binary5762279046363823267real_a @ Y3 @ X3 ) @ Z ) ) ) ).

% qbs_morphism_pair_swap
thf(fact_42_qbs__morphism__pair__swap,axiom,
    ! [F2: produc7929879615859924995b_real > c,X3: quasi_8309430206217406798od_a_b,Y3: quasi_borel_real,Z: quasi_borel_c] :
      ( ( member3001133531608298781real_c @ F2 @ ( qbs_mo5671163810086128451real_c @ ( binary1320184014764670247b_real @ X3 @ Y3 ) @ Z ) )
     => ( member8926022639343475119_a_b_c
        @ ( produc8366947261062197552_a_b_c
          @ ^ [X2: real,Y2: product_prod_a_b] : ( F2 @ ( produc9021675809588086653b_real @ Y2 @ X2 ) ) )
        @ ( qbs_mo2372680880966528981_a_b_c @ ( binary7782493704384473421od_a_b @ Y3 @ X3 ) @ Z ) ) ) ).

% qbs_morphism_pair_swap
thf(fact_43_qbs__morphism__pair__swap,axiom,
    ! [F2: product_prod_b_real > c,X3: quasi_borel_b,Y3: quasi_borel_real,Z: quasi_borel_c] :
      ( ( member1565719602809072902real_c @ F2 @ ( qbs_mo852117250817966124real_c @ ( binary1505106857224228350b_real @ X3 @ Y3 ) @ Z ) )
     => ( member5457248590727333528al_b_c
        @ ( produc2835462372567216025al_b_c
          @ ^ [X2: real,Y2: b] : ( F2 @ ( product_Pair_b_real @ Y2 @ X2 ) ) )
        @ ( qbs_mo4743646238736226750al_b_c @ ( binary5762279046363823268real_b @ Y3 @ X3 ) @ Z ) ) ) ).

% qbs_morphism_pair_swap
thf(fact_44_qbs__morphism__pair__swap,axiom,
    ! [F2: product_prod_a_real > b > c,X3: quasi_borel_a,Y3: quasi_borel_real,Z: quasi_borel_b_c] :
      ( ( member2979925738865732021al_b_c @ F2 @ ( qbs_mo4694180099308886521al_b_c @ ( binary5132260278890873469a_real @ X3 @ Y3 ) @ Z ) )
     => ( member6939723154228711331_a_b_c
        @ ( produc8409101302566321868_a_b_c
          @ ^ [X2: real,Y2: a] : ( F2 @ ( product_Pair_a_real @ Y2 @ X2 ) ) )
        @ ( qbs_mo8653977514671865831_a_b_c @ ( binary5762279046363823267real_a @ Y3 @ X3 ) @ Z ) ) ) ).

% qbs_morphism_pair_swap
thf(fact_45_qbs__morphism__pair__swap,axiom,
    ! [F2: product_prod_b_a > c,X3: quasi_borel_b,Y3: quasi_borel_a,Z: quasi_borel_c] :
      ( ( member7312788790154889110_b_a_c @ F2 @ ( qbs_mo8527926270663595026_b_a_c @ ( binary1131512637584519980bs_b_a @ X3 @ Y3 ) @ Z ) )
     => ( member1080921174361771732_a_b_c
        @ ( produc6028431345588019475_a_b_c
          @ ^ [X2: a,Y2: b] : ( F2 @ ( product_Pair_b_a @ Y2 @ X2 ) ) )
        @ ( qbs_mo2296058654870477648_a_b_c @ ( binary3918968219557196014bs_a_b @ Y3 @ X3 ) @ Z ) ) ) ).

% qbs_morphism_pair_swap
thf(fact_46_qbs__morphism__pair__swap,axiom,
    ! [F2: product_prod_real_a > b > c,X3: quasi_borel_real,Y3: quasi_borel_a,Z: quasi_borel_b_c] :
      ( ( member6939723154228711331_a_b_c @ F2 @ ( qbs_mo8653977514671865831_a_b_c @ ( binary5762279046363823267real_a @ X3 @ Y3 ) @ Z ) )
     => ( member2979925738865732021al_b_c
        @ ( produc7198824580026001574al_b_c
          @ ^ [X2: a,Y2: real] : ( F2 @ ( product_Pair_real_a @ Y2 @ X2 ) ) )
        @ ( qbs_mo4694180099308886521al_b_c @ ( binary5132260278890873469a_real @ Y3 @ X3 ) @ Z ) ) ) ).

% qbs_morphism_pair_swap
thf(fact_47_qbs__morphism__snd_H_H,axiom,
    ! [F2: b > c,X3: quasi_borel_b,Y3: quasi_borel_c,Z: quasi_borel_a] :
      ( ( member_b_c @ F2 @ ( qbs_morphism_b_c @ X3 @ Y3 ) )
     => ( member1080921174361771732_a_b_c
        @ ^ [K: product_prod_a_b] : ( F2 @ ( product_snd_a_b @ K ) )
        @ ( qbs_mo2296058654870477648_a_b_c @ ( binary3918968219557196014bs_a_b @ Z @ X3 ) @ Y3 ) ) ) ).

% qbs_morphism_snd''
thf(fact_48_qbs__morphism__snd_H_H,axiom,
    ! [F2: real > real,X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_nat] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
     => ( member4539693599630147619l_real
        @ ^ [K: produc7716430852924023517t_real] : ( F2 @ ( product_snd_nat_real @ K ) )
        @ ( qbs_mo8506632985670901265l_real @ ( binary2938201662863479403t_real @ Z @ X3 ) @ Y3 ) ) ) ).

% qbs_morphism_snd''
thf(fact_49_qbs__morphism__snd_H_H,axiom,
    ! [F2: real > $o,X3: quasi_borel_real,Y3: quasi_borel_o,Z: quasi_borel_nat] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
     => ( member7318680356153273975real_o
        @ ^ [K: produc7716430852924023517t_real] : ( F2 @ ( product_snd_nat_real @ K ) )
        @ ( qbs_mo8978908438751067763real_o @ ( binary2938201662863479403t_real @ Z @ X3 ) @ Y3 ) ) ) ).

% qbs_morphism_snd''
thf(fact_50_qbs__morphism__snd_H_H,axiom,
    ! [F2: real > nat,X3: quasi_borel_real,Y3: quasi_borel_nat,Z: quasi_borel_nat] :
      ( ( member_real_nat @ F2 @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) )
     => ( member3149932044224082247al_nat
        @ ^ [K: produc7716430852924023517t_real] : ( F2 @ ( product_snd_nat_real @ K ) )
        @ ( qbs_mo2463579765191384501al_nat @ ( binary2938201662863479403t_real @ Z @ X3 ) @ Y3 ) ) ) ).

% qbs_morphism_snd''
thf(fact_51_qbs__morphism__snd_H_H,axiom,
    ! [F2: real > real,X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_real] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
     => ( member6699615393305559423l_real
        @ ^ [K: produc2422161461964618553l_real] : ( F2 @ ( produc3484788084999411615l_real @ K ) )
        @ ( qbs_mo6849673928694174957l_real @ ( binary210465342804807751l_real @ Z @ X3 ) @ Y3 ) ) ) ).

% qbs_morphism_snd''
thf(fact_52_qbs__morphism__snd_H_H,axiom,
    ! [F2: real > $o,X3: quasi_borel_real,Y3: quasi_borel_o,Z: quasi_borel_real] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
     => ( member9025505449285005339real_o
        @ ^ [K: produc2422161461964618553l_real] : ( F2 @ ( produc3484788084999411615l_real @ K ) )
        @ ( qbs_mo7803983300892306071real_o @ ( binary210465342804807751l_real @ Z @ X3 ) @ Y3 ) ) ) ).

% qbs_morphism_snd''
thf(fact_53_qbs__morphism__snd_H_H,axiom,
    ! [F2: real > nat,X3: quasi_borel_real,Y3: quasi_borel_nat,Z: quasi_borel_real] :
      ( ( member_real_nat @ F2 @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) )
     => ( member6756320954723885219al_nat
        @ ^ [K: produc2422161461964618553l_real] : ( F2 @ ( produc3484788084999411615l_real @ K ) )
        @ ( qbs_mo818872531660866193al_nat @ ( binary210465342804807751l_real @ Z @ X3 ) @ Y3 ) ) ) ).

% qbs_morphism_snd''
thf(fact_54_qbs__morphism__snd_H_H,axiom,
    ! [F2: real > real,X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_b] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
     => ( member2870586958900744892l_real
        @ ^ [K: product_prod_b_real] : ( F2 @ ( product_snd_b_real @ K ) )
        @ ( qbs_mo4859408874308172928l_real @ ( binary1505106857224228350b_real @ Z @ X3 ) @ Y3 ) ) ) ).

% qbs_morphism_snd''
thf(fact_55_qbs__morphism__snd_H_H,axiom,
    ! [F2: real > $o,X3: quasi_borel_real,Y3: quasi_borel_o,Z: quasi_borel_b] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
     => ( member650940978409756446real_o
        @ ^ [K: product_prod_b_real] : ( F2 @ ( product_snd_b_real @ K ) )
        @ ( qbs_mo9125659348102352580real_o @ ( binary1505106857224228350b_real @ Z @ X3 ) @ Y3 ) ) ) ).

% qbs_morphism_snd''
thf(fact_56_qbs__morphism__snd_H_H,axiom,
    ! [F2: real > nat,X3: quasi_borel_real,Y3: quasi_borel_nat,Z: quasi_borel_b] :
      ( ( member_real_nat @ F2 @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) )
     => ( member4930280467232768096al_nat
        @ ^ [K: product_prod_b_real] : ( F2 @ ( product_snd_b_real @ K ) )
        @ ( qbs_mo4114621481787376548al_nat @ ( binary1505106857224228350b_real @ Z @ X3 ) @ Y3 ) ) ) ).

% qbs_morphism_snd''
thf(fact_57_exp__qbs__space,axiom,
    ! [X3: quasi_7706945541993221175real_a,Y3: quasi_borel_b_c] :
      ( ( qbs_sp6204010800219802454_a_b_c @ ( expone1656787320005700680_a_b_c @ X3 @ Y3 ) )
      = ( qbs_mo8653977514671865831_a_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_space
thf(fact_58_exp__qbs__space,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_nat] :
      ( ( qbs_space_real_nat @ ( expone4174669362753510615al_nat @ X3 @ Y3 ) )
      = ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) ) ).

% exp_qbs_space
thf(fact_59_exp__qbs__space,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_b_c] :
      ( ( qbs_space_real_b_c @ ( expone5053526631941837485al_b_c @ X3 @ Y3 ) )
      = ( qbs_mo6398413456135019852al_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_space
thf(fact_60_exp__qbs__space,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_a_b_c] :
      ( ( qbs_space_real_a_b_c @ ( expone6779206709035782606_a_b_c @ X3 @ Y3 ) )
      = ( qbs_mo534596117765811055_a_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_space
thf(fact_61_exp__qbs__space,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real] :
      ( ( qbs_space_nat_real @ ( expone8830732826479387735t_real @ X3 @ Y3 ) )
      = ( qbs_mo2000642995705457910t_real @ X3 @ Y3 ) ) ).

% exp_qbs_space
thf(fact_62_exp__qbs__space,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_c] :
      ( ( qbs_space_b_c @ ( exponent_exp_qbs_b_c @ X3 @ Y3 ) )
      = ( qbs_morphism_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_space
thf(fact_63_exp__qbs__space,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b_c] :
      ( ( qbs_space_a_b_c @ ( expone6081388564108922123_a_b_c @ X3 @ Y3 ) )
      = ( qbs_morphism_a_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_space
thf(fact_64_qbs__morphism__tuple,axiom,
    ! [F2: real > real,Z: quasi_borel_real,X3: quasi_borel_real,G2: real > $o,Y3: quasi_borel_o] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ Z @ X3 ) )
     => ( ( member_real_o @ G2 @ ( qbs_morphism_real_o @ Z @ Y3 ) )
       => ( member6586820919158520515real_o
          @ ^ [Z2: real] : ( product_Pair_real_o @ ( F2 @ Z2 ) @ ( G2 @ Z2 ) )
          @ ( qbs_mo6498981662437225095real_o @ Z @ ( binary4057238779996960701real_o @ X3 @ Y3 ) ) ) ) ) ).

% qbs_morphism_tuple
thf(fact_65_qbs__morphism__tuple,axiom,
    ! [F2: real > $o,Z: quasi_borel_real,X3: quasi_borel_o,G2: real > real,Y3: quasi_borel_real] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ Z @ X3 ) )
     => ( ( member_real_real @ G2 @ ( qbs_mo5229770564518008146l_real @ Z @ Y3 ) )
       => ( member8223553389164786773o_real
          @ ^ [Z2: real] : ( product_Pair_o_real @ ( F2 @ Z2 ) @ ( G2 @ Z2 ) )
          @ ( qbs_mo3903038352199750937o_real @ Z @ ( binary2548174404955791127o_real @ X3 @ Y3 ) ) ) ) ) ).

% qbs_morphism_tuple
thf(fact_66_qbs__morphism__tuple,axiom,
    ! [F2: real > $o,Z: quasi_borel_real,X3: quasi_borel_o,G2: real > $o,Y3: quasi_borel_o] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ Z @ X3 ) )
     => ( ( member_real_o @ G2 @ ( qbs_morphism_real_o @ Z @ Y3 ) )
       => ( member8624048055576332635od_o_o
          @ ^ [Z2: real] : ( product_Pair_o_o @ ( F2 @ Z2 ) @ ( G2 @ Z2 ) )
          @ ( qbs_mo8591899500417447169od_o_o @ Z @ ( binary9159730317414444269bs_o_o @ X3 @ Y3 ) ) ) ) ) ).

% qbs_morphism_tuple
thf(fact_67_qbs__morphism__tuple,axiom,
    ! [F2: real > real,Z: quasi_borel_real,X3: quasi_borel_real,G2: real > nat,Y3: quasi_borel_nat] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ Z @ X3 ) )
     => ( ( member_real_nat @ G2 @ ( qbs_mo6567951568834356598al_nat @ Z @ Y3 ) )
       => ( member4159480375084375953al_nat
          @ ^ [Z2: real] : ( produc3181502643871035669al_nat @ ( F2 @ Z2 ) @ ( G2 @ Z2 ) )
          @ ( qbs_mo8849718567295897911al_nat @ Z @ ( binary7505510235992378091al_nat @ X3 @ Y3 ) ) ) ) ) ).

% qbs_morphism_tuple
thf(fact_68_qbs__morphism__tuple,axiom,
    ! [F2: real > $o,Z: quasi_borel_real,X3: quasi_borel_o,G2: real > nat,Y3: quasi_borel_nat] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ Z @ X3 ) )
     => ( ( member_real_nat @ G2 @ ( qbs_mo6567951568834356598al_nat @ Z @ Y3 ) )
       => ( member7334495436961965817_o_nat
          @ ^ [Z2: real] : ( product_Pair_o_nat @ ( F2 @ Z2 ) @ ( G2 @ Z2 ) )
          @ ( qbs_mo7100413126075687229_o_nat @ Z @ ( binary4578070153795289531_o_nat @ X3 @ Y3 ) ) ) ) ) ).

% qbs_morphism_tuple
thf(fact_69_qbs__morphism__tuple,axiom,
    ! [F2: real > nat,Z: quasi_borel_real,X3: quasi_borel_nat,G2: real > $o,Y3: quasi_borel_o] :
      ( ( member_real_nat @ F2 @ ( qbs_mo6567951568834356598al_nat @ Z @ X3 ) )
     => ( ( member_real_o @ G2 @ ( qbs_morphism_real_o @ Z @ Y3 ) )
       => ( member8382098559140269471_nat_o
          @ ^ [Z2: real] : ( product_Pair_nat_o @ ( F2 @ Z2 ) @ ( G2 @ Z2 ) )
          @ ( qbs_mo1385575613276404451_nat_o @ Z @ ( binary7680741514903474841_nat_o @ X3 @ Y3 ) ) ) ) ) ).

% qbs_morphism_tuple
thf(fact_70_qbs__morphism__tuple,axiom,
    ! [F2: real > nat,Z: quasi_borel_real,X3: quasi_borel_nat,G2: real > nat,Y3: quasi_borel_nat] :
      ( ( member_real_nat @ F2 @ ( qbs_mo6567951568834356598al_nat @ Z @ X3 ) )
     => ( ( member_real_nat @ G2 @ ( qbs_mo6567951568834356598al_nat @ Z @ Y3 ) )
       => ( member278708040391457717at_nat
          @ ^ [Z2: real] : ( product_Pair_nat_nat @ ( F2 @ Z2 ) @ ( G2 @ Z2 ) )
          @ ( qbs_mo4077890138368776155at_nat @ Z @ ( binary6297550310575005455at_nat @ X3 @ Y3 ) ) ) ) ) ).

% qbs_morphism_tuple
thf(fact_71_qbs__morphism__tuple,axiom,
    ! [F2: real > real,Z: quasi_borel_real,X3: quasi_borel_real,G2: real > a,Y3: quasi_borel_a] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ Z @ X3 ) )
     => ( ( member_real_a @ G2 @ ( qbs_morphism_real_a @ Z @ Y3 ) )
       => ( member1006887528422719913real_a
          @ ^ [Z2: real] : ( product_Pair_real_a @ ( F2 @ Z2 ) @ ( G2 @ Z2 ) )
          @ ( qbs_mo1948987420364309741real_a @ Z @ ( binary5762279046363823267real_a @ X3 @ Y3 ) ) ) ) ) ).

% qbs_morphism_tuple
thf(fact_72_qbs__morphism__tuple,axiom,
    ! [F2: $o > real,Z: quasi_borel_o,X3: quasi_borel_real,G2: $o > a,Y3: quasi_borel_a] :
      ( ( member_o_real @ F2 @ ( qbs_morphism_o_real @ Z @ X3 ) )
     => ( ( member_o_a @ G2 @ ( qbs_morphism_o_a @ Z @ Y3 ) )
       => ( member4948893057617750905real_a
          @ ^ [Z2: $o] : ( product_Pair_real_a @ ( F2 @ Z2 ) @ ( G2 @ Z2 ) )
          @ ( qbs_mo4240396302186037607real_a @ Z @ ( binary5762279046363823267real_a @ X3 @ Y3 ) ) ) ) ) ).

% qbs_morphism_tuple
thf(fact_73_qbs__morphism__tuple,axiom,
    ! [F2: nat > real,Z: quasi_borel_nat,X3: quasi_borel_real,G2: nat > a,Y3: quasi_borel_a] :
      ( ( member_nat_real @ F2 @ ( qbs_mo2000642995705457910t_real @ Z @ X3 ) )
     => ( ( member_nat_a @ G2 @ ( qbs_morphism_nat_a @ Z @ Y3 ) )
       => ( member3792249494800367565real_a
          @ ^ [Z2: nat] : ( product_Pair_real_a @ ( F2 @ Z2 ) @ ( G2 @ Z2 ) )
          @ ( qbs_mo2610884258138134673real_a @ Z @ ( binary5762279046363823267real_a @ X3 @ Y3 ) ) ) ) ) ).

% qbs_morphism_tuple
thf(fact_74_prod_Oinject,axiom,
    ! [X12: real,X23: a,Y1: real,Y22: a] :
      ( ( ( product_Pair_real_a @ X12 @ X23 )
        = ( product_Pair_real_a @ Y1 @ Y22 ) )
      = ( ( X12 = Y1 )
        & ( X23 = Y22 ) ) ) ).

% prod.inject
thf(fact_75_prod_Oinject,axiom,
    ! [X12: real,X23: b,Y1: real,Y22: b] :
      ( ( ( product_Pair_real_b @ X12 @ X23 )
        = ( product_Pair_real_b @ Y1 @ Y22 ) )
      = ( ( X12 = Y1 )
        & ( X23 = Y22 ) ) ) ).

% prod.inject
thf(fact_76_prod_Oinject,axiom,
    ! [X12: b,X23: a,Y1: b,Y22: a] :
      ( ( ( product_Pair_b_a @ X12 @ X23 )
        = ( product_Pair_b_a @ Y1 @ Y22 ) )
      = ( ( X12 = Y1 )
        & ( X23 = Y22 ) ) ) ).

% prod.inject
thf(fact_77_prod_Oinject,axiom,
    ! [X12: a,X23: real,Y1: a,Y22: real] :
      ( ( ( product_Pair_a_real @ X12 @ X23 )
        = ( product_Pair_a_real @ Y1 @ Y22 ) )
      = ( ( X12 = Y1 )
        & ( X23 = Y22 ) ) ) ).

% prod.inject
thf(fact_78_prod_Oinject,axiom,
    ! [X12: b,X23: real,Y1: b,Y22: real] :
      ( ( ( product_Pair_b_real @ X12 @ X23 )
        = ( product_Pair_b_real @ Y1 @ Y22 ) )
      = ( ( X12 = Y1 )
        & ( X23 = Y22 ) ) ) ).

% prod.inject
thf(fact_79_prod_Oinject,axiom,
    ! [X12: product_prod_a_b,X23: real,Y1: product_prod_a_b,Y22: real] :
      ( ( ( produc9021675809588086653b_real @ X12 @ X23 )
        = ( produc9021675809588086653b_real @ Y1 @ Y22 ) )
      = ( ( X12 = Y1 )
        & ( X23 = Y22 ) ) ) ).

% prod.inject
thf(fact_80_old_Oprod_Oinject,axiom,
    ! [A: real,B: a,A2: real,B2: a] :
      ( ( ( product_Pair_real_a @ A @ B )
        = ( product_Pair_real_a @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_81_old_Oprod_Oinject,axiom,
    ! [A: real,B: b,A2: real,B2: b] :
      ( ( ( product_Pair_real_b @ A @ B )
        = ( product_Pair_real_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_82_old_Oprod_Oinject,axiom,
    ! [A: b,B: a,A2: b,B2: a] :
      ( ( ( product_Pair_b_a @ A @ B )
        = ( product_Pair_b_a @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_83_old_Oprod_Oinject,axiom,
    ! [A: a,B: real,A2: a,B2: real] :
      ( ( ( product_Pair_a_real @ A @ B )
        = ( product_Pair_a_real @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_84_old_Oprod_Oinject,axiom,
    ! [A: b,B: real,A2: b,B2: real] :
      ( ( ( product_Pair_b_real @ A @ B )
        = ( product_Pair_b_real @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_85_old_Oprod_Oinject,axiom,
    ! [A: product_prod_a_b,B: real,A2: product_prod_a_b,B2: real] :
      ( ( ( produc9021675809588086653b_real @ A @ B )
        = ( produc9021675809588086653b_real @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_86_curryI,axiom,
    ! [F2: product_prod_real_a > $o,A: real,B: a] :
      ( ( F2 @ ( product_Pair_real_a @ A @ B ) )
     => ( produc4069262006438169873al_a_o @ F2 @ A @ B ) ) ).

% curryI
thf(fact_87_curryI,axiom,
    ! [F2: product_prod_real_b > $o,A: real,B: b] :
      ( ( F2 @ ( product_Pair_real_b @ A @ B ) )
     => ( produc1170039606973775568al_b_o @ F2 @ A @ B ) ) ).

% curryI
thf(fact_88_curryI,axiom,
    ! [F2: product_prod_b_a > $o,A: b,B: a] :
      ( ( F2 @ ( product_Pair_b_a @ A @ B ) )
     => ( product_curry_b_a_o @ F2 @ A @ B ) ) ).

% curryI
thf(fact_89_curryI,axiom,
    ! [F2: product_prod_a_real > $o,A: a,B: real] :
      ( ( F2 @ ( product_Pair_a_real @ A @ B ) )
     => ( produc3073983294494581943real_o @ F2 @ A @ B ) ) ).

% curryI
thf(fact_90_curryI,axiom,
    ! [F2: product_prod_b_real > $o,A: b,B: real] :
      ( ( F2 @ ( product_Pair_b_real @ A @ B ) )
     => ( produc4418448331304069878real_o @ F2 @ A @ B ) ) ).

% curryI
thf(fact_91_curryI,axiom,
    ! [F2: produc7929879615859924995b_real > $o,A: product_prod_a_b,B: real] :
      ( ( F2 @ ( produc9021675809588086653b_real @ A @ B ) )
     => ( produc5183746550669782669real_o @ F2 @ A @ B ) ) ).

% curryI
thf(fact_92_case__prodI,axiom,
    ! [F2: real > a > $o,A: real,B: a] :
      ( ( F2 @ A @ B )
     => ( produc8713834143731921650al_a_o @ F2 @ ( product_Pair_real_a @ A @ B ) ) ) ).

% case_prodI
thf(fact_93_case__prodI,axiom,
    ! [F2: real > b > $o,A: real,B: b] :
      ( ( F2 @ A @ B )
     => ( produc5814611744267527345al_b_o @ F2 @ ( product_Pair_real_b @ A @ B ) ) ) ).

% case_prodI
thf(fact_94_case__prodI,axiom,
    ! [F2: b > a > $o,A: b,B: a] :
      ( ( F2 @ A @ B )
     => ( produc7672072387910335853_b_a_o @ F2 @ ( product_Pair_b_a @ A @ B ) ) ) ).

% case_prodI
thf(fact_95_case__prodI,axiom,
    ! [F2: a > real > $o,A: a,B: real] :
      ( ( F2 @ A @ B )
     => ( produc7718555431788333720real_o @ F2 @ ( product_Pair_a_real @ A @ B ) ) ) ).

% case_prodI
thf(fact_96_case__prodI,axiom,
    ! [F2: b > real > $o,A: b,B: real] :
      ( ( F2 @ A @ B )
     => ( produc9063020468597821655real_o @ F2 @ ( product_Pair_b_real @ A @ B ) ) ) ).

% case_prodI
thf(fact_97_case__prodI,axiom,
    ! [F2: product_prod_a_b > real > $o,A: product_prod_a_b,B: real] :
      ( ( F2 @ A @ B )
     => ( produc772314490721586030real_o @ F2 @ ( produc9021675809588086653b_real @ A @ B ) ) ) ).

% case_prodI
thf(fact_98_case__prodI2,axiom,
    ! [P: product_prod_real_a,C: real > a > $o] :
      ( ! [A3: real,B3: a] :
          ( ( P
            = ( product_Pair_real_a @ A3 @ B3 ) )
         => ( C @ A3 @ B3 ) )
     => ( produc8713834143731921650al_a_o @ C @ P ) ) ).

% case_prodI2
thf(fact_99_case__prodI2,axiom,
    ! [P: product_prod_real_b,C: real > b > $o] :
      ( ! [A3: real,B3: b] :
          ( ( P
            = ( product_Pair_real_b @ A3 @ B3 ) )
         => ( C @ A3 @ B3 ) )
     => ( produc5814611744267527345al_b_o @ C @ P ) ) ).

% case_prodI2
thf(fact_100_case__prodI2,axiom,
    ! [P: product_prod_b_a,C: b > a > $o] :
      ( ! [A3: b,B3: a] :
          ( ( P
            = ( product_Pair_b_a @ A3 @ B3 ) )
         => ( C @ A3 @ B3 ) )
     => ( produc7672072387910335853_b_a_o @ C @ P ) ) ).

% case_prodI2
thf(fact_101_case__prodI2,axiom,
    ! [P: product_prod_a_real,C: a > real > $o] :
      ( ! [A3: a,B3: real] :
          ( ( P
            = ( product_Pair_a_real @ A3 @ B3 ) )
         => ( C @ A3 @ B3 ) )
     => ( produc7718555431788333720real_o @ C @ P ) ) ).

% case_prodI2
thf(fact_102_case__prodI2,axiom,
    ! [P: product_prod_b_real,C: b > real > $o] :
      ( ! [A3: b,B3: real] :
          ( ( P
            = ( product_Pair_b_real @ A3 @ B3 ) )
         => ( C @ A3 @ B3 ) )
     => ( produc9063020468597821655real_o @ C @ P ) ) ).

% case_prodI2
thf(fact_103_case__prodI2,axiom,
    ! [P: produc7929879615859924995b_real,C: product_prod_a_b > real > $o] :
      ( ! [A3: product_prod_a_b,B3: real] :
          ( ( P
            = ( produc9021675809588086653b_real @ A3 @ B3 ) )
         => ( C @ A3 @ B3 ) )
     => ( produc772314490721586030real_o @ C @ P ) ) ).

% case_prodI2
thf(fact_104_mem__case__prodI,axiom,
    ! [Z3: real > real,C: real > a > set_real_real,A: real,B: a] :
      ( ( member_real_real @ Z3 @ ( C @ A @ B ) )
     => ( member_real_real @ Z3 @ ( produc7312632544308658771l_real @ C @ ( product_Pair_real_a @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_105_mem__case__prodI,axiom,
    ! [Z3: real > $o,C: real > a > set_real_o,A: real,B: a] :
      ( ( member_real_o @ Z3 @ ( C @ A @ B ) )
     => ( member_real_o @ Z3 @ ( produc9189443182227898589real_o @ C @ ( product_Pair_real_a @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_106_mem__case__prodI,axiom,
    ! [Z3: real > nat,C: real > a > set_real_nat,A: real,B: a] :
      ( ( member_real_nat @ Z3 @ ( C @ A @ B ) )
     => ( member_real_nat @ Z3 @ ( produc2853969746657022967al_nat @ C @ ( product_Pair_real_a @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_107_mem__case__prodI,axiom,
    ! [Z3: $o > real,C: real > a > set_o_real,A: real,B: a] :
      ( ( member_o_real @ Z3 @ ( C @ A @ B ) )
     => ( member_o_real @ Z3 @ ( produc1602803615379389039o_real @ C @ ( product_Pair_real_a @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_108_mem__case__prodI,axiom,
    ! [Z3: nat > real,C: real > a > set_nat_real,A: real,B: a] :
      ( ( member_nat_real @ Z3 @ ( C @ A @ B ) )
     => ( member_nat_real @ Z3 @ ( produc8887347644318195575t_real @ C @ ( product_Pair_real_a @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_109_mem__case__prodI,axiom,
    ! [Z3: real > real,C: real > b > set_real_real,A: real,B: b] :
      ( ( member_real_real @ Z3 @ ( C @ A @ B ) )
     => ( member_real_real @ Z3 @ ( produc4677890822933824468l_real @ C @ ( product_Pair_real_b @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_110_mem__case__prodI,axiom,
    ! [Z3: real > $o,C: real > b > set_real_o,A: real,B: b] :
      ( ( member_real_o @ Z3 @ ( C @ A @ B ) )
     => ( member_real_o @ Z3 @ ( produc7853392562275204252real_o @ C @ ( product_Pair_real_b @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_111_mem__case__prodI,axiom,
    ! [Z3: real > nat,C: real > b > set_real_nat,A: real,B: b] :
      ( ( member_real_nat @ Z3 @ ( C @ A @ B ) )
     => ( member_real_nat @ Z3 @ ( produc7833912894805526008al_nat @ C @ ( product_Pair_real_b @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_112_mem__case__prodI,axiom,
    ! [Z3: $o > real,C: real > b > set_o_real,A: real,B: b] :
      ( ( member_o_real @ Z3 @ ( C @ A @ B ) )
     => ( member_o_real @ Z3 @ ( produc266752995426694702o_real @ C @ ( product_Pair_real_b @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_113_mem__case__prodI,axiom,
    ! [Z3: nat > real,C: real > b > set_nat_real,A: real,B: b] :
      ( ( member_nat_real @ Z3 @ ( C @ A @ B ) )
     => ( member_nat_real @ Z3 @ ( produc4643918755611922808t_real @ C @ ( product_Pair_real_b @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_114_mem__case__prodI2,axiom,
    ! [P: product_prod_real_a,Z3: real > real,C: real > a > set_real_real] :
      ( ! [A3: real,B3: a] :
          ( ( P
            = ( product_Pair_real_a @ A3 @ B3 ) )
         => ( member_real_real @ Z3 @ ( C @ A3 @ B3 ) ) )
     => ( member_real_real @ Z3 @ ( produc7312632544308658771l_real @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_115_mem__case__prodI2,axiom,
    ! [P: product_prod_real_a,Z3: real > $o,C: real > a > set_real_o] :
      ( ! [A3: real,B3: a] :
          ( ( P
            = ( product_Pair_real_a @ A3 @ B3 ) )
         => ( member_real_o @ Z3 @ ( C @ A3 @ B3 ) ) )
     => ( member_real_o @ Z3 @ ( produc9189443182227898589real_o @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_116_mem__case__prodI2,axiom,
    ! [P: product_prod_real_a,Z3: real > nat,C: real > a > set_real_nat] :
      ( ! [A3: real,B3: a] :
          ( ( P
            = ( product_Pair_real_a @ A3 @ B3 ) )
         => ( member_real_nat @ Z3 @ ( C @ A3 @ B3 ) ) )
     => ( member_real_nat @ Z3 @ ( produc2853969746657022967al_nat @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_117_mem__case__prodI2,axiom,
    ! [P: product_prod_real_a,Z3: $o > real,C: real > a > set_o_real] :
      ( ! [A3: real,B3: a] :
          ( ( P
            = ( product_Pair_real_a @ A3 @ B3 ) )
         => ( member_o_real @ Z3 @ ( C @ A3 @ B3 ) ) )
     => ( member_o_real @ Z3 @ ( produc1602803615379389039o_real @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_118_mem__case__prodI2,axiom,
    ! [P: product_prod_real_a,Z3: nat > real,C: real > a > set_nat_real] :
      ( ! [A3: real,B3: a] :
          ( ( P
            = ( product_Pair_real_a @ A3 @ B3 ) )
         => ( member_nat_real @ Z3 @ ( C @ A3 @ B3 ) ) )
     => ( member_nat_real @ Z3 @ ( produc8887347644318195575t_real @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_119_mem__case__prodI2,axiom,
    ! [P: product_prod_real_b,Z3: real > real,C: real > b > set_real_real] :
      ( ! [A3: real,B3: b] :
          ( ( P
            = ( product_Pair_real_b @ A3 @ B3 ) )
         => ( member_real_real @ Z3 @ ( C @ A3 @ B3 ) ) )
     => ( member_real_real @ Z3 @ ( produc4677890822933824468l_real @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_120_mem__case__prodI2,axiom,
    ! [P: product_prod_real_b,Z3: real > $o,C: real > b > set_real_o] :
      ( ! [A3: real,B3: b] :
          ( ( P
            = ( product_Pair_real_b @ A3 @ B3 ) )
         => ( member_real_o @ Z3 @ ( C @ A3 @ B3 ) ) )
     => ( member_real_o @ Z3 @ ( produc7853392562275204252real_o @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_121_mem__case__prodI2,axiom,
    ! [P: product_prod_real_b,Z3: real > nat,C: real > b > set_real_nat] :
      ( ! [A3: real,B3: b] :
          ( ( P
            = ( product_Pair_real_b @ A3 @ B3 ) )
         => ( member_real_nat @ Z3 @ ( C @ A3 @ B3 ) ) )
     => ( member_real_nat @ Z3 @ ( produc7833912894805526008al_nat @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_122_mem__case__prodI2,axiom,
    ! [P: product_prod_real_b,Z3: $o > real,C: real > b > set_o_real] :
      ( ! [A3: real,B3: b] :
          ( ( P
            = ( product_Pair_real_b @ A3 @ B3 ) )
         => ( member_o_real @ Z3 @ ( C @ A3 @ B3 ) ) )
     => ( member_o_real @ Z3 @ ( produc266752995426694702o_real @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_123_mem__case__prodI2,axiom,
    ! [P: product_prod_real_b,Z3: nat > real,C: real > b > set_nat_real] :
      ( ! [A3: real,B3: b] :
          ( ( P
            = ( product_Pair_real_b @ A3 @ B3 ) )
         => ( member_nat_real @ Z3 @ ( C @ A3 @ B3 ) ) )
     => ( member_nat_real @ Z3 @ ( produc4643918755611922808t_real @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_124_curry__conv,axiom,
    ( product_curry_a_b_c
    = ( ^ [F: product_prod_a_b > c,A4: a,B4: b] : ( F @ ( product_Pair_a_b @ A4 @ B4 ) ) ) ) ).

% curry_conv
thf(fact_125_curry__conv,axiom,
    ( produc3831716361899747437_a_b_c
    = ( ^ [F: product_prod_real_a > b > c,A4: real,B4: a] : ( F @ ( product_Pair_real_a @ A4 @ B4 ) ) ) ) ).

% curry_conv
thf(fact_126_curry__conv,axiom,
    ( produc1339935578242556755_a_b_c
    = ( ^ [F: produc2857309735095370733al_a_b > c,A4: product_prod_real_a,B4: b] : ( F @ ( produc4061858189725916191al_a_b @ A4 @ B4 ) ) ) ) ).

% curry_conv
thf(fact_127_curry__case__prod,axiom,
    ! [F2: product_prod_real_a > b > c] :
      ( ( produc1339935578242556755_a_b_c @ ( produc431234068253794228_a_b_c @ F2 ) )
      = F2 ) ).

% curry_case_prod
thf(fact_128_curry__case__prod,axiom,
    ! [F2: real > a > b > c] :
      ( ( produc3831716361899747437_a_b_c @ ( produc8409101302566321868_a_b_c @ F2 ) )
      = F2 ) ).

% curry_case_prod
thf(fact_129_curry__case__prod,axiom,
    ! [F2: real > product_prod_a_b > c] :
      ( ( produc52276734196184271_a_b_c @ ( produc8366947261062197552_a_b_c @ F2 ) )
      = F2 ) ).

% curry_case_prod
thf(fact_130_curry__case__prod,axiom,
    ! [F2: a > b > c] :
      ( ( product_curry_a_b_c @ ( produc6028431345588019475_a_b_c @ F2 ) )
      = F2 ) ).

% curry_case_prod
thf(fact_131_curry__case__prod,axiom,
    ! [F2: real > b > c] :
      ( ( produc7369401904616417848al_b_c @ ( produc2835462372567216025al_b_c @ F2 ) )
      = F2 ) ).

% curry_case_prod
thf(fact_132_curry__case__prod,axiom,
    ! [F2: real > a > c] :
      ( ( produc933485449734318073al_a_c @ ( produc5622917954539892058al_a_c @ F2 ) )
      = F2 ) ).

% curry_case_prod
thf(fact_133_curry__case__prod,axiom,
    ! [F2: a > real > b > c] :
      ( ( produc2621439639359427143al_b_c @ ( produc7198824580026001574al_b_c @ F2 ) )
      = F2 ) ).

% curry_case_prod
thf(fact_134_case__prod__curry,axiom,
    ! [F2: produc2857309735095370733al_a_b > c] :
      ( ( produc431234068253794228_a_b_c @ ( produc1339935578242556755_a_b_c @ F2 ) )
      = F2 ) ).

% case_prod_curry
thf(fact_135_case__prod__curry,axiom,
    ! [F2: product_prod_real_a > b > c] :
      ( ( produc8409101302566321868_a_b_c @ ( produc3831716361899747437_a_b_c @ F2 ) )
      = F2 ) ).

% case_prod_curry
thf(fact_136_case__prod__curry,axiom,
    ! [F2: produc1405624045518934769od_a_b > c] :
      ( ( produc8366947261062197552_a_b_c @ ( produc52276734196184271_a_b_c @ F2 ) )
      = F2 ) ).

% case_prod_curry
thf(fact_137_case__prod__curry,axiom,
    ! [F2: product_prod_a_b > c] :
      ( ( produc6028431345588019475_a_b_c @ ( product_curry_a_b_c @ F2 ) )
      = F2 ) ).

% case_prod_curry
thf(fact_138_case__prod__curry,axiom,
    ! [F2: product_prod_real_b > c] :
      ( ( produc2835462372567216025al_b_c @ ( produc7369401904616417848al_b_c @ F2 ) )
      = F2 ) ).

% case_prod_curry
thf(fact_139_case__prod__curry,axiom,
    ! [F2: product_prod_real_a > c] :
      ( ( produc5622917954539892058al_a_c @ ( produc933485449734318073al_a_c @ F2 ) )
      = F2 ) ).

% case_prod_curry
thf(fact_140_case__prod__curry,axiom,
    ! [F2: product_prod_a_real > b > c] :
      ( ( produc7198824580026001574al_b_c @ ( produc2621439639359427143al_b_c @ F2 ) )
      = F2 ) ).

% case_prod_curry
thf(fact_141_case__prod__conv,axiom,
    ! [F2: real > a > b > c,A: real,B: a] :
      ( ( produc8409101302566321868_a_b_c @ F2 @ ( product_Pair_real_a @ A @ B ) )
      = ( F2 @ A @ B ) ) ).

% case_prod_conv
thf(fact_142_case__prod__conv,axiom,
    ! [F2: real > product_prod_a_b > c,A: real,B: product_prod_a_b] :
      ( ( produc8366947261062197552_a_b_c @ F2 @ ( produc6260613462353114019od_a_b @ A @ B ) )
      = ( F2 @ A @ B ) ) ).

% case_prod_conv
thf(fact_143_case__prod__conv,axiom,
    ! [F2: a > b > c,A: a,B: b] :
      ( ( produc6028431345588019475_a_b_c @ F2 @ ( product_Pair_a_b @ A @ B ) )
      = ( F2 @ A @ B ) ) ).

% case_prod_conv
thf(fact_144_case__prod__conv,axiom,
    ! [F2: real > b > c,A: real,B: b] :
      ( ( produc2835462372567216025al_b_c @ F2 @ ( product_Pair_real_b @ A @ B ) )
      = ( F2 @ A @ B ) ) ).

% case_prod_conv
thf(fact_145_case__prod__conv,axiom,
    ! [F2: real > a > c,A: real,B: a] :
      ( ( produc5622917954539892058al_a_c @ F2 @ ( product_Pair_real_a @ A @ B ) )
      = ( F2 @ A @ B ) ) ).

% case_prod_conv
thf(fact_146_case__prod__conv,axiom,
    ! [F2: a > real > b > c,A: a,B: real] :
      ( ( produc7198824580026001574al_b_c @ F2 @ ( product_Pair_a_real @ A @ B ) )
      = ( F2 @ A @ B ) ) ).

% case_prod_conv
thf(fact_147_prod_Ocollapse,axiom,
    ! [Prod: product_prod_real_b] :
      ( ( product_Pair_real_b @ ( product_fst_real_b @ Prod ) @ ( product_snd_real_b @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_148_prod_Ocollapse,axiom,
    ! [Prod: product_prod_b_a] :
      ( ( product_Pair_b_a @ ( product_fst_b_a @ Prod ) @ ( product_snd_b_a @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_149_prod_Ocollapse,axiom,
    ! [Prod: product_prod_a_real] :
      ( ( product_Pair_a_real @ ( product_fst_a_real @ Prod ) @ ( product_snd_a_real @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_150_prod_Ocollapse,axiom,
    ! [Prod: product_prod_b_real] :
      ( ( product_Pair_b_real @ ( product_fst_b_real @ Prod ) @ ( product_snd_b_real @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_151_prod_Ocollapse,axiom,
    ! [Prod: produc7929879615859924995b_real] :
      ( ( produc9021675809588086653b_real @ ( produc7266368915318857873b_real @ Prod ) @ ( produc7037151529651111887b_real @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_152_prod_Ocollapse,axiom,
    ! [Prod: produc2422161461964618553l_real] :
      ( ( produc4511245868158468465l_real @ ( produc5828954698716094813l_real @ Prod ) @ ( produc3484788084999411615l_real @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_153_prod_Ocollapse,axiom,
    ! [Prod: produc7716430852924023517t_real] :
      ( ( produc7837566107596912789t_real @ ( product_fst_nat_real @ Prod ) @ ( product_snd_nat_real @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_154_prod_Ocollapse,axiom,
    ! [Prod: product_prod_real_a] :
      ( ( product_Pair_real_a @ ( product_fst_real_a @ Prod ) @ ( product_snd_real_a @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_155_prod_Ocollapse,axiom,
    ! [Prod: produc1405624045518934769od_a_b] :
      ( ( produc6260613462353114019od_a_b @ ( produc4505306568083885239od_a_b @ Prod ) @ ( produc4276089182416139253od_a_b @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_156_prod_Ocollapse,axiom,
    ! [Prod: product_prod_a_b] :
      ( ( product_Pair_a_b @ ( product_fst_a_b @ Prod ) @ ( product_snd_a_b @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_157_prod_Oexpand,axiom,
    ! [Prod: produc2422161461964618553l_real,Prod2: produc2422161461964618553l_real] :
      ( ( ( ( produc5828954698716094813l_real @ Prod )
          = ( produc5828954698716094813l_real @ Prod2 ) )
        & ( ( produc3484788084999411615l_real @ Prod )
          = ( produc3484788084999411615l_real @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_158_prod_Oexpand,axiom,
    ! [Prod: produc7716430852924023517t_real,Prod2: produc7716430852924023517t_real] :
      ( ( ( ( product_fst_nat_real @ Prod )
          = ( product_fst_nat_real @ Prod2 ) )
        & ( ( product_snd_nat_real @ Prod )
          = ( product_snd_nat_real @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_159_prod_Oexpand,axiom,
    ! [Prod: product_prod_real_a,Prod2: product_prod_real_a] :
      ( ( ( ( product_fst_real_a @ Prod )
          = ( product_fst_real_a @ Prod2 ) )
        & ( ( product_snd_real_a @ Prod )
          = ( product_snd_real_a @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_160_prod_Oexpand,axiom,
    ! [Prod: produc1405624045518934769od_a_b,Prod2: produc1405624045518934769od_a_b] :
      ( ( ( ( produc4505306568083885239od_a_b @ Prod )
          = ( produc4505306568083885239od_a_b @ Prod2 ) )
        & ( ( produc4276089182416139253od_a_b @ Prod )
          = ( produc4276089182416139253od_a_b @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_161_prod_Oexpand,axiom,
    ! [Prod: product_prod_a_b,Prod2: product_prod_a_b] :
      ( ( ( ( product_fst_a_b @ Prod )
          = ( product_fst_a_b @ Prod2 ) )
        & ( ( product_snd_a_b @ Prod )
          = ( product_snd_a_b @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_162_prod_Osplit__sel,axiom,
    ! [P2: ( b > c ) > $o,F2: real > a > b > c,Prod: product_prod_real_a] :
      ( ( P2 @ ( produc8409101302566321868_a_b_c @ F2 @ Prod ) )
      = ( ( Prod
          = ( product_Pair_real_a @ ( product_fst_real_a @ Prod ) @ ( product_snd_real_a @ Prod ) ) )
       => ( P2 @ ( F2 @ ( product_fst_real_a @ Prod ) @ ( product_snd_real_a @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_163_prod_Osplit__sel,axiom,
    ! [P2: c > $o,F2: real > product_prod_a_b > c,Prod: produc1405624045518934769od_a_b] :
      ( ( P2 @ ( produc8366947261062197552_a_b_c @ F2 @ Prod ) )
      = ( ( Prod
          = ( produc6260613462353114019od_a_b @ ( produc4505306568083885239od_a_b @ Prod ) @ ( produc4276089182416139253od_a_b @ Prod ) ) )
       => ( P2 @ ( F2 @ ( produc4505306568083885239od_a_b @ Prod ) @ ( produc4276089182416139253od_a_b @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_164_prod_Osplit__sel,axiom,
    ! [P2: c > $o,F2: a > b > c,Prod: product_prod_a_b] :
      ( ( P2 @ ( produc6028431345588019475_a_b_c @ F2 @ Prod ) )
      = ( ( Prod
          = ( product_Pair_a_b @ ( product_fst_a_b @ Prod ) @ ( product_snd_a_b @ Prod ) ) )
       => ( P2 @ ( F2 @ ( product_fst_a_b @ Prod ) @ ( product_snd_a_b @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_165_prod_Osplit__sel,axiom,
    ! [P2: c > $o,F2: real > b > c,Prod: product_prod_real_b] :
      ( ( P2 @ ( produc2835462372567216025al_b_c @ F2 @ Prod ) )
      = ( ( Prod
          = ( product_Pair_real_b @ ( product_fst_real_b @ Prod ) @ ( product_snd_real_b @ Prod ) ) )
       => ( P2 @ ( F2 @ ( product_fst_real_b @ Prod ) @ ( product_snd_real_b @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_166_prod_Osplit__sel,axiom,
    ! [P2: c > $o,F2: real > a > c,Prod: product_prod_real_a] :
      ( ( P2 @ ( produc5622917954539892058al_a_c @ F2 @ Prod ) )
      = ( ( Prod
          = ( product_Pair_real_a @ ( product_fst_real_a @ Prod ) @ ( product_snd_real_a @ Prod ) ) )
       => ( P2 @ ( F2 @ ( product_fst_real_a @ Prod ) @ ( product_snd_real_a @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_167_prod_Osplit__sel,axiom,
    ! [P2: ( b > c ) > $o,F2: a > real > b > c,Prod: product_prod_a_real] :
      ( ( P2 @ ( produc7198824580026001574al_b_c @ F2 @ Prod ) )
      = ( ( Prod
          = ( product_Pair_a_real @ ( product_fst_a_real @ Prod ) @ ( product_snd_a_real @ Prod ) ) )
       => ( P2 @ ( F2 @ ( product_fst_a_real @ Prod ) @ ( product_snd_a_real @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_168_old_Oprod_Oexhaust,axiom,
    ! [Y4: product_prod_real_a] :
      ~ ! [A3: real,B3: a] :
          ( Y4
         != ( product_Pair_real_a @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_169_old_Oprod_Oexhaust,axiom,
    ! [Y4: product_prod_real_b] :
      ~ ! [A3: real,B3: b] :
          ( Y4
         != ( product_Pair_real_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_170_old_Oprod_Oexhaust,axiom,
    ! [Y4: product_prod_b_a] :
      ~ ! [A3: b,B3: a] :
          ( Y4
         != ( product_Pair_b_a @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_171_old_Oprod_Oexhaust,axiom,
    ! [Y4: product_prod_a_real] :
      ~ ! [A3: a,B3: real] :
          ( Y4
         != ( product_Pair_a_real @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_172_old_Oprod_Oexhaust,axiom,
    ! [Y4: product_prod_b_real] :
      ~ ! [A3: b,B3: real] :
          ( Y4
         != ( product_Pair_b_real @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_173_old_Oprod_Oexhaust,axiom,
    ! [Y4: produc7929879615859924995b_real] :
      ~ ! [A3: product_prod_a_b,B3: real] :
          ( Y4
         != ( produc9021675809588086653b_real @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_174_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_real_b] :
      ( Prod
      = ( product_Pair_real_b @ ( product_fst_real_b @ Prod ) @ ( product_snd_real_b @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_175_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_b_a] :
      ( Prod
      = ( product_Pair_b_a @ ( product_fst_b_a @ Prod ) @ ( product_snd_b_a @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_176_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_a_real] :
      ( Prod
      = ( product_Pair_a_real @ ( product_fst_a_real @ Prod ) @ ( product_snd_a_real @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_177_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_b_real] :
      ( Prod
      = ( product_Pair_b_real @ ( product_fst_b_real @ Prod ) @ ( product_snd_b_real @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_178_prod_Oexhaust__sel,axiom,
    ! [Prod: produc7929879615859924995b_real] :
      ( Prod
      = ( produc9021675809588086653b_real @ ( produc7266368915318857873b_real @ Prod ) @ ( produc7037151529651111887b_real @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_179_prod_Oexhaust__sel,axiom,
    ! [Prod: produc2422161461964618553l_real] :
      ( Prod
      = ( produc4511245868158468465l_real @ ( produc5828954698716094813l_real @ Prod ) @ ( produc3484788084999411615l_real @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_180_prod_Oexhaust__sel,axiom,
    ! [Prod: produc7716430852924023517t_real] :
      ( Prod
      = ( produc7837566107596912789t_real @ ( product_fst_nat_real @ Prod ) @ ( product_snd_nat_real @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_181_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_real_a] :
      ( Prod
      = ( product_Pair_real_a @ ( product_fst_real_a @ Prod ) @ ( product_snd_real_a @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_182_prod_Oexhaust__sel,axiom,
    ! [Prod: produc1405624045518934769od_a_b] :
      ( Prod
      = ( produc6260613462353114019od_a_b @ ( produc4505306568083885239od_a_b @ Prod ) @ ( produc4276089182416139253od_a_b @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_183_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_a_b] :
      ( Prod
      = ( product_Pair_a_b @ ( product_fst_a_b @ Prod ) @ ( product_snd_a_b @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_184_prod_Osplit__sel__asm,axiom,
    ! [P2: ( b > c ) > $o,F2: real > a > b > c,Prod: product_prod_real_a] :
      ( ( P2 @ ( produc8409101302566321868_a_b_c @ F2 @ Prod ) )
      = ( ~ ( ( Prod
              = ( product_Pair_real_a @ ( product_fst_real_a @ Prod ) @ ( product_snd_real_a @ Prod ) ) )
            & ~ ( P2 @ ( F2 @ ( product_fst_real_a @ Prod ) @ ( product_snd_real_a @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_185_prod_Osplit__sel__asm,axiom,
    ! [P2: c > $o,F2: real > product_prod_a_b > c,Prod: produc1405624045518934769od_a_b] :
      ( ( P2 @ ( produc8366947261062197552_a_b_c @ F2 @ Prod ) )
      = ( ~ ( ( Prod
              = ( produc6260613462353114019od_a_b @ ( produc4505306568083885239od_a_b @ Prod ) @ ( produc4276089182416139253od_a_b @ Prod ) ) )
            & ~ ( P2 @ ( F2 @ ( produc4505306568083885239od_a_b @ Prod ) @ ( produc4276089182416139253od_a_b @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_186_prod_Osplit__sel__asm,axiom,
    ! [P2: c > $o,F2: a > b > c,Prod: product_prod_a_b] :
      ( ( P2 @ ( produc6028431345588019475_a_b_c @ F2 @ Prod ) )
      = ( ~ ( ( Prod
              = ( product_Pair_a_b @ ( product_fst_a_b @ Prod ) @ ( product_snd_a_b @ Prod ) ) )
            & ~ ( P2 @ ( F2 @ ( product_fst_a_b @ Prod ) @ ( product_snd_a_b @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_187_prod_Osplit__sel__asm,axiom,
    ! [P2: c > $o,F2: real > b > c,Prod: product_prod_real_b] :
      ( ( P2 @ ( produc2835462372567216025al_b_c @ F2 @ Prod ) )
      = ( ~ ( ( Prod
              = ( product_Pair_real_b @ ( product_fst_real_b @ Prod ) @ ( product_snd_real_b @ Prod ) ) )
            & ~ ( P2 @ ( F2 @ ( product_fst_real_b @ Prod ) @ ( product_snd_real_b @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_188_prod_Osplit__sel__asm,axiom,
    ! [P2: c > $o,F2: real > a > c,Prod: product_prod_real_a] :
      ( ( P2 @ ( produc5622917954539892058al_a_c @ F2 @ Prod ) )
      = ( ~ ( ( Prod
              = ( product_Pair_real_a @ ( product_fst_real_a @ Prod ) @ ( product_snd_real_a @ Prod ) ) )
            & ~ ( P2 @ ( F2 @ ( product_fst_real_a @ Prod ) @ ( product_snd_real_a @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_189_prod_Osplit__sel__asm,axiom,
    ! [P2: ( b > c ) > $o,F2: a > real > b > c,Prod: product_prod_a_real] :
      ( ( P2 @ ( produc7198824580026001574al_b_c @ F2 @ Prod ) )
      = ( ~ ( ( Prod
              = ( product_Pair_a_real @ ( product_fst_a_real @ Prod ) @ ( product_snd_a_real @ Prod ) ) )
            & ~ ( P2 @ ( F2 @ ( product_fst_a_real @ Prod ) @ ( product_snd_a_real @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_190_curryD,axiom,
    ! [F2: product_prod_real_a > $o,A: real,B: a] :
      ( ( produc4069262006438169873al_a_o @ F2 @ A @ B )
     => ( F2 @ ( product_Pair_real_a @ A @ B ) ) ) ).

% curryD
thf(fact_191_curryD,axiom,
    ! [F2: product_prod_real_b > $o,A: real,B: b] :
      ( ( produc1170039606973775568al_b_o @ F2 @ A @ B )
     => ( F2 @ ( product_Pair_real_b @ A @ B ) ) ) ).

% curryD
thf(fact_192_curryD,axiom,
    ! [F2: product_prod_b_a > $o,A: b,B: a] :
      ( ( product_curry_b_a_o @ F2 @ A @ B )
     => ( F2 @ ( product_Pair_b_a @ A @ B ) ) ) ).

% curryD
thf(fact_193_curryD,axiom,
    ! [F2: product_prod_a_real > $o,A: a,B: real] :
      ( ( produc3073983294494581943real_o @ F2 @ A @ B )
     => ( F2 @ ( product_Pair_a_real @ A @ B ) ) ) ).

% curryD
thf(fact_194_curryD,axiom,
    ! [F2: product_prod_b_real > $o,A: b,B: real] :
      ( ( produc4418448331304069878real_o @ F2 @ A @ B )
     => ( F2 @ ( product_Pair_b_real @ A @ B ) ) ) ).

% curryD
thf(fact_195_curryD,axiom,
    ! [F2: produc7929879615859924995b_real > $o,A: product_prod_a_b,B: real] :
      ( ( produc5183746550669782669real_o @ F2 @ A @ B )
     => ( F2 @ ( produc9021675809588086653b_real @ A @ B ) ) ) ).

% curryD
thf(fact_196_curryE,axiom,
    ! [F2: product_prod_real_a > $o,A: real,B: a] :
      ( ( produc4069262006438169873al_a_o @ F2 @ A @ B )
     => ( F2 @ ( product_Pair_real_a @ A @ B ) ) ) ).

% curryE
thf(fact_197_curryE,axiom,
    ! [F2: product_prod_real_b > $o,A: real,B: b] :
      ( ( produc1170039606973775568al_b_o @ F2 @ A @ B )
     => ( F2 @ ( product_Pair_real_b @ A @ B ) ) ) ).

% curryE
thf(fact_198_curryE,axiom,
    ! [F2: product_prod_b_a > $o,A: b,B: a] :
      ( ( product_curry_b_a_o @ F2 @ A @ B )
     => ( F2 @ ( product_Pair_b_a @ A @ B ) ) ) ).

% curryE
thf(fact_199_curryE,axiom,
    ! [F2: product_prod_a_real > $o,A: a,B: real] :
      ( ( produc3073983294494581943real_o @ F2 @ A @ B )
     => ( F2 @ ( product_Pair_a_real @ A @ B ) ) ) ).

% curryE
thf(fact_200_curryE,axiom,
    ! [F2: product_prod_b_real > $o,A: b,B: real] :
      ( ( produc4418448331304069878real_o @ F2 @ A @ B )
     => ( F2 @ ( product_Pair_b_real @ A @ B ) ) ) ).

% curryE
thf(fact_201_curryE,axiom,
    ! [F2: produc7929879615859924995b_real > $o,A: product_prod_a_b,B: real] :
      ( ( produc5183746550669782669real_o @ F2 @ A @ B )
     => ( F2 @ ( produc9021675809588086653b_real @ A @ B ) ) ) ).

% curryE
thf(fact_202_curry__K,axiom,
    ! [C: c] :
      ( ( product_curry_a_b_c
        @ ^ [X2: product_prod_a_b] : C )
      = ( ^ [X2: a,Y2: b] : C ) ) ).

% curry_K
thf(fact_203_curry__K,axiom,
    ! [C: b > c] :
      ( ( produc3831716361899747437_a_b_c
        @ ^ [X2: product_prod_real_a] : C )
      = ( ^ [X2: real,Y2: a] : C ) ) ).

% curry_K
thf(fact_204_curry__K,axiom,
    ! [C: c] :
      ( ( produc1339935578242556755_a_b_c
        @ ^ [X2: produc2857309735095370733al_a_b] : C )
      = ( ^ [X2: product_prod_real_a,Y2: b] : C ) ) ).

% curry_K
thf(fact_205_fst__eqD,axiom,
    ! [X4: real,Y4: b,A: real] :
      ( ( ( product_fst_real_b @ ( product_Pair_real_b @ X4 @ Y4 ) )
        = A )
     => ( X4 = A ) ) ).

% fst_eqD
thf(fact_206_fst__eqD,axiom,
    ! [X4: b,Y4: a,A: b] :
      ( ( ( product_fst_b_a @ ( product_Pair_b_a @ X4 @ Y4 ) )
        = A )
     => ( X4 = A ) ) ).

% fst_eqD
thf(fact_207_fst__eqD,axiom,
    ! [X4: a,Y4: real,A: a] :
      ( ( ( product_fst_a_real @ ( product_Pair_a_real @ X4 @ Y4 ) )
        = A )
     => ( X4 = A ) ) ).

% fst_eqD
thf(fact_208_fst__eqD,axiom,
    ! [X4: b,Y4: real,A: b] :
      ( ( ( product_fst_b_real @ ( product_Pair_b_real @ X4 @ Y4 ) )
        = A )
     => ( X4 = A ) ) ).

% fst_eqD
thf(fact_209_fst__eqD,axiom,
    ! [X4: product_prod_a_b,Y4: real,A: product_prod_a_b] :
      ( ( ( produc7266368915318857873b_real @ ( produc9021675809588086653b_real @ X4 @ Y4 ) )
        = A )
     => ( X4 = A ) ) ).

% fst_eqD
thf(fact_210_fst__eqD,axiom,
    ! [X4: real,Y4: product_prod_a_b,A: real] :
      ( ( ( produc4505306568083885239od_a_b @ ( produc6260613462353114019od_a_b @ X4 @ Y4 ) )
        = A )
     => ( X4 = A ) ) ).

% fst_eqD
thf(fact_211_fst__eqD,axiom,
    ! [X4: a,Y4: b,A: a] :
      ( ( ( product_fst_a_b @ ( product_Pair_a_b @ X4 @ Y4 ) )
        = A )
     => ( X4 = A ) ) ).

% fst_eqD
thf(fact_212_fst__eqD,axiom,
    ! [X4: real,Y4: real,A: real] :
      ( ( ( produc5828954698716094813l_real @ ( produc4511245868158468465l_real @ X4 @ Y4 ) )
        = A )
     => ( X4 = A ) ) ).

% fst_eqD
thf(fact_213_fst__eqD,axiom,
    ! [X4: nat,Y4: real,A: nat] :
      ( ( ( product_fst_nat_real @ ( produc7837566107596912789t_real @ X4 @ Y4 ) )
        = A )
     => ( X4 = A ) ) ).

% fst_eqD
thf(fact_214_fst__eqD,axiom,
    ! [X4: real,Y4: a,A: real] :
      ( ( ( product_fst_real_a @ ( product_Pair_real_a @ X4 @ Y4 ) )
        = A )
     => ( X4 = A ) ) ).

% fst_eqD
thf(fact_215_snd__eqD,axiom,
    ! [X4: real,Y4: a,A: a] :
      ( ( ( product_snd_real_a @ ( product_Pair_real_a @ X4 @ Y4 ) )
        = A )
     => ( Y4 = A ) ) ).

% snd_eqD
thf(fact_216_snd__eqD,axiom,
    ! [X4: real,Y4: b,A: b] :
      ( ( ( product_snd_real_b @ ( product_Pair_real_b @ X4 @ Y4 ) )
        = A )
     => ( Y4 = A ) ) ).

% snd_eqD
thf(fact_217_snd__eqD,axiom,
    ! [X4: b,Y4: a,A: a] :
      ( ( ( product_snd_b_a @ ( product_Pair_b_a @ X4 @ Y4 ) )
        = A )
     => ( Y4 = A ) ) ).

% snd_eqD
thf(fact_218_snd__eqD,axiom,
    ! [X4: a,Y4: real,A: real] :
      ( ( ( product_snd_a_real @ ( product_Pair_a_real @ X4 @ Y4 ) )
        = A )
     => ( Y4 = A ) ) ).

% snd_eqD
thf(fact_219_snd__eqD,axiom,
    ! [X4: b,Y4: real,A: real] :
      ( ( ( product_snd_b_real @ ( product_Pair_b_real @ X4 @ Y4 ) )
        = A )
     => ( Y4 = A ) ) ).

% snd_eqD
thf(fact_220_snd__eqD,axiom,
    ! [X4: product_prod_a_b,Y4: real,A: real] :
      ( ( ( produc7037151529651111887b_real @ ( produc9021675809588086653b_real @ X4 @ Y4 ) )
        = A )
     => ( Y4 = A ) ) ).

% snd_eqD
thf(fact_221_snd__eqD,axiom,
    ! [X4: real,Y4: product_prod_a_b,A: product_prod_a_b] :
      ( ( ( produc4276089182416139253od_a_b @ ( produc6260613462353114019od_a_b @ X4 @ Y4 ) )
        = A )
     => ( Y4 = A ) ) ).

% snd_eqD
thf(fact_222_snd__eqD,axiom,
    ! [X4: a,Y4: b,A: b] :
      ( ( ( product_snd_a_b @ ( product_Pair_a_b @ X4 @ Y4 ) )
        = A )
     => ( Y4 = A ) ) ).

% snd_eqD
thf(fact_223_fst__conv,axiom,
    ! [X12: real,X23: b] :
      ( ( product_fst_real_b @ ( product_Pair_real_b @ X12 @ X23 ) )
      = X12 ) ).

% fst_conv
thf(fact_224_fst__conv,axiom,
    ! [X12: b,X23: a] :
      ( ( product_fst_b_a @ ( product_Pair_b_a @ X12 @ X23 ) )
      = X12 ) ).

% fst_conv
thf(fact_225_fst__conv,axiom,
    ! [X12: a,X23: real] :
      ( ( product_fst_a_real @ ( product_Pair_a_real @ X12 @ X23 ) )
      = X12 ) ).

% fst_conv
thf(fact_226_fst__conv,axiom,
    ! [X12: b,X23: real] :
      ( ( product_fst_b_real @ ( product_Pair_b_real @ X12 @ X23 ) )
      = X12 ) ).

% fst_conv
thf(fact_227_fst__conv,axiom,
    ! [X12: product_prod_a_b,X23: real] :
      ( ( produc7266368915318857873b_real @ ( produc9021675809588086653b_real @ X12 @ X23 ) )
      = X12 ) ).

% fst_conv
thf(fact_228_fst__conv,axiom,
    ! [X12: real,X23: product_prod_a_b] :
      ( ( produc4505306568083885239od_a_b @ ( produc6260613462353114019od_a_b @ X12 @ X23 ) )
      = X12 ) ).

% fst_conv
thf(fact_229_fst__conv,axiom,
    ! [X12: a,X23: b] :
      ( ( product_fst_a_b @ ( product_Pair_a_b @ X12 @ X23 ) )
      = X12 ) ).

% fst_conv
thf(fact_230_fst__conv,axiom,
    ! [X12: real,X23: real] :
      ( ( produc5828954698716094813l_real @ ( produc4511245868158468465l_real @ X12 @ X23 ) )
      = X12 ) ).

% fst_conv
thf(fact_231_fst__conv,axiom,
    ! [X12: nat,X23: real] :
      ( ( product_fst_nat_real @ ( produc7837566107596912789t_real @ X12 @ X23 ) )
      = X12 ) ).

% fst_conv
thf(fact_232_fst__conv,axiom,
    ! [X12: real,X23: a] :
      ( ( product_fst_real_a @ ( product_Pair_real_a @ X12 @ X23 ) )
      = X12 ) ).

% fst_conv
thf(fact_233_prod__eqI,axiom,
    ! [P: produc2422161461964618553l_real,Q: produc2422161461964618553l_real] :
      ( ( ( produc5828954698716094813l_real @ P )
        = ( produc5828954698716094813l_real @ Q ) )
     => ( ( ( produc3484788084999411615l_real @ P )
          = ( produc3484788084999411615l_real @ Q ) )
       => ( P = Q ) ) ) ).

% prod_eqI
thf(fact_234_prod__eqI,axiom,
    ! [P: produc7716430852924023517t_real,Q: produc7716430852924023517t_real] :
      ( ( ( product_fst_nat_real @ P )
        = ( product_fst_nat_real @ Q ) )
     => ( ( ( product_snd_nat_real @ P )
          = ( product_snd_nat_real @ Q ) )
       => ( P = Q ) ) ) ).

% prod_eqI
thf(fact_235_prod__eqI,axiom,
    ! [P: product_prod_real_a,Q: product_prod_real_a] :
      ( ( ( product_fst_real_a @ P )
        = ( product_fst_real_a @ Q ) )
     => ( ( ( product_snd_real_a @ P )
          = ( product_snd_real_a @ Q ) )
       => ( P = Q ) ) ) ).

% prod_eqI
thf(fact_236_prod__eqI,axiom,
    ! [P: produc1405624045518934769od_a_b,Q: produc1405624045518934769od_a_b] :
      ( ( ( produc4505306568083885239od_a_b @ P )
        = ( produc4505306568083885239od_a_b @ Q ) )
     => ( ( ( produc4276089182416139253od_a_b @ P )
          = ( produc4276089182416139253od_a_b @ Q ) )
       => ( P = Q ) ) ) ).

% prod_eqI
thf(fact_237_prod__eqI,axiom,
    ! [P: product_prod_a_b,Q: product_prod_a_b] :
      ( ( ( product_fst_a_b @ P )
        = ( product_fst_a_b @ Q ) )
     => ( ( ( product_snd_a_b @ P )
          = ( product_snd_a_b @ Q ) )
       => ( P = Q ) ) ) ).

% prod_eqI
thf(fact_238_snd__conv,axiom,
    ! [X12: real,X23: a] :
      ( ( product_snd_real_a @ ( product_Pair_real_a @ X12 @ X23 ) )
      = X23 ) ).

% snd_conv
thf(fact_239_snd__conv,axiom,
    ! [X12: real,X23: b] :
      ( ( product_snd_real_b @ ( product_Pair_real_b @ X12 @ X23 ) )
      = X23 ) ).

% snd_conv
thf(fact_240_snd__conv,axiom,
    ! [X12: b,X23: a] :
      ( ( product_snd_b_a @ ( product_Pair_b_a @ X12 @ X23 ) )
      = X23 ) ).

% snd_conv
thf(fact_241_snd__conv,axiom,
    ! [X12: a,X23: real] :
      ( ( product_snd_a_real @ ( product_Pair_a_real @ X12 @ X23 ) )
      = X23 ) ).

% snd_conv
thf(fact_242_snd__conv,axiom,
    ! [X12: b,X23: real] :
      ( ( product_snd_b_real @ ( product_Pair_b_real @ X12 @ X23 ) )
      = X23 ) ).

% snd_conv
thf(fact_243_snd__conv,axiom,
    ! [X12: product_prod_a_b,X23: real] :
      ( ( produc7037151529651111887b_real @ ( produc9021675809588086653b_real @ X12 @ X23 ) )
      = X23 ) ).

% snd_conv
thf(fact_244_snd__conv,axiom,
    ! [X12: real,X23: product_prod_a_b] :
      ( ( produc4276089182416139253od_a_b @ ( produc6260613462353114019od_a_b @ X12 @ X23 ) )
      = X23 ) ).

% snd_conv
thf(fact_245_snd__conv,axiom,
    ! [X12: a,X23: b] :
      ( ( product_snd_a_b @ ( product_Pair_a_b @ X12 @ X23 ) )
      = X23 ) ).

% snd_conv
thf(fact_246_curry__def,axiom,
    ( product_curry_a_b_c
    = ( ^ [C2: product_prod_a_b > c,X2: a,Y2: b] : ( C2 @ ( product_Pair_a_b @ X2 @ Y2 ) ) ) ) ).

% curry_def
thf(fact_247_curry__def,axiom,
    ( produc3831716361899747437_a_b_c
    = ( ^ [C2: product_prod_real_a > b > c,X2: real,Y2: a] : ( C2 @ ( product_Pair_real_a @ X2 @ Y2 ) ) ) ) ).

% curry_def
thf(fact_248_curry__def,axiom,
    ( produc1339935578242556755_a_b_c
    = ( ^ [C2: produc2857309735095370733al_a_b > c,X2: product_prod_real_a,Y2: b] : ( C2 @ ( produc4061858189725916191al_a_b @ X2 @ Y2 ) ) ) ) ).

% curry_def
thf(fact_249_surj__pair,axiom,
    ! [P: product_prod_real_a] :
    ? [X5: real,Y5: a] :
      ( P
      = ( product_Pair_real_a @ X5 @ Y5 ) ) ).

% surj_pair
thf(fact_250_surj__pair,axiom,
    ! [P: product_prod_real_b] :
    ? [X5: real,Y5: b] :
      ( P
      = ( product_Pair_real_b @ X5 @ Y5 ) ) ).

% surj_pair
thf(fact_251_surj__pair,axiom,
    ! [P: product_prod_b_a] :
    ? [X5: b,Y5: a] :
      ( P
      = ( product_Pair_b_a @ X5 @ Y5 ) ) ).

% surj_pair
thf(fact_252_surj__pair,axiom,
    ! [P: product_prod_a_real] :
    ? [X5: a,Y5: real] :
      ( P
      = ( product_Pair_a_real @ X5 @ Y5 ) ) ).

% surj_pair
thf(fact_253_surj__pair,axiom,
    ! [P: product_prod_b_real] :
    ? [X5: b,Y5: real] :
      ( P
      = ( product_Pair_b_real @ X5 @ Y5 ) ) ).

% surj_pair
thf(fact_254_surj__pair,axiom,
    ! [P: produc7929879615859924995b_real] :
    ? [X5: product_prod_a_b,Y5: real] :
      ( P
      = ( produc9021675809588086653b_real @ X5 @ Y5 ) ) ).

% surj_pair
thf(fact_255_case__prodD,axiom,
    ! [F2: real > a > $o,A: real,B: a] :
      ( ( produc8713834143731921650al_a_o @ F2 @ ( product_Pair_real_a @ A @ B ) )
     => ( F2 @ A @ B ) ) ).

% case_prodD
thf(fact_256_case__prodD,axiom,
    ! [F2: real > b > $o,A: real,B: b] :
      ( ( produc5814611744267527345al_b_o @ F2 @ ( product_Pair_real_b @ A @ B ) )
     => ( F2 @ A @ B ) ) ).

% case_prodD
thf(fact_257_case__prodD,axiom,
    ! [F2: b > a > $o,A: b,B: a] :
      ( ( produc7672072387910335853_b_a_o @ F2 @ ( product_Pair_b_a @ A @ B ) )
     => ( F2 @ A @ B ) ) ).

% case_prodD
thf(fact_258_case__prodD,axiom,
    ! [F2: a > real > $o,A: a,B: real] :
      ( ( produc7718555431788333720real_o @ F2 @ ( product_Pair_a_real @ A @ B ) )
     => ( F2 @ A @ B ) ) ).

% case_prodD
thf(fact_259_case__prodD,axiom,
    ! [F2: b > real > $o,A: b,B: real] :
      ( ( produc9063020468597821655real_o @ F2 @ ( product_Pair_b_real @ A @ B ) )
     => ( F2 @ A @ B ) ) ).

% case_prodD
thf(fact_260_case__prodD,axiom,
    ! [F2: product_prod_a_b > real > $o,A: product_prod_a_b,B: real] :
      ( ( produc772314490721586030real_o @ F2 @ ( produc9021675809588086653b_real @ A @ B ) )
     => ( F2 @ A @ B ) ) ).

% case_prodD
thf(fact_261_case__prodE,axiom,
    ! [C: real > a > $o,P: product_prod_real_a] :
      ( ( produc8713834143731921650al_a_o @ C @ P )
     => ~ ! [X5: real,Y5: a] :
            ( ( P
              = ( product_Pair_real_a @ X5 @ Y5 ) )
           => ~ ( C @ X5 @ Y5 ) ) ) ).

% case_prodE
thf(fact_262_case__prodE,axiom,
    ! [C: real > b > $o,P: product_prod_real_b] :
      ( ( produc5814611744267527345al_b_o @ C @ P )
     => ~ ! [X5: real,Y5: b] :
            ( ( P
              = ( product_Pair_real_b @ X5 @ Y5 ) )
           => ~ ( C @ X5 @ Y5 ) ) ) ).

% case_prodE
thf(fact_263_case__prodE,axiom,
    ! [C: b > a > $o,P: product_prod_b_a] :
      ( ( produc7672072387910335853_b_a_o @ C @ P )
     => ~ ! [X5: b,Y5: a] :
            ( ( P
              = ( product_Pair_b_a @ X5 @ Y5 ) )
           => ~ ( C @ X5 @ Y5 ) ) ) ).

% case_prodE
thf(fact_264_case__prodE,axiom,
    ! [C: a > real > $o,P: product_prod_a_real] :
      ( ( produc7718555431788333720real_o @ C @ P )
     => ~ ! [X5: a,Y5: real] :
            ( ( P
              = ( product_Pair_a_real @ X5 @ Y5 ) )
           => ~ ( C @ X5 @ Y5 ) ) ) ).

% case_prodE
thf(fact_265_case__prodE,axiom,
    ! [C: b > real > $o,P: product_prod_b_real] :
      ( ( produc9063020468597821655real_o @ C @ P )
     => ~ ! [X5: b,Y5: real] :
            ( ( P
              = ( product_Pair_b_real @ X5 @ Y5 ) )
           => ~ ( C @ X5 @ Y5 ) ) ) ).

% case_prodE
thf(fact_266_case__prodE,axiom,
    ! [C: product_prod_a_b > real > $o,P: produc7929879615859924995b_real] :
      ( ( produc772314490721586030real_o @ C @ P )
     => ~ ! [X5: product_prod_a_b,Y5: real] :
            ( ( P
              = ( produc9021675809588086653b_real @ X5 @ Y5 ) )
           => ~ ( C @ X5 @ Y5 ) ) ) ).

% case_prodE
thf(fact_267_prod__cases,axiom,
    ! [P2: product_prod_real_a > $o,P: product_prod_real_a] :
      ( ! [A3: real,B3: a] : ( P2 @ ( product_Pair_real_a @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_268_prod__cases,axiom,
    ! [P2: product_prod_real_b > $o,P: product_prod_real_b] :
      ( ! [A3: real,B3: b] : ( P2 @ ( product_Pair_real_b @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_269_prod__cases,axiom,
    ! [P2: product_prod_b_a > $o,P: product_prod_b_a] :
      ( ! [A3: b,B3: a] : ( P2 @ ( product_Pair_b_a @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_270_prod__cases,axiom,
    ! [P2: product_prod_a_real > $o,P: product_prod_a_real] :
      ( ! [A3: a,B3: real] : ( P2 @ ( product_Pair_a_real @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_271_prod__cases,axiom,
    ! [P2: product_prod_b_real > $o,P: product_prod_b_real] :
      ( ! [A3: b,B3: real] : ( P2 @ ( product_Pair_b_real @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_272_prod__cases,axiom,
    ! [P2: produc7929879615859924995b_real > $o,P: produc7929879615859924995b_real] :
      ( ! [A3: product_prod_a_b,B3: real] : ( P2 @ ( produc9021675809588086653b_real @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_273_mem__Collect__eq,axiom,
    ! [A: nat,P2: nat > $o] :
      ( ( member_nat @ A @ ( collect_nat @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_274_mem__Collect__eq,axiom,
    ! [A: real > real,P2: ( real > real ) > $o] :
      ( ( member_real_real @ A @ ( collect_real_real @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_275_mem__Collect__eq,axiom,
    ! [A: real > $o,P2: ( real > $o ) > $o] :
      ( ( member_real_o @ A @ ( collect_real_o @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_276_mem__Collect__eq,axiom,
    ! [A: real > nat,P2: ( real > nat ) > $o] :
      ( ( member_real_nat @ A @ ( collect_real_nat @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_277_mem__Collect__eq,axiom,
    ! [A: $o > real,P2: ( $o > real ) > $o] :
      ( ( member_o_real @ A @ ( collect_o_real @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_278_mem__Collect__eq,axiom,
    ! [A: nat > real,P2: ( nat > real ) > $o] :
      ( ( member_nat_real @ A @ ( collect_nat_real @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_279_mem__Collect__eq,axiom,
    ! [A: product_prod_a_b > c,P2: ( product_prod_a_b > c ) > $o] :
      ( ( member1080921174361771732_a_b_c @ A @ ( collec2250730349472415762_a_b_c @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_280_mem__Collect__eq,axiom,
    ! [A: a > b > c,P2: ( a > b > c ) > $o] :
      ( ( member_a_b_c @ A @ ( collect_a_b_c @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_281_mem__Collect__eq,axiom,
    ! [A: real > b > c,P2: ( real > b > c ) > $o] :
      ( ( member_real_b_c @ A @ ( collect_real_b_c @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_282_mem__Collect__eq,axiom,
    ! [A: product_prod_a_real > b > c,P2: ( product_prod_a_real > b > c ) > $o] :
      ( ( member2979925738865732021al_b_c @ A @ ( collec8928082604386625267al_b_c @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_283_Collect__mem__eq,axiom,
    ! [A5: set_nat] :
      ( ( collect_nat
        @ ^ [X2: nat] : ( member_nat @ X2 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_284_Collect__mem__eq,axiom,
    ! [A5: set_real_real] :
      ( ( collect_real_real
        @ ^ [X2: real > real] : ( member_real_real @ X2 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_285_Collect__mem__eq,axiom,
    ! [A5: set_real_o] :
      ( ( collect_real_o
        @ ^ [X2: real > $o] : ( member_real_o @ X2 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_286_Collect__mem__eq,axiom,
    ! [A5: set_real_nat] :
      ( ( collect_real_nat
        @ ^ [X2: real > nat] : ( member_real_nat @ X2 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_287_Collect__mem__eq,axiom,
    ! [A5: set_o_real] :
      ( ( collect_o_real
        @ ^ [X2: $o > real] : ( member_o_real @ X2 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_288_Collect__mem__eq,axiom,
    ! [A5: set_nat_real] :
      ( ( collect_nat_real
        @ ^ [X2: nat > real] : ( member_nat_real @ X2 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_289_Collect__mem__eq,axiom,
    ! [A5: set_Pr3745489628154206067_a_b_c] :
      ( ( collec2250730349472415762_a_b_c
        @ ^ [X2: product_prod_a_b > c] : ( member1080921174361771732_a_b_c @ X2 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_290_Collect__mem__eq,axiom,
    ! [A5: set_a_b_c] :
      ( ( collect_a_b_c
        @ ^ [X2: a > b > c] : ( member_a_b_c @ X2 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_291_Collect__mem__eq,axiom,
    ! [A5: set_real_b_c] :
      ( ( collect_real_b_c
        @ ^ [X2: real > b > c] : ( member_real_b_c @ X2 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_292_Collect__mem__eq,axiom,
    ! [A5: set_Pr1939300435541301716al_b_c] :
      ( ( collec8928082604386625267al_b_c
        @ ^ [X2: product_prod_a_real > b > c] : ( member2979925738865732021al_b_c @ X2 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_293_Collect__cong,axiom,
    ! [P2: nat > $o,Q2: nat > $o] :
      ( ! [X5: nat] :
          ( ( P2 @ X5 )
          = ( Q2 @ X5 ) )
     => ( ( collect_nat @ P2 )
        = ( collect_nat @ Q2 ) ) ) ).

% Collect_cong
thf(fact_294_Collect__cong,axiom,
    ! [P2: ( real > a > b > c ) > $o,Q2: ( real > a > b > c ) > $o] :
      ( ! [X5: real > a > b > c] :
          ( ( P2 @ X5 )
          = ( Q2 @ X5 ) )
     => ( ( collect_real_a_b_c @ P2 )
        = ( collect_real_a_b_c @ Q2 ) ) ) ).

% Collect_cong
thf(fact_295_Collect__cong,axiom,
    ! [P2: ( real > b > c ) > $o,Q2: ( real > b > c ) > $o] :
      ( ! [X5: real > b > c] :
          ( ( P2 @ X5 )
          = ( Q2 @ X5 ) )
     => ( ( collect_real_b_c @ P2 )
        = ( collect_real_b_c @ Q2 ) ) ) ).

% Collect_cong
thf(fact_296_Collect__cong,axiom,
    ! [P2: ( real > product_prod_a_b > c ) > $o,Q2: ( real > product_prod_a_b > c ) > $o] :
      ( ! [X5: real > product_prod_a_b > c] :
          ( ( P2 @ X5 )
          = ( Q2 @ X5 ) )
     => ( ( collec9182426333961588829_a_b_c @ P2 )
        = ( collec9182426333961588829_a_b_c @ Q2 ) ) ) ).

% Collect_cong
thf(fact_297_split__beta,axiom,
    ( produc8409101302566321868_a_b_c
    = ( ^ [F: real > a > b > c,Prod3: product_prod_real_a] : ( F @ ( product_fst_real_a @ Prod3 ) @ ( product_snd_real_a @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_298_split__beta,axiom,
    ( produc8366947261062197552_a_b_c
    = ( ^ [F: real > product_prod_a_b > c,Prod3: produc1405624045518934769od_a_b] : ( F @ ( produc4505306568083885239od_a_b @ Prod3 ) @ ( produc4276089182416139253od_a_b @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_299_split__beta,axiom,
    ( produc6028431345588019475_a_b_c
    = ( ^ [F: a > b > c,Prod3: product_prod_a_b] : ( F @ ( product_fst_a_b @ Prod3 ) @ ( product_snd_a_b @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_300_split__beta,axiom,
    ( produc2835462372567216025al_b_c
    = ( ^ [F: real > b > c,Prod3: product_prod_real_b] : ( F @ ( product_fst_real_b @ Prod3 ) @ ( product_snd_real_b @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_301_split__beta,axiom,
    ( produc5622917954539892058al_a_c
    = ( ^ [F: real > a > c,Prod3: product_prod_real_a] : ( F @ ( product_fst_real_a @ Prod3 ) @ ( product_snd_real_a @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_302_split__beta,axiom,
    ( produc7198824580026001574al_b_c
    = ( ^ [F: a > real > b > c,Prod3: product_prod_a_real] : ( F @ ( product_fst_a_real @ Prod3 ) @ ( product_snd_a_real @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_303_Pair__inject,axiom,
    ! [A: real,B: a,A2: real,B2: a] :
      ( ( ( product_Pair_real_a @ A @ B )
        = ( product_Pair_real_a @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_304_Pair__inject,axiom,
    ! [A: real,B: b,A2: real,B2: b] :
      ( ( ( product_Pair_real_b @ A @ B )
        = ( product_Pair_real_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_305_Pair__inject,axiom,
    ! [A: b,B: a,A2: b,B2: a] :
      ( ( ( product_Pair_b_a @ A @ B )
        = ( product_Pair_b_a @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_306_Pair__inject,axiom,
    ! [A: a,B: real,A2: a,B2: real] :
      ( ( ( product_Pair_a_real @ A @ B )
        = ( product_Pair_a_real @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_307_Pair__inject,axiom,
    ! [A: b,B: real,A2: b,B2: real] :
      ( ( ( product_Pair_b_real @ A @ B )
        = ( product_Pair_b_real @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_308_Pair__inject,axiom,
    ! [A: product_prod_a_b,B: real,A2: product_prod_a_b,B2: real] :
      ( ( ( produc9021675809588086653b_real @ A @ B )
        = ( produc9021675809588086653b_real @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_309_prod__eq__iff,axiom,
    ( ( ^ [Y6: produc2422161461964618553l_real,Z4: produc2422161461964618553l_real] : ( Y6 = Z4 ) )
    = ( ^ [S: produc2422161461964618553l_real,T: produc2422161461964618553l_real] :
          ( ( ( produc5828954698716094813l_real @ S )
            = ( produc5828954698716094813l_real @ T ) )
          & ( ( produc3484788084999411615l_real @ S )
            = ( produc3484788084999411615l_real @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_310_prod__eq__iff,axiom,
    ( ( ^ [Y6: produc7716430852924023517t_real,Z4: produc7716430852924023517t_real] : ( Y6 = Z4 ) )
    = ( ^ [S: produc7716430852924023517t_real,T: produc7716430852924023517t_real] :
          ( ( ( product_fst_nat_real @ S )
            = ( product_fst_nat_real @ T ) )
          & ( ( product_snd_nat_real @ S )
            = ( product_snd_nat_real @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_311_prod__eq__iff,axiom,
    ( ( ^ [Y6: product_prod_real_a,Z4: product_prod_real_a] : ( Y6 = Z4 ) )
    = ( ^ [S: product_prod_real_a,T: product_prod_real_a] :
          ( ( ( product_fst_real_a @ S )
            = ( product_fst_real_a @ T ) )
          & ( ( product_snd_real_a @ S )
            = ( product_snd_real_a @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_312_prod__eq__iff,axiom,
    ( ( ^ [Y6: produc1405624045518934769od_a_b,Z4: produc1405624045518934769od_a_b] : ( Y6 = Z4 ) )
    = ( ^ [S: produc1405624045518934769od_a_b,T: produc1405624045518934769od_a_b] :
          ( ( ( produc4505306568083885239od_a_b @ S )
            = ( produc4505306568083885239od_a_b @ T ) )
          & ( ( produc4276089182416139253od_a_b @ S )
            = ( produc4276089182416139253od_a_b @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_313_prod__eq__iff,axiom,
    ( ( ^ [Y6: product_prod_a_b,Z4: product_prod_a_b] : ( Y6 = Z4 ) )
    = ( ^ [S: product_prod_a_b,T: product_prod_a_b] :
          ( ( ( product_fst_a_b @ S )
            = ( product_fst_a_b @ T ) )
          & ( ( product_snd_a_b @ S )
            = ( product_snd_a_b @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_314_case__prod__beta,axiom,
    ( produc8409101302566321868_a_b_c
    = ( ^ [F: real > a > b > c,P3: product_prod_real_a] : ( F @ ( product_fst_real_a @ P3 ) @ ( product_snd_real_a @ P3 ) ) ) ) ).

% case_prod_beta
thf(fact_315_case__prod__beta,axiom,
    ( produc8366947261062197552_a_b_c
    = ( ^ [F: real > product_prod_a_b > c,P3: produc1405624045518934769od_a_b] : ( F @ ( produc4505306568083885239od_a_b @ P3 ) @ ( produc4276089182416139253od_a_b @ P3 ) ) ) ) ).

% case_prod_beta
thf(fact_316_case__prod__beta,axiom,
    ( produc6028431345588019475_a_b_c
    = ( ^ [F: a > b > c,P3: product_prod_a_b] : ( F @ ( product_fst_a_b @ P3 ) @ ( product_snd_a_b @ P3 ) ) ) ) ).

% case_prod_beta
thf(fact_317_case__prod__beta,axiom,
    ( produc2835462372567216025al_b_c
    = ( ^ [F: real > b > c,P3: product_prod_real_b] : ( F @ ( product_fst_real_b @ P3 ) @ ( product_snd_real_b @ P3 ) ) ) ) ).

% case_prod_beta
thf(fact_318_case__prod__beta,axiom,
    ( produc5622917954539892058al_a_c
    = ( ^ [F: real > a > c,P3: product_prod_real_a] : ( F @ ( product_fst_real_a @ P3 ) @ ( product_snd_real_a @ P3 ) ) ) ) ).

% case_prod_beta
thf(fact_319_case__prod__beta,axiom,
    ( produc7198824580026001574al_b_c
    = ( ^ [F: a > real > b > c,P3: product_prod_a_real] : ( F @ ( product_fst_a_real @ P3 ) @ ( product_snd_a_real @ P3 ) ) ) ) ).

% case_prod_beta
thf(fact_320_mem__case__prodE,axiom,
    ! [Z3: real > real,C: real > a > set_real_real,P: product_prod_real_a] :
      ( ( member_real_real @ Z3 @ ( produc7312632544308658771l_real @ C @ P ) )
     => ~ ! [X5: real,Y5: a] :
            ( ( P
              = ( product_Pair_real_a @ X5 @ Y5 ) )
           => ~ ( member_real_real @ Z3 @ ( C @ X5 @ Y5 ) ) ) ) ).

% mem_case_prodE
thf(fact_321_mem__case__prodE,axiom,
    ! [Z3: real > $o,C: real > a > set_real_o,P: product_prod_real_a] :
      ( ( member_real_o @ Z3 @ ( produc9189443182227898589real_o @ C @ P ) )
     => ~ ! [X5: real,Y5: a] :
            ( ( P
              = ( product_Pair_real_a @ X5 @ Y5 ) )
           => ~ ( member_real_o @ Z3 @ ( C @ X5 @ Y5 ) ) ) ) ).

% mem_case_prodE
thf(fact_322_mem__case__prodE,axiom,
    ! [Z3: real > nat,C: real > a > set_real_nat,P: product_prod_real_a] :
      ( ( member_real_nat @ Z3 @ ( produc2853969746657022967al_nat @ C @ P ) )
     => ~ ! [X5: real,Y5: a] :
            ( ( P
              = ( product_Pair_real_a @ X5 @ Y5 ) )
           => ~ ( member_real_nat @ Z3 @ ( C @ X5 @ Y5 ) ) ) ) ).

% mem_case_prodE
thf(fact_323_mem__case__prodE,axiom,
    ! [Z3: $o > real,C: real > a > set_o_real,P: product_prod_real_a] :
      ( ( member_o_real @ Z3 @ ( produc1602803615379389039o_real @ C @ P ) )
     => ~ ! [X5: real,Y5: a] :
            ( ( P
              = ( product_Pair_real_a @ X5 @ Y5 ) )
           => ~ ( member_o_real @ Z3 @ ( C @ X5 @ Y5 ) ) ) ) ).

% mem_case_prodE
thf(fact_324_mem__case__prodE,axiom,
    ! [Z3: nat > real,C: real > a > set_nat_real,P: product_prod_real_a] :
      ( ( member_nat_real @ Z3 @ ( produc8887347644318195575t_real @ C @ P ) )
     => ~ ! [X5: real,Y5: a] :
            ( ( P
              = ( product_Pair_real_a @ X5 @ Y5 ) )
           => ~ ( member_nat_real @ Z3 @ ( C @ X5 @ Y5 ) ) ) ) ).

% mem_case_prodE
thf(fact_325_mem__case__prodE,axiom,
    ! [Z3: real > real,C: real > b > set_real_real,P: product_prod_real_b] :
      ( ( member_real_real @ Z3 @ ( produc4677890822933824468l_real @ C @ P ) )
     => ~ ! [X5: real,Y5: b] :
            ( ( P
              = ( product_Pair_real_b @ X5 @ Y5 ) )
           => ~ ( member_real_real @ Z3 @ ( C @ X5 @ Y5 ) ) ) ) ).

% mem_case_prodE
thf(fact_326_mem__case__prodE,axiom,
    ! [Z3: real > $o,C: real > b > set_real_o,P: product_prod_real_b] :
      ( ( member_real_o @ Z3 @ ( produc7853392562275204252real_o @ C @ P ) )
     => ~ ! [X5: real,Y5: b] :
            ( ( P
              = ( product_Pair_real_b @ X5 @ Y5 ) )
           => ~ ( member_real_o @ Z3 @ ( C @ X5 @ Y5 ) ) ) ) ).

% mem_case_prodE
thf(fact_327_mem__case__prodE,axiom,
    ! [Z3: real > nat,C: real > b > set_real_nat,P: product_prod_real_b] :
      ( ( member_real_nat @ Z3 @ ( produc7833912894805526008al_nat @ C @ P ) )
     => ~ ! [X5: real,Y5: b] :
            ( ( P
              = ( product_Pair_real_b @ X5 @ Y5 ) )
           => ~ ( member_real_nat @ Z3 @ ( C @ X5 @ Y5 ) ) ) ) ).

% mem_case_prodE
thf(fact_328_mem__case__prodE,axiom,
    ! [Z3: $o > real,C: real > b > set_o_real,P: product_prod_real_b] :
      ( ( member_o_real @ Z3 @ ( produc266752995426694702o_real @ C @ P ) )
     => ~ ! [X5: real,Y5: b] :
            ( ( P
              = ( product_Pair_real_b @ X5 @ Y5 ) )
           => ~ ( member_o_real @ Z3 @ ( C @ X5 @ Y5 ) ) ) ) ).

% mem_case_prodE
thf(fact_329_mem__case__prodE,axiom,
    ! [Z3: nat > real,C: real > b > set_nat_real,P: product_prod_real_b] :
      ( ( member_nat_real @ Z3 @ ( produc4643918755611922808t_real @ C @ P ) )
     => ~ ! [X5: real,Y5: b] :
            ( ( P
              = ( product_Pair_real_b @ X5 @ Y5 ) )
           => ~ ( member_nat_real @ Z3 @ ( C @ X5 @ Y5 ) ) ) ) ).

% mem_case_prodE
thf(fact_330_Product__Type_OCollect__case__prodD,axiom,
    ! [X4: produc2422161461964618553l_real,A5: real > real > $o] :
      ( ( member7849222048561428706l_real @ X4 @ ( collec3799799289383736868l_real @ ( produc5414030515140494994real_o @ A5 ) ) )
     => ( A5 @ ( produc5828954698716094813l_real @ X4 ) @ ( produc3484788084999411615l_real @ X4 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_331_Product__Type_OCollect__case__prodD,axiom,
    ! [X4: produc7716430852924023517t_real,A5: nat > real > $o] :
      ( ( member557208447399453958t_real @ X4 @ ( collec413939898802455368t_real @ ( produc3110475541085787246real_o @ A5 ) ) )
     => ( A5 @ ( product_fst_nat_real @ X4 ) @ ( product_snd_nat_real @ X4 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_332_Product__Type_OCollect__case__prodD,axiom,
    ! [X4: product_prod_real_a,A5: real > a > $o] :
      ( ( member7555082150335017566real_a @ X4 @ ( collec725494962398077084real_a @ ( produc8713834143731921650al_a_o @ A5 ) ) )
     => ( A5 @ ( product_fst_real_a @ X4 ) @ ( product_snd_real_a @ X4 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_333_Product__Type_OCollect__case__prodD,axiom,
    ! [X4: produc1405624045518934769od_a_b,A5: real > product_prod_a_b > $o] :
      ( ( member8825075204131838472od_a_b @ X4 @ ( collec7371081925754722886od_a_b @ ( produc7880493329054155208_a_b_o @ A5 ) ) )
     => ( A5 @ ( produc4505306568083885239od_a_b @ X4 ) @ ( produc4276089182416139253od_a_b @ X4 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_334_Product__Type_OCollect__case__prodD,axiom,
    ! [X4: product_prod_a_b,A5: a > b > $o] :
      ( ( member1426531481828664017od_a_b @ X4 @ ( collec3336397801687681299od_a_b @ ( produc3537405659489547051_a_b_o @ A5 ) ) )
     => ( A5 @ ( product_fst_a_b @ X4 ) @ ( product_snd_a_b @ X4 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_335_surjective__pairing,axiom,
    ! [T2: product_prod_real_b] :
      ( T2
      = ( product_Pair_real_b @ ( product_fst_real_b @ T2 ) @ ( product_snd_real_b @ T2 ) ) ) ).

% surjective_pairing
thf(fact_336_surjective__pairing,axiom,
    ! [T2: product_prod_b_a] :
      ( T2
      = ( product_Pair_b_a @ ( product_fst_b_a @ T2 ) @ ( product_snd_b_a @ T2 ) ) ) ).

% surjective_pairing
thf(fact_337_surjective__pairing,axiom,
    ! [T2: product_prod_a_real] :
      ( T2
      = ( product_Pair_a_real @ ( product_fst_a_real @ T2 ) @ ( product_snd_a_real @ T2 ) ) ) ).

% surjective_pairing
thf(fact_338_surjective__pairing,axiom,
    ! [T2: product_prod_b_real] :
      ( T2
      = ( product_Pair_b_real @ ( product_fst_b_real @ T2 ) @ ( product_snd_b_real @ T2 ) ) ) ).

% surjective_pairing
thf(fact_339_surjective__pairing,axiom,
    ! [T2: produc7929879615859924995b_real] :
      ( T2
      = ( produc9021675809588086653b_real @ ( produc7266368915318857873b_real @ T2 ) @ ( produc7037151529651111887b_real @ T2 ) ) ) ).

% surjective_pairing
thf(fact_340_surjective__pairing,axiom,
    ! [T2: produc2422161461964618553l_real] :
      ( T2
      = ( produc4511245868158468465l_real @ ( produc5828954698716094813l_real @ T2 ) @ ( produc3484788084999411615l_real @ T2 ) ) ) ).

% surjective_pairing
thf(fact_341_surjective__pairing,axiom,
    ! [T2: produc7716430852924023517t_real] :
      ( T2
      = ( produc7837566107596912789t_real @ ( product_fst_nat_real @ T2 ) @ ( product_snd_nat_real @ T2 ) ) ) ).

% surjective_pairing
thf(fact_342_surjective__pairing,axiom,
    ! [T2: product_prod_real_a] :
      ( T2
      = ( product_Pair_real_a @ ( product_fst_real_a @ T2 ) @ ( product_snd_real_a @ T2 ) ) ) ).

% surjective_pairing
thf(fact_343_surjective__pairing,axiom,
    ! [T2: produc1405624045518934769od_a_b] :
      ( T2
      = ( produc6260613462353114019od_a_b @ ( produc4505306568083885239od_a_b @ T2 ) @ ( produc4276089182416139253od_a_b @ T2 ) ) ) ).

% surjective_pairing
thf(fact_344_surjective__pairing,axiom,
    ! [T2: product_prod_a_b] :
      ( T2
      = ( product_Pair_a_b @ ( product_fst_a_b @ T2 ) @ ( product_snd_a_b @ T2 ) ) ) ).

% surjective_pairing
thf(fact_345_case__prod__Pair__iden,axiom,
    ! [P: product_prod_real_a] :
      ( ( produc6985666349104981613real_a @ product_Pair_real_a @ P )
      = P ) ).

% case_prod_Pair_iden
thf(fact_346_case__prod__Pair__iden,axiom,
    ! [P: product_prod_real_b] :
      ( ( produc1702242903178270831real_b @ product_Pair_real_b @ P )
      = P ) ).

% case_prod_Pair_iden
thf(fact_347_case__prod__Pair__iden,axiom,
    ! [P: product_prod_b_a] :
      ( ( produc1560760645774121403od_b_a @ product_Pair_b_a @ P )
      = P ) ).

% case_prod_Pair_iden
thf(fact_348_case__prod__Pair__iden,axiom,
    ! [P: product_prod_a_real] :
      ( ( produc6687215780671738713a_real @ product_Pair_a_real @ P )
      = P ) ).

% case_prod_Pair_iden
thf(fact_349_case__prod__Pair__iden,axiom,
    ! [P: product_prod_b_real] :
      ( ( produc2223249912936697051b_real @ product_Pair_b_real @ P )
      = P ) ).

% case_prod_Pair_iden
thf(fact_350_case__prod__Pair__iden,axiom,
    ! [P: produc7929879615859924995b_real] :
      ( ( produc4864254028770240685b_real @ produc9021675809588086653b_real @ P )
      = P ) ).

% case_prod_Pair_iden
thf(fact_351_qbs__morphism__Pair1,axiom,
    ! [X4: product_prod_a_b,X3: quasi_8309430206217406798od_a_b,Y3: quasi_borel_real] :
      ( ( member1426531481828664017od_a_b @ X4 @ ( qbs_sp9036631423635625438od_a_b @ X3 ) )
     => ( member7738959517937940581b_real @ ( produc9021675809588086653b_real @ X4 ) @ ( qbs_mo4103121066176565929b_real @ Y3 @ ( binary1320184014764670247b_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair1
thf(fact_352_qbs__morphism__Pair1,axiom,
    ! [X4: real,X3: quasi_borel_real,Y3: quasi_borel_a] :
      ( ( member_real @ X4 @ ( qbs_space_real @ X3 ) )
     => ( member1097457462631741663real_a @ ( product_Pair_real_a @ X4 ) @ ( qbs_mo8447752867430417485real_a @ Y3 @ ( binary5762279046363823267real_a @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair1
thf(fact_353_qbs__morphism__Pair1,axiom,
    ! [X4: a,X3: quasi_borel_a,Y3: quasi_borel_b] :
      ( ( member_a @ X4 @ ( qbs_space_a @ X3 ) )
     => ( member1389369442121846245od_a_b @ ( product_Pair_a_b @ X4 ) @ ( qbs_mo6254947889137414753od_a_b @ Y3 @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair1
thf(fact_354_qbs__morphism__Pair1,axiom,
    ! [X4: nat,X3: quasi_borel_nat,Y3: quasi_borel_real] :
      ( ( member_nat @ X4 @ ( qbs_space_nat @ X3 ) )
     => ( member969486235890772753t_real @ ( produc7837566107596912789t_real @ X4 ) @ ( qbs_mo3601394221918002359t_real @ Y3 @ ( binary2938201662863479403t_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair1
thf(fact_355_qbs__morphism__Pair1,axiom,
    ! [X4: real,X3: quasi_borel_real,Y3: quasi_borel_real] :
      ( ( member_real @ X4 @ ( qbs_space_real @ X3 ) )
     => ( member9086635009091248365l_real @ ( produc4511245868158468465l_real @ X4 ) @ ( qbs_mo6845038431372961811l_real @ Y3 @ ( binary210465342804807751l_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair1
thf(fact_356_qbs__morphism__Pair1,axiom,
    ! [X4: real,X3: quasi_borel_real,Y3: quasi_8309430206217406798od_a_b] :
      ( ( member_real @ X4 @ ( qbs_space_real @ X3 ) )
     => ( member5735645606013430835od_a_b @ ( produc6260613462353114019od_a_b @ X4 ) @ ( qbs_mo4447768093767446177od_a_b @ Y3 @ ( binary7782493704384473421od_a_b @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair1
thf(fact_357_qbs__morphism__Pair1,axiom,
    ! [X4: real,X3: quasi_borel_real,Y3: quasi_borel_b] :
      ( ( member_real @ X4 @ ( qbs_space_real @ X3 ) )
     => ( member5108440089302923873real_b @ ( product_Pair_real_b @ X4 ) @ ( qbs_mo3164329421503706703real_b @ Y3 @ ( binary5762279046363823268real_b @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair1
thf(fact_358_qbs__morphism__Pair1,axiom,
    ! [X4: b,X3: quasi_borel_b,Y3: quasi_borel_real] :
      ( ( member_b @ X4 @ ( qbs_space_b @ X3 ) )
     => ( member5043115841524054460b_real @ ( product_Pair_b_real @ X4 ) @ ( qbs_mo7027939533285103232b_real @ Y3 @ ( binary1505106857224228350b_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair1
thf(fact_359_qbs__morphism__Pair1,axiom,
    ! [X4: b,X3: quasi_borel_b,Y3: quasi_borel_a] :
      ( ( member_b @ X4 @ ( qbs_space_b @ X3 ) )
     => ( member1322126701802329700od_b_a @ ( product_Pair_b_a @ X4 ) @ ( qbs_mo4106932603193326048od_b_a @ Y3 @ ( binary1131512637584519980bs_b_a @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair1
thf(fact_360_qbs__morphism__Pair1,axiom,
    ! [X4: a,X3: quasi_borel_a,Y3: quasi_borel_real] :
      ( ( member_a @ X4 @ ( qbs_space_a @ X3 ) )
     => ( member7821820149384076987a_real @ ( product_Pair_a_real @ X4 ) @ ( qbs_mo1431720918096972543a_real @ Y3 @ ( binary5132260278890873469a_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair1
thf(fact_361_qbs__morphism__Pair2,axiom,
    ! [Y4: real,Y3: quasi_borel_real,X3: quasi_8309430206217406798od_a_b] :
      ( ( member_real @ Y4 @ ( qbs_space_real @ Y3 ) )
     => ( member3452904153566040133b_real
        @ ^ [X2: product_prod_a_b] : ( produc9021675809588086653b_real @ X2 @ Y4 )
        @ ( qbs_mo1748651627253660595b_real @ X3 @ ( binary1320184014764670247b_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair2
thf(fact_362_qbs__morphism__Pair2,axiom,
    ! [Y4: a,Y3: quasi_borel_a,X3: quasi_borel_real] :
      ( ( member_a @ Y4 @ ( qbs_space_a @ Y3 ) )
     => ( member1006887528422719913real_a
        @ ^ [X2: real] : ( product_Pair_real_a @ X2 @ Y4 )
        @ ( qbs_mo1948987420364309741real_a @ X3 @ ( binary5762279046363823267real_a @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair2
thf(fact_363_qbs__morphism__Pair2,axiom,
    ! [Y4: b,Y3: quasi_borel_b,X3: quasi_borel_a] :
      ( ( member_b @ Y4 @ ( qbs_space_b @ Y3 ) )
     => ( member2028809742453662374od_a_b
        @ ^ [X2: a] : ( product_Pair_a_b @ X2 @ Y4 )
        @ ( qbs_mo6894388189469230882od_a_b @ X3 @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair2
thf(fact_364_qbs__morphism__Pair2,axiom,
    ! [Y4: real,Y3: quasi_borel_real,X3: quasi_borel_nat] :
      ( ( member_real @ Y4 @ ( qbs_space_real @ Y3 ) )
     => ( member4237364305948650477t_real
        @ ^ [X2: nat] : ( produc7837566107596912789t_real @ X2 @ Y4 )
        @ ( qbs_mo2896996399151425555t_real @ X3 @ ( binary2938201662863479403t_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair2
thf(fact_365_qbs__morphism__Pair2,axiom,
    ! [Y4: real,Y3: quasi_borel_real,X3: quasi_borel_real] :
      ( ( member_real @ Y4 @ ( qbs_space_real @ Y3 ) )
     => ( member9086635009091248365l_real
        @ ^ [X2: real] : ( produc4511245868158468465l_real @ X2 @ Y4 )
        @ ( qbs_mo6845038431372961811l_real @ X3 @ ( binary210465342804807751l_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair2
thf(fact_366_qbs__morphism__Pair2,axiom,
    ! [Y4: product_prod_a_b,Y3: quasi_8309430206217406798od_a_b,X3: quasi_borel_real] :
      ( ( member1426531481828664017od_a_b @ Y4 @ ( qbs_sp9036631423635625438od_a_b @ Y3 ) )
     => ( member798328933530555475od_a_b
        @ ^ [X2: real] : ( produc6260613462353114019od_a_b @ X2 @ Y4 )
        @ ( qbs_mo6802237532690351511od_a_b @ X3 @ ( binary7782493704384473421od_a_b @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair2
thf(fact_367_qbs__morphism__Pair2,axiom,
    ! [Y4: b,Y3: quasi_borel_b,X3: quasi_borel_real] :
      ( ( member_b @ Y4 @ ( qbs_space_b @ Y3 ) )
     => ( member1077921568469065898real_b
        @ ^ [X2: real] : ( product_Pair_real_b @ X2 @ Y4 )
        @ ( qbs_mo1948987424667538542real_b @ X3 @ ( binary5762279046363823268real_b @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair2
thf(fact_368_qbs__morphism__Pair2,axiom,
    ! [Y4: real,Y3: quasi_borel_real,X3: quasi_borel_b] :
      ( ( member_real @ Y4 @ ( qbs_space_real @ Y3 ) )
     => ( member9073634362357912435b_real
        @ ^ [X2: b] : ( product_Pair_b_real @ X2 @ Y4 )
        @ ( qbs_mo8243281530121271393b_real @ X3 @ ( binary1505106857224228350b_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair2
thf(fact_369_qbs__morphism__Pair2,axiom,
    ! [Y4: a,Y3: quasi_borel_a,X3: quasi_borel_b] :
      ( ( member_a @ Y4 @ ( qbs_space_a @ Y3 ) )
     => ( member682686401470513571od_b_a
        @ ^ [X2: b] : ( product_Pair_b_a @ X2 @ Y4 )
        @ ( qbs_mo3467492302861509919od_b_a @ X3 @ ( binary1131512637584519980bs_b_a @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair2
thf(fact_370_qbs__morphism__Pair2,axiom,
    ! [Y4: real,Y3: quasi_borel_real,X3: quasi_borel_a] :
      ( ( member_real @ Y4 @ ( qbs_space_real @ Y3 ) )
     => ( member7912390083593098737a_real
        @ ^ [X2: a] : ( product_Pair_a_real @ X2 @ Y4 )
        @ ( qbs_mo7930486365163080287a_real @ X3 @ ( binary5132260278890873469a_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_Pair2
thf(fact_371_qbs__morphism__pair__swap_H,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_nat] :
      ( member4575602350711296188t_real
      @ ( produc3658697984569465395t_real
        @ ^ [X2: real,Y2: nat] : ( produc7837566107596912789t_real @ Y2 @ X2 ) )
      @ ( qbs_mo6219505925795312824t_real @ ( binary7505510235992378091al_nat @ X3 @ Y3 ) @ ( binary2938201662863479403t_real @ Y3 @ X3 ) ) ) ).

% qbs_morphism_pair_swap'
thf(fact_372_qbs__morphism__pair__swap_H,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_a] :
      ( member1911251678417996246a_real
      @ ( produc6468399846837644415a_real
        @ ^ [X2: real,Y2: a] : ( product_Pair_a_real @ Y2 @ X2 ) )
      @ ( qbs_mo7490864734950732570a_real @ ( binary5762279046363823267real_a @ X3 @ Y3 ) @ ( binary5132260278890873469a_real @ Y3 @ X3 ) ) ) ).

% qbs_morphism_pair_swap'
thf(fact_373_qbs__morphism__pair__swap_H,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b] :
      ( member2048427316534540090od_b_a
      @ ( produc6204743795672244857od_b_a
        @ ^ [X2: a,Y2: b] : ( product_Pair_b_a @ Y2 @ X2 ) )
      @ ( qbs_mo6969259349150898102od_b_a @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) @ ( binary1131512637584519980bs_b_a @ Y3 @ X3 ) ) ) ).

% qbs_morphism_pair_swap'
thf(fact_374_qbs__morphism__pair__swap_H,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real] :
      ( member2568373704639994300al_nat
      @ ( produc4028160848036898611al_nat
        @ ^ [X2: nat,Y2: real] : ( produc3181502643871035669al_nat @ Y2 @ X2 ) )
      @ ( qbs_mo6270607485908303288al_nat @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ ( binary7505510235992378091al_nat @ Y3 @ X3 ) ) ) ).

% qbs_morphism_pair_swap'
thf(fact_375_qbs__morphism__pair__swap_H,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_real] :
      ( member1176752664076369724l_real
      @ ( produc3818700948422621747l_real
        @ ^ [X2: real,Y2: real] : ( produc4511245868158468465l_real @ Y2 @ X2 ) )
      @ ( qbs_mo2469384092090603576l_real @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ ( binary210465342804807751l_real @ Y3 @ X3 ) ) ) ).

% qbs_morphism_pair_swap'
thf(fact_376_qbs__morphism__pair__swap_H,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_b] :
      ( member4112490518706476760b_real
      @ ( produc6781195011795835521b_real
        @ ^ [X2: real,Y2: b] : ( product_Pair_b_real @ Y2 @ X2 ) )
      @ ( qbs_mo8843654461432590492b_real @ ( binary5762279046363823268real_b @ X3 @ Y3 ) @ ( binary1505106857224228350b_real @ Y3 @ X3 ) ) ) ).

% qbs_morphism_pair_swap'
thf(fact_377_qbs__morphism__pair__swap_H,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_real] :
      ( member6570605000191323352real_b
      @ ( produc6367669841173908169real_b
        @ ^ [X2: b,Y2: real] : ( product_Pair_real_b @ Y2 @ X2 ) )
      @ ( qbs_mo964639070500085148real_b @ ( binary1505106857224228350b_real @ X3 @ Y3 ) @ ( binary5762279046363823268real_b @ Y3 @ X3 ) ) ) ).

% qbs_morphism_pair_swap'
thf(fact_378_qbs__morphism__pair__swap_H,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_a] :
      ( member8031109563763403326od_a_b
      @ ( produc4348216232050026237od_a_b
        @ ^ [X2: b,Y2: a] : ( product_Pair_a_b @ Y2 @ X2 ) )
      @ ( qbs_mo5809342105149557690od_a_b @ ( binary1131512637584519980bs_b_a @ X3 @ Y3 ) @ ( binary3918968219557196014bs_a_b @ Y3 @ X3 ) ) ) ).

% qbs_morphism_pair_swap'
thf(fact_379_qbs__morphism__pair__swap_H,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_real] :
      ( member7336383406213373910real_a
      @ ( produc7204482282939075911real_a
        @ ^ [X2: a,Y2: real] : ( product_Pair_real_a @ Y2 @ X2 ) )
      @ ( qbs_mo1801451512265252890real_a @ ( binary5132260278890873469a_real @ X3 @ Y3 ) @ ( binary5762279046363823267real_a @ Y3 @ X3 ) ) ) ).

% qbs_morphism_pair_swap'
thf(fact_380_qbs__morphism__pair__swap_H,axiom,
    ! [X3: quasi_8309430206217406798od_a_b,Y3: quasi_borel_real] :
      ( member3401719653428956202od_a_b
      @ ( produc7563370495284026267od_a_b
        @ ^ [X2: product_prod_a_b,Y2: real] : ( produc6260613462353114019od_a_b @ Y2 @ X2 ) )
      @ ( qbs_mo5848977342254397294od_a_b @ ( binary1320184014764670247b_real @ X3 @ Y3 ) @ ( binary7782493704384473421od_a_b @ Y3 @ X3 ) ) ) ).

% qbs_morphism_pair_swap'
thf(fact_381_qbs__morphism__pair__assoc1,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_a,Z: quasi_borel_real] :
      ( member6467857599393752846a_real
      @ ( produc2366039360659038085a_real
        @ ( produc6084165586602240843a_real
          @ ^ [X2: real,Y2: a,Z2: real] : ( produc7202077334067413022a_real @ X2 @ ( product_Pair_a_real @ Y2 @ Z2 ) ) ) )
      @ ( qbs_mo3062588052112934026a_real @ ( binary4458851957466795618a_real @ ( binary5762279046363823267real_a @ X3 @ Y3 ) @ Z ) @ ( binary5186011302153701620a_real @ X3 @ ( binary5132260278890873469a_real @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_pair_assoc1
thf(fact_382_qbs__morphism__pair__assoc1,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_a,Z: quasi_borel_b] :
      ( member6382016976150658836od_a_b
      @ ( produc5843769907698324285od_a_b
        @ ( produc676494897689647675od_a_b
          @ ^ [X2: real,Y2: a,Z2: b] : ( produc6260613462353114019od_a_b @ X2 @ ( product_Pair_a_b @ Y2 @ Z2 ) ) ) )
      @ ( qbs_mo8829274664976099928od_a_b @ ( binary5583738431757275593al_a_b @ ( binary5762279046363823267real_a @ X3 @ Y3 ) @ Z ) @ ( binary7782493704384473421od_a_b @ X3 @ ( binary3918968219557196014bs_a_b @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_pair_assoc1
thf(fact_383_qbs__morphism__pair__assoc1,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b,Z: quasi_borel_real] :
      ( member2987586328326561472b_real
      @ ( produc8055844373564447025b_real
        @ ( produc9044096160893509247b_real
          @ ^ [X2: a,Y2: b,Z2: real] : ( produc2985895893881137921b_real @ X2 @ ( product_Pair_b_real @ Y2 @ Z2 ) ) ) )
      @ ( qbs_mo6341451220534818052b_real @ ( binary1320184014764670247b_real @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) @ Z ) @ ( binary4507776135912497323b_real @ X3 @ ( binary1505106857224228350b_real @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_pair_assoc1
thf(fact_384_qbs__morphism__pair__assoc1,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b,Z: quasi_borel_a] :
      ( member8221711689792786638od_b_a
      @ ( produc7338457282281373709od_b_a
        @ ( produc8259942874711402915od_b_a
          @ ^ [X2: a,Y2: b,Z2: a] : ( produc6867761796305373823od_b_a @ X2 @ ( product_Pair_b_a @ Y2 @ Z2 ) ) ) )
      @ ( qbs_mo2059056275032847306od_b_a @ ( binary4734953372773062595_a_b_a @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) @ Z ) @ ( binary6545827321095910997od_b_a @ X3 @ ( binary1131512637584519980bs_b_a @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_pair_assoc1
thf(fact_385_qbs__morphism__pair__assoc1,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real,Z: quasi_borel_a] :
      ( member7499785281930035052real_a
      @ ( produc9176919279565958955real_a
        @ ( produc4687352827581996041real_a
          @ ^ [X2: nat,Y2: real,Z2: a] : ( produc7589944403593686320real_a @ X2 @ ( product_Pair_real_a @ Y2 @ Z2 ) ) ) )
      @ ( qbs_mo8719434009619300072real_a @ ( binary8766389241107001550real_a @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ Z ) @ ( binary3428804855623336198real_a @ X3 @ ( binary5762279046363823267real_a @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_pair_assoc1
thf(fact_386_qbs__morphism__pair__assoc1,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real,Z: quasi_borel_real] :
      ( member4015531503906496844l_real
      @ ( produc8797550820259539773l_real
        @ ( produc3186984222206015699l_real
          @ ^ [X2: nat,Y2: real,Z2: real] : ( produc432849518260344464l_real @ X2 @ ( produc4511245868158468465l_real @ Y2 @ Z2 ) ) ) )
      @ ( qbs_mo4946346083397520144l_real @ ( binary1691657305350012124l_real @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ Z ) @ ( binary8928417486187439162l_real @ X3 @ ( binary210465342804807751l_real @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_pair_assoc1
thf(fact_387_qbs__morphism__pair__assoc1,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real,Z: quasi_borel_b] :
      ( member6542205321770129068real_b
      @ ( produc2883147689336301163real_b
        @ ( produc5024734715871732425real_b
          @ ^ [X2: nat,Y2: real,Z2: b] : ( produc7589944407896915121real_b @ X2 @ ( product_Pair_real_b @ Y2 @ Z2 ) ) ) )
      @ ( qbs_mo1130700570939999912real_b @ ( binary8766389241107001551real_b @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ Z ) @ ( binary3428804859926564999real_b @ X3 @ ( binary5762279046363823268real_b @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_pair_assoc1
thf(fact_388_qbs__morphism__pair__assoc1,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_a] :
      ( member3279392707579314980real_a
      @ ( produc4759738011708243043real_a
        @ ( produc4597325331665930305real_a
          @ ^ [X2: real,Y2: real,Z2: a] : ( produc7719343836334750220real_a @ X2 @ ( product_Pair_real_a @ Y2 @ Z2 ) ) ) )
      @ ( qbs_mo1244333309467768736real_a @ ( binary9151934077636108402real_a @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ Z ) @ ( binary5703277804421038818real_a @ X3 @ ( binary5762279046363823267real_a @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_pair_assoc1
thf(fact_389_qbs__morphism__pair__assoc1,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_real] :
      ( member3534035092496637004l_real
      @ ( produc4567365250268142269l_real
        @ ( produc479521131423582035l_real
          @ ^ [X2: real,Y2: real,Z2: real] : ( produc2480879129069238452l_real @ X2 @ ( produc4511245868158468465l_real @ Y2 @ Z2 ) ) ) )
      @ ( qbs_mo6369161977534675728l_real @ ( binary1932660566412066360l_real @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ Z ) @ ( binary1928025069090853214l_real @ X3 @ ( binary210465342804807751l_real @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_pair_assoc1
thf(fact_390_qbs__morphism__pair__assoc1,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_b] :
      ( member1983118029457844964real_b
      @ ( produc6394376609883718691real_b
        @ ( produc3639745371506024321real_b
          @ ^ [X2: real,Y2: real,Z2: b] : ( produc7719343840637979021real_b @ X2 @ ( product_Pair_real_b @ Y2 @ Z2 ) ) ) )
      @ ( qbs_mo2540277189681680352real_b @ ( binary9151934077636108403real_b @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ Z ) @ ( binary5703277808724267619real_b @ X3 @ ( binary5762279046363823268real_b @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_pair_assoc1
thf(fact_391_qbs__morphism__pair__assoc2,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real,Z: quasi_borel_a] :
      ( member8056175666426758540real_a
      @ ( produc6397957386345362947real_a
        @ ^ [X2: nat] :
            ( produc3451031820153531490real_a
            @ ^ [Y2: real] : ( produc3704156752222575864real_a @ ( produc7837566107596912789t_real @ X2 @ Y2 ) ) ) )
      @ ( qbs_mo7923402374075632904real_a @ ( binary3428804855623336198real_a @ X3 @ ( binary5762279046363823267real_a @ Y3 @ Z ) ) @ ( binary8766389241107001550real_a @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ Z ) ) ) ).

% qbs_morphism_pair_assoc2
thf(fact_392_qbs__morphism__pair__assoc2,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_a] :
      ( member2989449720747205332real_a
      @ ( produc362417245211911371real_a
        @ ^ [X2: real] :
            ( produc5758724918922914182real_a
            @ ^ [Y2: real] : ( produc1944628072695043996real_a @ ( produc4511245868158468465l_real @ X2 @ Y2 ) ) ) )
      @ ( qbs_mo7500760462844412752real_a @ ( binary5703277804421038818real_a @ X3 @ ( binary5762279046363823267real_a @ Y3 @ Z ) ) @ ( binary9151934077636108402real_a @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ Z ) ) ) ).

% qbs_morphism_pair_assoc2
thf(fact_393_qbs__morphism__pair__assoc2,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_real,Z: quasi_borel_a] :
      ( member5549080165685610692real_a
      @ ( produc4782087570003592629real_a
        @ ^ [X2: b] :
            ( produc2285661021275603391real_a
            @ ^ [Y2: real] : ( produc8758052238057444683real_a @ ( product_Pair_b_real @ X2 @ Y2 ) ) ) )
      @ ( qbs_mo5498880057880791048real_a @ ( binary3368772609616540057real_a @ X3 @ ( binary5762279046363823267real_a @ Y3 @ Z ) ) @ ( binary1056560443234028277real_a @ ( binary1505106857224228350b_real @ X3 @ Y3 ) @ Z ) ) ) ).

% qbs_morphism_pair_assoc2
thf(fact_394_qbs__morphism__pair__assoc2,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_real,Z: quasi_borel_a] :
      ( member2625846272573851012real_a
      @ ( produc4321783275215622901real_a
        @ ^ [X2: a] :
            ( produc797698983980804864real_a
            @ ^ [Y2: real] : ( produc7270090200762646156real_a @ ( product_Pair_a_real @ X2 @ Y2 ) ) ) )
      @ ( qbs_mo5038575763092821320real_a @ ( binary8652196059846479640real_a @ X3 @ ( binary5762279046363823267real_a @ Y3 @ Z ) ) @ ( binary8791970442794005558real_a @ ( binary5132260278890873469a_real @ X3 @ Y3 ) @ Z ) ) ) ).

% qbs_morphism_pair_assoc2
thf(fact_395_qbs__morphism__pair__assoc2,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_a,Z: quasi_borel_b] :
      ( member5091408939496246444_b_a_b
      @ ( produc2629378445033950059_b_a_b
        @ ^ [X2: b] :
            ( produc1486175004042977619_b_a_b
            @ ^ [Y2: a] : ( produc2065383426920866992_b_a_b @ ( product_Pair_b_a @ X2 @ Y2 ) ) ) )
      @ ( qbs_mo6931319482857846824_b_a_b @ ( binary8693842607039999702od_a_b @ X3 @ ( binary3918968219557196014bs_a_b @ Y3 @ Z ) ) @ ( binary1743448951711404166_b_a_b @ ( binary1131512637584519980bs_b_a @ X3 @ Y3 ) @ Z ) ) ) ).

% qbs_morphism_pair_assoc2
thf(fact_396_qbs__morphism__pair__assoc2,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real,Z: quasi_borel_real] :
      ( member4885773378525087052l_real
      @ ( produc2884315481524634613l_real
        @ ^ [X2: nat] :
            ( produc3833802901578820670l_real
            @ ^ [Y2: real] : ( produc2419461374277693234l_real @ ( produc7837566107596912789t_real @ X2 @ Y2 ) ) ) )
      @ ( qbs_mo755802412384648208l_real @ ( binary8928417486187439162l_real @ X3 @ ( binary210465342804807751l_real @ Y3 @ Z ) ) @ ( binary1691657305350012124l_real @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ Z ) ) ) ).

% qbs_morphism_pair_assoc2
thf(fact_397_qbs__morphism__pair__assoc2,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_real] :
      ( member8821136346366007628l_real
      @ ( produc2342748465123298421l_real
        @ ^ [X2: real] :
            ( produc2533721948286029850l_real
            @ ^ [Y2: real] : ( produc2485514626390451598l_real @ ( produc4511245868158468465l_real @ X2 @ Y2 ) ) ) )
      @ ( qbs_mo3754741441441833232l_real @ ( binary1928025069090853214l_real @ X3 @ ( binary210465342804807751l_real @ Y3 @ Z ) ) @ ( binary1932660566412066360l_real @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ Z ) ) ) ).

% qbs_morphism_pair_assoc2
thf(fact_398_qbs__morphism__pair__assoc2,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_real,Z: quasi_borel_real] :
      ( member7298653907059486722l_real
      @ ( produc7431690996478455617l_real
        @ ^ [X2: b] :
            ( produc8236158995258570593l_real
            @ ^ [Y2: real] : ( produc1406393253423837599l_real @ ( product_Pair_b_real @ X2 @ Y2 ) ) ) )
      @ ( qbs_mo7737694685705485822l_real @ ( binary64487366330547815l_real @ X3 @ ( binary210465342804807751l_real @ Y3 @ Z ) ) @ ( binary8613699258364902005l_real @ ( binary1505106857224228350b_real @ X3 @ Y3 ) @ Z ) ) ) ).

% qbs_morphism_pair_assoc2
thf(fact_399_qbs__morphism__pair__assoc2,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_real,Z: quasi_borel_real] :
      ( member3108408312887599616l_real
      @ ( produc8043167689634541759l_real
        @ ^ [X2: a] :
            ( produc7569259519718662240l_real
            @ ^ [Y2: real] : ( produc739493777883929246l_real @ ( product_Pair_a_real @ X2 @ Y2 ) ) ) )
      @ ( qbs_mo8349171378861571964l_real @ ( binary5581385260385500840l_real @ X3 @ ( binary210465342804807751l_real @ Y3 @ Z ) ) @ ( binary7946799782824993652l_real @ ( binary5132260278890873469a_real @ X3 @ Y3 ) @ Z ) ) ) ).

% qbs_morphism_pair_assoc2
thf(fact_400_qbs__morphism__pair__assoc2,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real,Z: quasi_borel_b] :
      ( member128747509785894348real_b
      @ ( produc7961561948777721411real_b
        @ ^ [X2: nat] :
            ( produc6309598231035532322real_b
            @ ^ [Y2: real] : ( produc3704156752222575865real_b @ ( produc7837566107596912789t_real @ X2 @ Y2 ) ) ) )
      @ ( qbs_mo9148312218546427336real_b @ ( binary3428804859926564999real_b @ X3 @ ( binary5762279046363823268real_b @ Y3 @ Z ) ) @ ( binary8766389241107001551real_b @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ Z ) ) ) ).

% qbs_morphism_pair_assoc2
thf(fact_401_case__prod__unfold,axiom,
    ( produc8409101302566321868_a_b_c
    = ( ^ [C2: real > a > b > c,P3: product_prod_real_a] : ( C2 @ ( product_fst_real_a @ P3 ) @ ( product_snd_real_a @ P3 ) ) ) ) ).

% case_prod_unfold
thf(fact_402_case__prod__unfold,axiom,
    ( produc8366947261062197552_a_b_c
    = ( ^ [C2: real > product_prod_a_b > c,P3: produc1405624045518934769od_a_b] : ( C2 @ ( produc4505306568083885239od_a_b @ P3 ) @ ( produc4276089182416139253od_a_b @ P3 ) ) ) ) ).

% case_prod_unfold
thf(fact_403_case__prod__unfold,axiom,
    ( produc6028431345588019475_a_b_c
    = ( ^ [C2: a > b > c,P3: product_prod_a_b] : ( C2 @ ( product_fst_a_b @ P3 ) @ ( product_snd_a_b @ P3 ) ) ) ) ).

% case_prod_unfold
thf(fact_404_case__prod__unfold,axiom,
    ( produc2835462372567216025al_b_c
    = ( ^ [C2: real > b > c,P3: product_prod_real_b] : ( C2 @ ( product_fst_real_b @ P3 ) @ ( product_snd_real_b @ P3 ) ) ) ) ).

% case_prod_unfold
thf(fact_405_case__prod__unfold,axiom,
    ( produc5622917954539892058al_a_c
    = ( ^ [C2: real > a > c,P3: product_prod_real_a] : ( C2 @ ( product_fst_real_a @ P3 ) @ ( product_snd_real_a @ P3 ) ) ) ) ).

% case_prod_unfold
thf(fact_406_case__prod__unfold,axiom,
    ( produc7198824580026001574al_b_c
    = ( ^ [C2: a > real > b > c,P3: product_prod_a_real] : ( C2 @ ( product_fst_a_real @ P3 ) @ ( product_snd_a_real @ P3 ) ) ) ) ).

% case_prod_unfold
thf(fact_407_case__prod__beta_H,axiom,
    ( produc8409101302566321868_a_b_c
    = ( ^ [F: real > a > b > c,X2: product_prod_real_a] : ( F @ ( product_fst_real_a @ X2 ) @ ( product_snd_real_a @ X2 ) ) ) ) ).

% case_prod_beta'
thf(fact_408_case__prod__beta_H,axiom,
    ( produc8366947261062197552_a_b_c
    = ( ^ [F: real > product_prod_a_b > c,X2: produc1405624045518934769od_a_b] : ( F @ ( produc4505306568083885239od_a_b @ X2 ) @ ( produc4276089182416139253od_a_b @ X2 ) ) ) ) ).

% case_prod_beta'
thf(fact_409_case__prod__beta_H,axiom,
    ( produc6028431345588019475_a_b_c
    = ( ^ [F: a > b > c,X2: product_prod_a_b] : ( F @ ( product_fst_a_b @ X2 ) @ ( product_snd_a_b @ X2 ) ) ) ) ).

% case_prod_beta'
thf(fact_410_case__prod__beta_H,axiom,
    ( produc2835462372567216025al_b_c
    = ( ^ [F: real > b > c,X2: product_prod_real_b] : ( F @ ( product_fst_real_b @ X2 ) @ ( product_snd_real_b @ X2 ) ) ) ) ).

% case_prod_beta'
thf(fact_411_case__prod__beta_H,axiom,
    ( produc5622917954539892058al_a_c
    = ( ^ [F: real > a > c,X2: product_prod_real_a] : ( F @ ( product_fst_real_a @ X2 ) @ ( product_snd_real_a @ X2 ) ) ) ) ).

% case_prod_beta'
thf(fact_412_case__prod__beta_H,axiom,
    ( produc7198824580026001574al_b_c
    = ( ^ [F: a > real > b > c,X2: product_prod_a_real] : ( F @ ( product_fst_a_real @ X2 ) @ ( product_snd_a_real @ X2 ) ) ) ) ).

% case_prod_beta'
thf(fact_413_old_Oprod_Ocase,axiom,
    ! [F2: real > a > b > c,X12: real,X23: a] :
      ( ( produc8409101302566321868_a_b_c @ F2 @ ( product_Pair_real_a @ X12 @ X23 ) )
      = ( F2 @ X12 @ X23 ) ) ).

% old.prod.case
thf(fact_414_old_Oprod_Ocase,axiom,
    ! [F2: real > product_prod_a_b > c,X12: real,X23: product_prod_a_b] :
      ( ( produc8366947261062197552_a_b_c @ F2 @ ( produc6260613462353114019od_a_b @ X12 @ X23 ) )
      = ( F2 @ X12 @ X23 ) ) ).

% old.prod.case
thf(fact_415_old_Oprod_Ocase,axiom,
    ! [F2: a > b > c,X12: a,X23: b] :
      ( ( produc6028431345588019475_a_b_c @ F2 @ ( product_Pair_a_b @ X12 @ X23 ) )
      = ( F2 @ X12 @ X23 ) ) ).

% old.prod.case
thf(fact_416_old_Oprod_Ocase,axiom,
    ! [F2: real > b > c,X12: real,X23: b] :
      ( ( produc2835462372567216025al_b_c @ F2 @ ( product_Pair_real_b @ X12 @ X23 ) )
      = ( F2 @ X12 @ X23 ) ) ).

% old.prod.case
thf(fact_417_old_Oprod_Ocase,axiom,
    ! [F2: real > a > c,X12: real,X23: a] :
      ( ( produc5622917954539892058al_a_c @ F2 @ ( product_Pair_real_a @ X12 @ X23 ) )
      = ( F2 @ X12 @ X23 ) ) ).

% old.prod.case
thf(fact_418_old_Oprod_Ocase,axiom,
    ! [F2: a > real > b > c,X12: a,X23: real] :
      ( ( produc7198824580026001574al_b_c @ F2 @ ( product_Pair_a_real @ X12 @ X23 ) )
      = ( F2 @ X12 @ X23 ) ) ).

% old.prod.case
thf(fact_419_qbs__morphism__cong,axiom,
    ! [X3: quasi_borel_real,F2: real > real,G2: real > real,Y3: quasi_borel_real] :
      ( ! [X5: real] :
          ( ( member_real @ X5 @ ( qbs_space_real @ X3 ) )
         => ( ( F2 @ X5 )
            = ( G2 @ X5 ) ) )
     => ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
       => ( member_real_real @ G2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_cong
thf(fact_420_qbs__morphism__cong,axiom,
    ! [X3: quasi_borel_real,F2: real > $o,G2: real > $o,Y3: quasi_borel_o] :
      ( ! [X5: real] :
          ( ( member_real @ X5 @ ( qbs_space_real @ X3 ) )
         => ( ( F2 @ X5 )
            = ( G2 @ X5 ) ) )
     => ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
       => ( member_real_o @ G2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_cong
thf(fact_421_qbs__morphism__cong,axiom,
    ! [X3: quasi_borel_o,F2: $o > real,G2: $o > real,Y3: quasi_borel_real] :
      ( ! [X5: $o] :
          ( ( member_o @ X5 @ ( qbs_space_o @ X3 ) )
         => ( ( F2 @ X5 )
            = ( G2 @ X5 ) ) )
     => ( ( member_o_real @ F2 @ ( qbs_morphism_o_real @ X3 @ Y3 ) )
       => ( member_o_real @ G2 @ ( qbs_morphism_o_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_cong
thf(fact_422_qbs__morphism__cong,axiom,
    ! [X3: quasi_borel_real,F2: real > nat,G2: real > nat,Y3: quasi_borel_nat] :
      ( ! [X5: real] :
          ( ( member_real @ X5 @ ( qbs_space_real @ X3 ) )
         => ( ( F2 @ X5 )
            = ( G2 @ X5 ) ) )
     => ( ( member_real_nat @ F2 @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) )
       => ( member_real_nat @ G2 @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_cong
thf(fact_423_qbs__morphism__cong,axiom,
    ! [X3: quasi_borel_nat,F2: nat > real,G2: nat > real,Y3: quasi_borel_real] :
      ( ! [X5: nat] :
          ( ( member_nat @ X5 @ ( qbs_space_nat @ X3 ) )
         => ( ( F2 @ X5 )
            = ( G2 @ X5 ) ) )
     => ( ( member_nat_real @ F2 @ ( qbs_mo2000642995705457910t_real @ X3 @ Y3 ) )
       => ( member_nat_real @ G2 @ ( qbs_mo2000642995705457910t_real @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_cong
thf(fact_424_qbs__morphism__cong,axiom,
    ! [X3: quasi_8309430206217406798od_a_b,F2: product_prod_a_b > c,G2: product_prod_a_b > c,Y3: quasi_borel_c] :
      ( ! [X5: product_prod_a_b] :
          ( ( member1426531481828664017od_a_b @ X5 @ ( qbs_sp9036631423635625438od_a_b @ X3 ) )
         => ( ( F2 @ X5 )
            = ( G2 @ X5 ) ) )
     => ( ( member1080921174361771732_a_b_c @ F2 @ ( qbs_mo2296058654870477648_a_b_c @ X3 @ Y3 ) )
       => ( member1080921174361771732_a_b_c @ G2 @ ( qbs_mo2296058654870477648_a_b_c @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_cong
thf(fact_425_qbs__morphism__cong,axiom,
    ! [X3: quasi_borel_real,F2: real > b > c,G2: real > b > c,Y3: quasi_borel_b_c] :
      ( ! [X5: real] :
          ( ( member_real @ X5 @ ( qbs_space_real @ X3 ) )
         => ( ( F2 @ X5 )
            = ( G2 @ X5 ) ) )
     => ( ( member_real_b_c @ F2 @ ( qbs_mo6398413456135019852al_b_c @ X3 @ Y3 ) )
       => ( member_real_b_c @ G2 @ ( qbs_mo6398413456135019852al_b_c @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_cong
thf(fact_426_qbs__morphism__cong,axiom,
    ! [X3: quasi_borel_a,F2: a > b > c,G2: a > b > c,Y3: quasi_borel_b_c] :
      ( ! [X5: a] :
          ( ( member_a @ X5 @ ( qbs_space_a @ X3 ) )
         => ( ( F2 @ X5 )
            = ( G2 @ X5 ) ) )
     => ( ( member_a_b_c @ F2 @ ( qbs_morphism_a_b_c @ X3 @ Y3 ) )
       => ( member_a_b_c @ G2 @ ( qbs_morphism_a_b_c @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_cong
thf(fact_427_qbs__morphism__cong,axiom,
    ! [X3: quasi_5298506126099802441a_real,F2: product_prod_a_real > b > c,G2: product_prod_a_real > b > c,Y3: quasi_borel_b_c] :
      ( ! [X5: product_prod_a_real] :
          ( ( member7037815648067680368a_real @ X5 @ ( qbs_sp3633700080301449891a_real @ X3 ) )
         => ( ( F2 @ X5 )
            = ( G2 @ X5 ) ) )
     => ( ( member2979925738865732021al_b_c @ F2 @ ( qbs_mo4694180099308886521al_b_c @ X3 @ Y3 ) )
       => ( member2979925738865732021al_b_c @ G2 @ ( qbs_mo4694180099308886521al_b_c @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_cong
thf(fact_428_qbs__morphism__cong,axiom,
    ! [X3: quasi_7706945541993221175real_a,F2: product_prod_real_a > b > c,G2: product_prod_real_a > b > c,Y3: quasi_borel_b_c] :
      ( ! [X5: product_prod_real_a] :
          ( ( member7555082150335017566real_a @ X5 @ ( qbs_sp4150966582568787089real_a @ X3 ) )
         => ( ( F2 @ X5 )
            = ( G2 @ X5 ) ) )
     => ( ( member6939723154228711331_a_b_c @ F2 @ ( qbs_mo8653977514671865831_a_b_c @ X3 @ Y3 ) )
       => ( member6939723154228711331_a_b_c @ G2 @ ( qbs_mo8653977514671865831_a_b_c @ X3 @ Y3 ) ) ) ) ).

% qbs_morphism_cong
thf(fact_429_qbs__morphismE_I2_J,axiom,
    ! [F2: real > real,X3: quasi_borel_real,Y3: quasi_borel_real,X4: real] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
     => ( ( member_real @ X4 @ ( qbs_space_real @ X3 ) )
       => ( member_real @ ( F2 @ X4 ) @ ( qbs_space_real @ Y3 ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_430_qbs__morphismE_I2_J,axiom,
    ! [F2: real > $o,X3: quasi_borel_real,Y3: quasi_borel_o,X4: real] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
     => ( ( member_real @ X4 @ ( qbs_space_real @ X3 ) )
       => ( member_o @ ( F2 @ X4 ) @ ( qbs_space_o @ Y3 ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_431_qbs__morphismE_I2_J,axiom,
    ! [F2: $o > real,X3: quasi_borel_o,Y3: quasi_borel_real,X4: $o] :
      ( ( member_o_real @ F2 @ ( qbs_morphism_o_real @ X3 @ Y3 ) )
     => ( ( member_o @ X4 @ ( qbs_space_o @ X3 ) )
       => ( member_real @ ( F2 @ X4 ) @ ( qbs_space_real @ Y3 ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_432_qbs__morphismE_I2_J,axiom,
    ! [F2: real > nat,X3: quasi_borel_real,Y3: quasi_borel_nat,X4: real] :
      ( ( member_real_nat @ F2 @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) )
     => ( ( member_real @ X4 @ ( qbs_space_real @ X3 ) )
       => ( member_nat @ ( F2 @ X4 ) @ ( qbs_space_nat @ Y3 ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_433_qbs__morphismE_I2_J,axiom,
    ! [F2: nat > real,X3: quasi_borel_nat,Y3: quasi_borel_real,X4: nat] :
      ( ( member_nat_real @ F2 @ ( qbs_mo2000642995705457910t_real @ X3 @ Y3 ) )
     => ( ( member_nat @ X4 @ ( qbs_space_nat @ X3 ) )
       => ( member_real @ ( F2 @ X4 ) @ ( qbs_space_real @ Y3 ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_434_qbs__morphismE_I2_J,axiom,
    ! [F2: product_prod_a_b > c,X3: quasi_8309430206217406798od_a_b,Y3: quasi_borel_c,X4: product_prod_a_b] :
      ( ( member1080921174361771732_a_b_c @ F2 @ ( qbs_mo2296058654870477648_a_b_c @ X3 @ Y3 ) )
     => ( ( member1426531481828664017od_a_b @ X4 @ ( qbs_sp9036631423635625438od_a_b @ X3 ) )
       => ( member_c @ ( F2 @ X4 ) @ ( qbs_space_c @ Y3 ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_435_qbs__morphismE_I2_J,axiom,
    ! [F2: real > b > c,X3: quasi_borel_real,Y3: quasi_borel_b_c,X4: real] :
      ( ( member_real_b_c @ F2 @ ( qbs_mo6398413456135019852al_b_c @ X3 @ Y3 ) )
     => ( ( member_real @ X4 @ ( qbs_space_real @ X3 ) )
       => ( member_b_c @ ( F2 @ X4 ) @ ( qbs_space_b_c @ Y3 ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_436_qbs__morphismE_I2_J,axiom,
    ! [F2: a > b > c,X3: quasi_borel_a,Y3: quasi_borel_b_c,X4: a] :
      ( ( member_a_b_c @ F2 @ ( qbs_morphism_a_b_c @ X3 @ Y3 ) )
     => ( ( member_a @ X4 @ ( qbs_space_a @ X3 ) )
       => ( member_b_c @ ( F2 @ X4 ) @ ( qbs_space_b_c @ Y3 ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_437_qbs__morphismE_I2_J,axiom,
    ! [F2: ( real > real ) > real > real,X3: quasi_1840791737016710247l_real,Y3: quasi_1840791737016710247l_real,X4: real > real] :
      ( ( member1867607144002920228l_real @ F2 @ ( qbs_mo1324329472873391464l_real @ X3 @ Y3 ) )
     => ( ( member_real_real @ X4 @ ( qbs_space_real_real @ X3 ) )
       => ( member_real_real @ ( F2 @ X4 ) @ ( qbs_space_real_real @ Y3 ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_438_qbs__morphismE_I2_J,axiom,
    ! [F2: ( real > real ) > real > $o,X3: quasi_1840791737016710247l_real,Y3: quasi_borel_real_o,X4: real > real] :
      ( ( member449094008869209420real_o @ F2 @ ( qbs_mo3982420634722495346real_o @ X3 @ Y3 ) )
     => ( ( member_real_real @ X4 @ ( qbs_space_real_real @ X3 ) )
       => ( member_real_o @ ( F2 @ X4 ) @ ( qbs_space_real_o @ Y3 ) ) ) ) ).

% qbs_morphismE(2)
thf(fact_439_snd__def,axiom,
    ( produc4276089182416139253od_a_b
    = ( produc6808296595376970456od_a_b
      @ ^ [X1: real,X22: product_prod_a_b] : X22 ) ) ).

% snd_def
thf(fact_440_snd__def,axiom,
    ( product_snd_a_b
    = ( produc6028431345588019474_a_b_b
      @ ^ [X1: a,X22: b] : X22 ) ) ).

% snd_def
thf(fact_441_fst__def,axiom,
    ( produc4505306568083885239od_a_b
    = ( produc8877026340877948028b_real
      @ ^ [X1: real,X22: product_prod_a_b] : X1 ) ) ).

% fst_def
thf(fact_442_fst__def,axiom,
    ( product_fst_a_b
    = ( produc6028431345588019473_a_b_a
      @ ^ [X1: a,X22: b] : X1 ) ) ).

% fst_def
thf(fact_443_fst__def,axiom,
    ( produc5828954698716094813l_real
    = ( produc313441363659479858l_real
      @ ^ [X1: real,X22: real] : X1 ) ) ).

% fst_def
thf(fact_444_fst__def,axiom,
    ( product_fst_nat_real
    = ( produc6270885368079350906al_nat
      @ ^ [X1: nat,X22: real] : X1 ) ) ).

% fst_def
thf(fact_445_fst__def,axiom,
    ( product_fst_real_a
    = ( produc1204397526812833490a_real
      @ ^ [X1: real,X22: a] : X1 ) ) ).

% fst_def
thf(fact_446_cond__case__prod__eta,axiom,
    ! [F2: real > a > b > c,G2: product_prod_real_a > b > c] :
      ( ! [X5: real,Y5: a] :
          ( ( F2 @ X5 @ Y5 )
          = ( G2 @ ( product_Pair_real_a @ X5 @ Y5 ) ) )
     => ( ( produc8409101302566321868_a_b_c @ F2 )
        = G2 ) ) ).

% cond_case_prod_eta
thf(fact_447_cond__case__prod__eta,axiom,
    ! [F2: real > product_prod_a_b > c,G2: produc1405624045518934769od_a_b > c] :
      ( ! [X5: real,Y5: product_prod_a_b] :
          ( ( F2 @ X5 @ Y5 )
          = ( G2 @ ( produc6260613462353114019od_a_b @ X5 @ Y5 ) ) )
     => ( ( produc8366947261062197552_a_b_c @ F2 )
        = G2 ) ) ).

% cond_case_prod_eta
thf(fact_448_cond__case__prod__eta,axiom,
    ! [F2: a > b > c,G2: product_prod_a_b > c] :
      ( ! [X5: a,Y5: b] :
          ( ( F2 @ X5 @ Y5 )
          = ( G2 @ ( product_Pair_a_b @ X5 @ Y5 ) ) )
     => ( ( produc6028431345588019475_a_b_c @ F2 )
        = G2 ) ) ).

% cond_case_prod_eta
thf(fact_449_cond__case__prod__eta,axiom,
    ! [F2: real > b > c,G2: product_prod_real_b > c] :
      ( ! [X5: real,Y5: b] :
          ( ( F2 @ X5 @ Y5 )
          = ( G2 @ ( product_Pair_real_b @ X5 @ Y5 ) ) )
     => ( ( produc2835462372567216025al_b_c @ F2 )
        = G2 ) ) ).

% cond_case_prod_eta
thf(fact_450_cond__case__prod__eta,axiom,
    ! [F2: real > a > c,G2: product_prod_real_a > c] :
      ( ! [X5: real,Y5: a] :
          ( ( F2 @ X5 @ Y5 )
          = ( G2 @ ( product_Pair_real_a @ X5 @ Y5 ) ) )
     => ( ( produc5622917954539892058al_a_c @ F2 )
        = G2 ) ) ).

% cond_case_prod_eta
thf(fact_451_cond__case__prod__eta,axiom,
    ! [F2: a > real > b > c,G2: product_prod_a_real > b > c] :
      ( ! [X5: a,Y5: real] :
          ( ( F2 @ X5 @ Y5 )
          = ( G2 @ ( product_Pair_a_real @ X5 @ Y5 ) ) )
     => ( ( produc7198824580026001574al_b_c @ F2 )
        = G2 ) ) ).

% cond_case_prod_eta
thf(fact_452_case__prod__eta,axiom,
    ! [F2: product_prod_real_a > b > c] :
      ( ( produc8409101302566321868_a_b_c
        @ ^ [X2: real,Y2: a] : ( F2 @ ( product_Pair_real_a @ X2 @ Y2 ) ) )
      = F2 ) ).

% case_prod_eta
thf(fact_453_case__prod__eta,axiom,
    ! [F2: produc1405624045518934769od_a_b > c] :
      ( ( produc8366947261062197552_a_b_c
        @ ^ [X2: real,Y2: product_prod_a_b] : ( F2 @ ( produc6260613462353114019od_a_b @ X2 @ Y2 ) ) )
      = F2 ) ).

% case_prod_eta
thf(fact_454_case__prod__eta,axiom,
    ! [F2: product_prod_a_b > c] :
      ( ( produc6028431345588019475_a_b_c
        @ ^ [X2: a,Y2: b] : ( F2 @ ( product_Pair_a_b @ X2 @ Y2 ) ) )
      = F2 ) ).

% case_prod_eta
thf(fact_455_case__prod__eta,axiom,
    ! [F2: product_prod_real_b > c] :
      ( ( produc2835462372567216025al_b_c
        @ ^ [X2: real,Y2: b] : ( F2 @ ( product_Pair_real_b @ X2 @ Y2 ) ) )
      = F2 ) ).

% case_prod_eta
thf(fact_456_case__prod__eta,axiom,
    ! [F2: product_prod_real_a > c] :
      ( ( produc5622917954539892058al_a_c
        @ ^ [X2: real,Y2: a] : ( F2 @ ( product_Pair_real_a @ X2 @ Y2 ) ) )
      = F2 ) ).

% case_prod_eta
thf(fact_457_case__prod__eta,axiom,
    ! [F2: product_prod_a_real > b > c] :
      ( ( produc7198824580026001574al_b_c
        @ ^ [X2: a,Y2: real] : ( F2 @ ( product_Pair_a_real @ X2 @ Y2 ) ) )
      = F2 ) ).

% case_prod_eta
thf(fact_458_case__prodE2,axiom,
    ! [Q2: ( b > c ) > $o,P2: real > a > b > c,Z3: product_prod_real_a] :
      ( ( Q2 @ ( produc8409101302566321868_a_b_c @ P2 @ Z3 ) )
     => ~ ! [X5: real,Y5: a] :
            ( ( Z3
              = ( product_Pair_real_a @ X5 @ Y5 ) )
           => ~ ( Q2 @ ( P2 @ X5 @ Y5 ) ) ) ) ).

% case_prodE2
thf(fact_459_case__prodE2,axiom,
    ! [Q2: c > $o,P2: real > product_prod_a_b > c,Z3: produc1405624045518934769od_a_b] :
      ( ( Q2 @ ( produc8366947261062197552_a_b_c @ P2 @ Z3 ) )
     => ~ ! [X5: real,Y5: product_prod_a_b] :
            ( ( Z3
              = ( produc6260613462353114019od_a_b @ X5 @ Y5 ) )
           => ~ ( Q2 @ ( P2 @ X5 @ Y5 ) ) ) ) ).

% case_prodE2
thf(fact_460_case__prodE2,axiom,
    ! [Q2: c > $o,P2: a > b > c,Z3: product_prod_a_b] :
      ( ( Q2 @ ( produc6028431345588019475_a_b_c @ P2 @ Z3 ) )
     => ~ ! [X5: a,Y5: b] :
            ( ( Z3
              = ( product_Pair_a_b @ X5 @ Y5 ) )
           => ~ ( Q2 @ ( P2 @ X5 @ Y5 ) ) ) ) ).

% case_prodE2
thf(fact_461_case__prodE2,axiom,
    ! [Q2: c > $o,P2: real > b > c,Z3: product_prod_real_b] :
      ( ( Q2 @ ( produc2835462372567216025al_b_c @ P2 @ Z3 ) )
     => ~ ! [X5: real,Y5: b] :
            ( ( Z3
              = ( product_Pair_real_b @ X5 @ Y5 ) )
           => ~ ( Q2 @ ( P2 @ X5 @ Y5 ) ) ) ) ).

% case_prodE2
thf(fact_462_case__prodE2,axiom,
    ! [Q2: c > $o,P2: real > a > c,Z3: product_prod_real_a] :
      ( ( Q2 @ ( produc5622917954539892058al_a_c @ P2 @ Z3 ) )
     => ~ ! [X5: real,Y5: a] :
            ( ( Z3
              = ( product_Pair_real_a @ X5 @ Y5 ) )
           => ~ ( Q2 @ ( P2 @ X5 @ Y5 ) ) ) ) ).

% case_prodE2
thf(fact_463_case__prodE2,axiom,
    ! [Q2: ( b > c ) > $o,P2: a > real > b > c,Z3: product_prod_a_real] :
      ( ( Q2 @ ( produc7198824580026001574al_b_c @ P2 @ Z3 ) )
     => ~ ! [X5: a,Y5: real] :
            ( ( Z3
              = ( product_Pair_a_real @ X5 @ Y5 ) )
           => ~ ( Q2 @ ( P2 @ X5 @ Y5 ) ) ) ) ).

% case_prodE2
thf(fact_464_qbs__morphism__const,axiom,
    ! [Y4: real,Y3: quasi_borel_real,X3: quasi_borel_real] :
      ( ( member_real @ Y4 @ ( qbs_space_real @ Y3 ) )
     => ( member_real_real
        @ ^ [Uu: real] : Y4
        @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) ) ) ).

% qbs_morphism_const
thf(fact_465_qbs__morphism__const,axiom,
    ! [Y4: $o,Y3: quasi_borel_o,X3: quasi_borel_real] :
      ( ( member_o @ Y4 @ ( qbs_space_o @ Y3 ) )
     => ( member_real_o
        @ ^ [Uu: real] : Y4
        @ ( qbs_morphism_real_o @ X3 @ Y3 ) ) ) ).

% qbs_morphism_const
thf(fact_466_qbs__morphism__const,axiom,
    ! [Y4: real,Y3: quasi_borel_real,X3: quasi_borel_o] :
      ( ( member_real @ Y4 @ ( qbs_space_real @ Y3 ) )
     => ( member_o_real
        @ ^ [Uu: $o] : Y4
        @ ( qbs_morphism_o_real @ X3 @ Y3 ) ) ) ).

% qbs_morphism_const
thf(fact_467_qbs__morphism__const,axiom,
    ! [Y4: nat,Y3: quasi_borel_nat,X3: quasi_borel_real] :
      ( ( member_nat @ Y4 @ ( qbs_space_nat @ Y3 ) )
     => ( member_real_nat
        @ ^ [Uu: real] : Y4
        @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) ) ) ).

% qbs_morphism_const
thf(fact_468_qbs__morphism__const,axiom,
    ! [Y4: real,Y3: quasi_borel_real,X3: quasi_borel_nat] :
      ( ( member_real @ Y4 @ ( qbs_space_real @ Y3 ) )
     => ( member_nat_real
        @ ^ [Uu: nat] : Y4
        @ ( qbs_mo2000642995705457910t_real @ X3 @ Y3 ) ) ) ).

% qbs_morphism_const
thf(fact_469_qbs__morphism__const,axiom,
    ! [Y4: c,Y3: quasi_borel_c,X3: quasi_8309430206217406798od_a_b] :
      ( ( member_c @ Y4 @ ( qbs_space_c @ Y3 ) )
     => ( member1080921174361771732_a_b_c
        @ ^ [Uu: product_prod_a_b] : Y4
        @ ( qbs_mo2296058654870477648_a_b_c @ X3 @ Y3 ) ) ) ).

% qbs_morphism_const
thf(fact_470_qbs__morphism__const,axiom,
    ! [Y4: b > c,Y3: quasi_borel_b_c,X3: quasi_borel_real] :
      ( ( member_b_c @ Y4 @ ( qbs_space_b_c @ Y3 ) )
     => ( member_real_b_c
        @ ^ [Uu: real] : Y4
        @ ( qbs_mo6398413456135019852al_b_c @ X3 @ Y3 ) ) ) ).

% qbs_morphism_const
thf(fact_471_qbs__morphism__const,axiom,
    ! [Y4: b > c,Y3: quasi_borel_b_c,X3: quasi_borel_a] :
      ( ( member_b_c @ Y4 @ ( qbs_space_b_c @ Y3 ) )
     => ( member_a_b_c
        @ ^ [Uu: a] : Y4
        @ ( qbs_morphism_a_b_c @ X3 @ Y3 ) ) ) ).

% qbs_morphism_const
thf(fact_472_qbs__morphism__const,axiom,
    ! [Y4: b > c,Y3: quasi_borel_b_c,X3: quasi_5298506126099802441a_real] :
      ( ( member_b_c @ Y4 @ ( qbs_space_b_c @ Y3 ) )
     => ( member2979925738865732021al_b_c
        @ ^ [Uu: product_prod_a_real] : Y4
        @ ( qbs_mo4694180099308886521al_b_c @ X3 @ Y3 ) ) ) ).

% qbs_morphism_const
thf(fact_473_qbs__morphism__const,axiom,
    ! [Y4: b > c,Y3: quasi_borel_b_c,X3: quasi_7706945541993221175real_a] :
      ( ( member_b_c @ Y4 @ ( qbs_space_b_c @ Y3 ) )
     => ( member6939723154228711331_a_b_c
        @ ^ [Uu: product_prod_real_a] : Y4
        @ ( qbs_mo8653977514671865831_a_b_c @ X3 @ Y3 ) ) ) ).

% qbs_morphism_const
thf(fact_474_curry__morphism,axiom,
    ! [X3: quasi_7706945541993221175real_a,Y3: quasi_borel_b,Z: quasi_borel_c] : ( member8287799436898144304_a_b_c @ produc1339935578242556755_a_b_c @ ( qbs_mo3240663002281175710_a_b_c @ ( expone4396966978608342712_a_b_c @ ( binary5583738431757275593al_a_b @ X3 @ Y3 ) @ Z ) @ ( expone1656787320005700680_a_b_c @ X3 @ ( exponent_exp_qbs_b_c @ Y3 @ Z ) ) ) ) ).

% curry_morphism
thf(fact_475_curry__morphism,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_a,Z: quasi_borel_b_c] : ( member1848793607253476468_a_b_c @ produc3831716361899747437_a_b_c @ ( qbs_mo5607759823917069466_a_b_c @ ( expone1656787320005700680_a_b_c @ ( binary5762279046363823267real_a @ X3 @ Y3 ) @ Z ) @ ( expone6779206709035782606_a_b_c @ X3 @ ( expone6081388564108922123_a_b_c @ Y3 @ Z ) ) ) ) ).

% curry_morphism
thf(fact_476_curry__morphism,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b,Z: quasi_borel_c] : ( member4936940837166441592_a_b_c @ product_curry_a_b_c @ ( qbs_mo5865412927109505822_a_b_c @ ( expone8870078507744808369_a_b_c @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) @ Z ) @ ( expone6081388564108922123_a_b_c @ X3 @ ( exponent_exp_qbs_b_c @ Y3 @ Z ) ) ) ) ).

% curry_morphism
thf(fact_477_curry__morphism,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_b,Z: quasi_borel_c] : ( member3456600720300365306al_b_c @ produc7369401904616417848al_b_c @ ( qbs_mo329309372081770728al_b_c @ ( expone3484251596743573917al_b_c @ ( binary5762279046363823268real_b @ X3 @ Y3 ) @ Z ) @ ( expone5053526631941837485al_b_c @ X3 @ ( exponent_exp_qbs_b_c @ Y3 @ Z ) ) ) ) ).

% curry_morphism
thf(fact_478_curry__morphism,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_a,Z: quasi_borel_b_c] : ( member4407520735122637906_a_b_c @ produc2762368449492327216_a_b_c @ ( qbs_mo5419803789476310848_a_b_c @ ( expone2531462757953172339_a_b_c @ ( binary1131512637584519980bs_b_a @ X3 @ Y3 ) @ Z ) @ ( expone1357566065582756271_a_b_c @ X3 @ ( expone6081388564108922123_a_b_c @ Y3 @ Z ) ) ) ) ).

% curry_morphism
thf(fact_479_qbs__morphism__Pair2_H,axiom,
    ! [Y4: a,Y3: quasi_borel_a,F2: product_prod_real_a > real,X3: quasi_borel_real,Z: quasi_borel_real] :
      ( ( member_a @ Y4 @ ( qbs_space_a @ Y3 ) )
     => ( ( member7939111694857414313a_real @ F2 @ ( qbs_mo704561573410066541a_real @ ( binary5762279046363823267real_a @ X3 @ Y3 ) @ Z ) )
       => ( member_real_real
          @ ^ [X2: real] : ( F2 @ ( product_Pair_real_a @ X2 @ Y4 ) )
          @ ( qbs_mo5229770564518008146l_real @ X3 @ Z ) ) ) ) ).

% qbs_morphism_Pair2'
thf(fact_480_qbs__morphism__Pair2_H,axiom,
    ! [Y4: a,Y3: quasi_borel_a,F2: product_prod_real_a > $o,X3: quasi_borel_real,Z: quasi_borel_o] :
      ( ( member_a @ Y4 @ ( qbs_space_a @ Y3 ) )
     => ( ( member346752906940258161al_a_o @ F2 @ ( qbs_mo8821471276632854295al_a_o @ ( binary5762279046363823267real_a @ X3 @ Y3 ) @ Z ) )
       => ( member_real_o
          @ ^ [X2: real] : ( F2 @ ( product_Pair_real_a @ X2 @ Y4 ) )
          @ ( qbs_morphism_real_o @ X3 @ Z ) ) ) ) ).

% qbs_morphism_Pair2'
thf(fact_481_qbs__morphism__Pair2_H,axiom,
    ! [Y4: a,Y3: quasi_borel_a,F2: product_prod_real_a > nat,X3: quasi_borel_real,Z: quasi_borel_nat] :
      ( ( member_a @ Y4 @ ( qbs_space_a @ Y3 ) )
     => ( ( member5377495750445857485_a_nat @ F2 @ ( qbs_mo4561836765000465937_a_nat @ ( binary5762279046363823267real_a @ X3 @ Y3 ) @ Z ) )
       => ( member_real_nat
          @ ^ [X2: real] : ( F2 @ ( product_Pair_real_a @ X2 @ Y4 ) )
          @ ( qbs_mo6567951568834356598al_nat @ X3 @ Z ) ) ) ) ).

% qbs_morphism_Pair2'
thf(fact_482_qbs__morphism__Pair2_H,axiom,
    ! [Y4: b,Y3: quasi_borel_b,F2: product_prod_a_b > c,X3: quasi_borel_a,Z: quasi_borel_c] :
      ( ( member_b @ Y4 @ ( qbs_space_b @ Y3 ) )
     => ( ( member1080921174361771732_a_b_c @ F2 @ ( qbs_mo2296058654870477648_a_b_c @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) @ Z ) )
       => ( member_a_c
          @ ^ [X2: a] : ( F2 @ ( product_Pair_a_b @ X2 @ Y4 ) )
          @ ( qbs_morphism_a_c @ X3 @ Z ) ) ) ) ).

% qbs_morphism_Pair2'
thf(fact_483_qbs__morphism__Pair2_H,axiom,
    ! [Y4: real,Y3: quasi_borel_real,F2: produc7716430852924023517t_real > real,X3: quasi_borel_nat,Z: quasi_borel_real] :
      ( ( member_real @ Y4 @ ( qbs_space_real @ Y3 ) )
     => ( ( member4539693599630147619l_real @ F2 @ ( qbs_mo8506632985670901265l_real @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ Z ) )
       => ( member_nat_real
          @ ^ [X2: nat] : ( F2 @ ( produc7837566107596912789t_real @ X2 @ Y4 ) )
          @ ( qbs_mo2000642995705457910t_real @ X3 @ Z ) ) ) ) ).

% qbs_morphism_Pair2'
thf(fact_484_qbs__morphism__Pair2_H,axiom,
    ! [Y4: real,Y3: quasi_borel_real,F2: produc2422161461964618553l_real > real,X3: quasi_borel_real,Z: quasi_borel_real] :
      ( ( member_real @ Y4 @ ( qbs_space_real @ Y3 ) )
     => ( ( member6699615393305559423l_real @ F2 @ ( qbs_mo6849673928694174957l_real @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ Z ) )
       => ( member_real_real
          @ ^ [X2: real] : ( F2 @ ( produc4511245868158468465l_real @ X2 @ Y4 ) )
          @ ( qbs_mo5229770564518008146l_real @ X3 @ Z ) ) ) ) ).

% qbs_morphism_Pair2'
thf(fact_485_qbs__morphism__Pair2_H,axiom,
    ! [Y4: real,Y3: quasi_borel_real,F2: produc2422161461964618553l_real > $o,X3: quasi_borel_real,Z: quasi_borel_o] :
      ( ( member_real @ Y4 @ ( qbs_space_real @ Y3 ) )
     => ( ( member9025505449285005339real_o @ F2 @ ( qbs_mo7803983300892306071real_o @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ Z ) )
       => ( member_real_o
          @ ^ [X2: real] : ( F2 @ ( produc4511245868158468465l_real @ X2 @ Y4 ) )
          @ ( qbs_morphism_real_o @ X3 @ Z ) ) ) ) ).

% qbs_morphism_Pair2'
thf(fact_486_qbs__morphism__Pair2_H,axiom,
    ! [Y4: real,Y3: quasi_borel_real,F2: produc2422161461964618553l_real > nat,X3: quasi_borel_real,Z: quasi_borel_nat] :
      ( ( member_real @ Y4 @ ( qbs_space_real @ Y3 ) )
     => ( ( member6756320954723885219al_nat @ F2 @ ( qbs_mo818872531660866193al_nat @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ Z ) )
       => ( member_real_nat
          @ ^ [X2: real] : ( F2 @ ( produc4511245868158468465l_real @ X2 @ Y4 ) )
          @ ( qbs_mo6567951568834356598al_nat @ X3 @ Z ) ) ) ) ).

% qbs_morphism_Pair2'
thf(fact_487_qbs__morphism__Pair2_H,axiom,
    ! [Y4: b,Y3: quasi_borel_b,F2: product_prod_real_b > real,X3: quasi_borel_real,Z: quasi_borel_real] :
      ( ( member_b @ Y4 @ ( qbs_space_b @ Y3 ) )
     => ( ( member5160407386997391786b_real @ F2 @ ( qbs_mo7149229302404819822b_real @ ( binary5762279046363823268real_b @ X3 @ Y3 ) @ Z ) )
       => ( member_real_real
          @ ^ [X2: real] : ( F2 @ ( product_Pair_real_b @ X2 @ Y4 ) )
          @ ( qbs_mo5229770564518008146l_real @ X3 @ Z ) ) ) ) ).

% qbs_morphism_Pair2'
thf(fact_488_qbs__morphism__Pair2_H,axiom,
    ! [Y4: b,Y3: quasi_borel_b,F2: product_prod_real_b > $o,X3: quasi_borel_real,Z: quasi_borel_o] :
      ( ( member_b @ Y4 @ ( qbs_space_b @ Y3 ) )
     => ( ( member6782669361822357936al_b_o @ F2 @ ( qbs_mo6034015694660178262al_b_o @ ( binary5762279046363823268real_b @ X3 @ Y3 ) @ Z ) )
       => ( member_real_o
          @ ^ [X2: real] : ( F2 @ ( product_Pair_real_b @ X2 @ Y4 ) )
          @ ( qbs_morphism_real_o @ X3 @ Z ) ) ) ) ).

% qbs_morphism_Pair2'
thf(fact_489_qbs__morphism__Pair1_H,axiom,
    ! [X4: a,X3: quasi_borel_a,F2: product_prod_a_b > c,Y3: quasi_borel_b,Z: quasi_borel_c] :
      ( ( member_a @ X4 @ ( qbs_space_a @ X3 ) )
     => ( ( member1080921174361771732_a_b_c @ F2 @ ( qbs_mo2296058654870477648_a_b_c @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) @ Z ) )
       => ( member_b_c
          @ ^ [Y2: b] : ( F2 @ ( product_Pair_a_b @ X4 @ Y2 ) )
          @ ( qbs_morphism_b_c @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_Pair1'
thf(fact_490_qbs__morphism__Pair1_H,axiom,
    ! [X4: nat,X3: quasi_borel_nat,F2: produc7716430852924023517t_real > real,Y3: quasi_borel_real,Z: quasi_borel_real] :
      ( ( member_nat @ X4 @ ( qbs_space_nat @ X3 ) )
     => ( ( member4539693599630147619l_real @ F2 @ ( qbs_mo8506632985670901265l_real @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ Z ) )
       => ( member_real_real
          @ ^ [Y2: real] : ( F2 @ ( produc7837566107596912789t_real @ X4 @ Y2 ) )
          @ ( qbs_mo5229770564518008146l_real @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_Pair1'
thf(fact_491_qbs__morphism__Pair1_H,axiom,
    ! [X4: nat,X3: quasi_borel_nat,F2: produc7716430852924023517t_real > $o,Y3: quasi_borel_real,Z: quasi_borel_o] :
      ( ( member_nat @ X4 @ ( qbs_space_nat @ X3 ) )
     => ( ( member7318680356153273975real_o @ F2 @ ( qbs_mo8978908438751067763real_o @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ Z ) )
       => ( member_real_o
          @ ^ [Y2: real] : ( F2 @ ( produc7837566107596912789t_real @ X4 @ Y2 ) )
          @ ( qbs_morphism_real_o @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_Pair1'
thf(fact_492_qbs__morphism__Pair1_H,axiom,
    ! [X4: nat,X3: quasi_borel_nat,F2: produc7716430852924023517t_real > nat,Y3: quasi_borel_real,Z: quasi_borel_nat] :
      ( ( member_nat @ X4 @ ( qbs_space_nat @ X3 ) )
     => ( ( member3149932044224082247al_nat @ F2 @ ( qbs_mo2463579765191384501al_nat @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ Z ) )
       => ( member_real_nat
          @ ^ [Y2: real] : ( F2 @ ( produc7837566107596912789t_real @ X4 @ Y2 ) )
          @ ( qbs_mo6567951568834356598al_nat @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_Pair1'
thf(fact_493_qbs__morphism__Pair1_H,axiom,
    ! [X4: real,X3: quasi_borel_real,F2: produc2422161461964618553l_real > real,Y3: quasi_borel_real,Z: quasi_borel_real] :
      ( ( member_real @ X4 @ ( qbs_space_real @ X3 ) )
     => ( ( member6699615393305559423l_real @ F2 @ ( qbs_mo6849673928694174957l_real @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ Z ) )
       => ( member_real_real
          @ ^ [Y2: real] : ( F2 @ ( produc4511245868158468465l_real @ X4 @ Y2 ) )
          @ ( qbs_mo5229770564518008146l_real @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_Pair1'
thf(fact_494_qbs__morphism__Pair1_H,axiom,
    ! [X4: real,X3: quasi_borel_real,F2: produc2422161461964618553l_real > $o,Y3: quasi_borel_real,Z: quasi_borel_o] :
      ( ( member_real @ X4 @ ( qbs_space_real @ X3 ) )
     => ( ( member9025505449285005339real_o @ F2 @ ( qbs_mo7803983300892306071real_o @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ Z ) )
       => ( member_real_o
          @ ^ [Y2: real] : ( F2 @ ( produc4511245868158468465l_real @ X4 @ Y2 ) )
          @ ( qbs_morphism_real_o @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_Pair1'
thf(fact_495_qbs__morphism__Pair1_H,axiom,
    ! [X4: real,X3: quasi_borel_real,F2: produc2422161461964618553l_real > nat,Y3: quasi_borel_real,Z: quasi_borel_nat] :
      ( ( member_real @ X4 @ ( qbs_space_real @ X3 ) )
     => ( ( member6756320954723885219al_nat @ F2 @ ( qbs_mo818872531660866193al_nat @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ Z ) )
       => ( member_real_nat
          @ ^ [Y2: real] : ( F2 @ ( produc4511245868158468465l_real @ X4 @ Y2 ) )
          @ ( qbs_mo6567951568834356598al_nat @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_Pair1'
thf(fact_496_qbs__morphism__Pair1_H,axiom,
    ! [X4: b,X3: quasi_borel_b,F2: product_prod_b_real > real,Y3: quasi_borel_real,Z: quasi_borel_real] :
      ( ( member_b @ X4 @ ( qbs_space_b @ X3 ) )
     => ( ( member2870586958900744892l_real @ F2 @ ( qbs_mo4859408874308172928l_real @ ( binary1505106857224228350b_real @ X3 @ Y3 ) @ Z ) )
       => ( member_real_real
          @ ^ [Y2: real] : ( F2 @ ( product_Pair_b_real @ X4 @ Y2 ) )
          @ ( qbs_mo5229770564518008146l_real @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_Pair1'
thf(fact_497_qbs__morphism__Pair1_H,axiom,
    ! [X4: b,X3: quasi_borel_b,F2: product_prod_b_real > $o,Y3: quasi_borel_real,Z: quasi_borel_o] :
      ( ( member_b @ X4 @ ( qbs_space_b @ X3 ) )
     => ( ( member650940978409756446real_o @ F2 @ ( qbs_mo9125659348102352580real_o @ ( binary1505106857224228350b_real @ X3 @ Y3 ) @ Z ) )
       => ( member_real_o
          @ ^ [Y2: real] : ( F2 @ ( product_Pair_b_real @ X4 @ Y2 ) )
          @ ( qbs_morphism_real_o @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_Pair1'
thf(fact_498_qbs__morphism__Pair1_H,axiom,
    ! [X4: b,X3: quasi_borel_b,F2: product_prod_b_real > nat,Y3: quasi_borel_real,Z: quasi_borel_nat] :
      ( ( member_b @ X4 @ ( qbs_space_b @ X3 ) )
     => ( ( member4930280467232768096al_nat @ F2 @ ( qbs_mo4114621481787376548al_nat @ ( binary1505106857224228350b_real @ X3 @ Y3 ) @ Z ) )
       => ( member_real_nat
          @ ^ [Y2: real] : ( F2 @ ( product_Pair_b_real @ X4 @ Y2 ) )
          @ ( qbs_mo6567951568834356598al_nat @ Y3 @ Z ) ) ) ) ).

% qbs_morphism_Pair1'
thf(fact_499_snd__qbs__morphism,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_a] : ( member6092897582725862615al_a_a @ product_snd_real_a @ ( qbs_mo5379295239341213437al_a_a @ ( binary5762279046363823267real_a @ X3 @ Y3 ) @ Y3 ) ) ).

% snd_qbs_morphism
thf(fact_500_snd__qbs__morphism,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b] : ( member1080921170058542931_a_b_b @ product_snd_a_b @ ( qbs_mo2296058654870477647_a_b_b @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) @ Y3 ) ) ).

% snd_qbs_morphism
thf(fact_501_snd__qbs__morphism,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real] : ( member4539693599630147619l_real @ product_snd_nat_real @ ( qbs_mo8506632985670901265l_real @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ Y3 ) ) ).

% snd_qbs_morphism
thf(fact_502_snd__qbs__morphism,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_real] : ( member6699615393305559423l_real @ produc3484788084999411615l_real @ ( qbs_mo6849673928694174957l_real @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ Y3 ) ) ).

% snd_qbs_morphism
thf(fact_503_snd__qbs__morphism,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_8309430206217406798od_a_b] : ( member1128530179153673047od_a_b @ produc4276089182416139253od_a_b @ ( qbs_mo2335099457226402941od_a_b @ ( binary7782493704384473421od_a_b @ X3 @ Y3 ) @ Y3 ) ) ).

% snd_qbs_morphism
thf(fact_504_snd__qbs__morphism,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_b] : ( member5457248586424104727al_b_b @ product_snd_real_b @ ( qbs_mo4743646238736226749al_b_b @ ( binary5762279046363823268real_b @ X3 @ Y3 ) @ Y3 ) ) ).

% snd_qbs_morphism
thf(fact_505_snd__qbs__morphism,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_real] : ( member2870586958900744892l_real @ product_snd_b_real @ ( qbs_mo4859408874308172928l_real @ ( binary1505106857224228350b_real @ X3 @ Y3 ) @ Y3 ) ) ).

% snd_qbs_morphism
thf(fact_506_snd__qbs__morphism,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_a] : ( member7312788781548431508_b_a_a @ product_snd_b_a @ ( qbs_mo8527926270663595024_b_a_a @ ( binary1131512637584519980bs_b_a @ X3 @ Y3 ) @ Y3 ) ) ).

% snd_qbs_morphism
thf(fact_507_snd__qbs__morphism,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_real] : ( member2203687483360836539l_real @ product_snd_a_real @ ( qbs_mo4192509398768264575l_real @ ( binary5132260278890873469a_real @ X3 @ Y3 ) @ Y3 ) ) ).

% snd_qbs_morphism
thf(fact_508_fst__qbs__morphism,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_a] : ( member7939111694857414313a_real @ product_fst_real_a @ ( qbs_mo704561573410066541a_real @ ( binary5762279046363823267real_a @ X3 @ Y3 ) @ X3 ) ) ).

% fst_qbs_morphism
thf(fact_509_fst__qbs__morphism,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b] : ( member1080921165755314130_a_b_a @ product_fst_a_b @ ( qbs_mo2296058654870477646_a_b_a @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) @ X3 ) ) ).

% fst_qbs_morphism
thf(fact_510_fst__qbs__morphism,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real] : ( member3149932044224082247al_nat @ product_fst_nat_real @ ( qbs_mo2463579765191384501al_nat @ ( binary2938201662863479403t_real @ X3 @ Y3 ) @ X3 ) ) ).

% fst_qbs_morphism
thf(fact_511_fst__qbs__morphism,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_real] : ( member6699615393305559423l_real @ produc5828954698716094813l_real @ ( qbs_mo6849673928694174957l_real @ ( binary210465342804807751l_real @ X3 @ Y3 ) @ X3 ) ) ).

% fst_qbs_morphism
thf(fact_512_fst__qbs__morphism,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_8309430206217406798od_a_b] : ( member6209306361823650387b_real @ produc4505306568083885239od_a_b @ ( qbs_mo1721096491341367575b_real @ ( binary7782493704384473421od_a_b @ X3 @ Y3 ) @ X3 ) ) ).

% fst_qbs_morphism
thf(fact_513_fst__qbs__morphism,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_b] : ( member5160407386997391786b_real @ product_fst_real_b @ ( qbs_mo7149229302404819822b_real @ ( binary5762279046363823268real_b @ X3 @ Y3 ) @ X3 ) ) ).

% fst_qbs_morphism
thf(fact_514_fst__qbs__morphism,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_real] : ( member1565719598505844101real_b @ product_fst_b_real @ ( qbs_mo852117250817966123real_b @ ( binary1505106857224228350b_real @ X3 @ Y3 ) @ X3 ) ) ).

% fst_qbs_morphism
thf(fact_515_fst__qbs__morphism,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_a] : ( member7312788785851660309_b_a_b @ product_fst_b_a @ ( qbs_mo8527926270663595025_b_a_b @ ( binary1131512637584519980bs_b_a @ X3 @ Y3 ) @ X3 ) ) ).

% fst_qbs_morphism
thf(fact_516_fst__qbs__morphism,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_real] : ( member77757556907816773real_a @ product_fst_a_real @ ( qbs_mo8587527250377943403real_a @ ( binary5132260278890873469a_real @ X3 @ Y3 ) @ X3 ) ) ).

% fst_qbs_morphism
thf(fact_517_calculation,axiom,
    ( ( ^ [R: real] : ( k @ ( produc4505306568083885239od_a_b @ ( alpha @ R ) ) @ ( product_fst_a_b @ ( produc4276089182416139253od_a_b @ ( alpha @ R ) ) ) ) )
    = ( comp_P5170362070794227966c_real @ ( produc8409101302566321868_a_b_c @ k )
      @ ^ [R: real] : ( product_Pair_real_a @ ( produc4505306568083885239od_a_b @ ( alpha @ R ) ) @ ( product_fst_a_b @ ( produc4276089182416139253od_a_b @ ( alpha @ R ) ) ) ) ) ) ).

% calculation
thf(fact_518_exE__realizer,axiom,
    ! [P2: a > real > $o,P: product_prod_real_a,Q2: ( b > c ) > $o,F2: real > a > b > c] :
      ( ( P2 @ ( product_snd_real_a @ P ) @ ( product_fst_real_a @ P ) )
     => ( ! [X5: real,Y5: a] :
            ( ( P2 @ Y5 @ X5 )
           => ( Q2 @ ( F2 @ X5 @ Y5 ) ) )
       => ( Q2 @ ( produc8409101302566321868_a_b_c @ F2 @ P ) ) ) ) ).

% exE_realizer
thf(fact_519_exE__realizer,axiom,
    ! [P2: product_prod_a_b > real > $o,P: produc1405624045518934769od_a_b,Q2: c > $o,F2: real > product_prod_a_b > c] :
      ( ( P2 @ ( produc4276089182416139253od_a_b @ P ) @ ( produc4505306568083885239od_a_b @ P ) )
     => ( ! [X5: real,Y5: product_prod_a_b] :
            ( ( P2 @ Y5 @ X5 )
           => ( Q2 @ ( F2 @ X5 @ Y5 ) ) )
       => ( Q2 @ ( produc8366947261062197552_a_b_c @ F2 @ P ) ) ) ) ).

% exE_realizer
thf(fact_520_exE__realizer,axiom,
    ! [P2: b > a > $o,P: product_prod_a_b,Q2: c > $o,F2: a > b > c] :
      ( ( P2 @ ( product_snd_a_b @ P ) @ ( product_fst_a_b @ P ) )
     => ( ! [X5: a,Y5: b] :
            ( ( P2 @ Y5 @ X5 )
           => ( Q2 @ ( F2 @ X5 @ Y5 ) ) )
       => ( Q2 @ ( produc6028431345588019475_a_b_c @ F2 @ P ) ) ) ) ).

% exE_realizer
thf(fact_521_exE__realizer,axiom,
    ! [P2: b > real > $o,P: product_prod_real_b,Q2: c > $o,F2: real > b > c] :
      ( ( P2 @ ( product_snd_real_b @ P ) @ ( product_fst_real_b @ P ) )
     => ( ! [X5: real,Y5: b] :
            ( ( P2 @ Y5 @ X5 )
           => ( Q2 @ ( F2 @ X5 @ Y5 ) ) )
       => ( Q2 @ ( produc2835462372567216025al_b_c @ F2 @ P ) ) ) ) ).

% exE_realizer
thf(fact_522_exE__realizer,axiom,
    ! [P2: a > real > $o,P: product_prod_real_a,Q2: c > $o,F2: real > a > c] :
      ( ( P2 @ ( product_snd_real_a @ P ) @ ( product_fst_real_a @ P ) )
     => ( ! [X5: real,Y5: a] :
            ( ( P2 @ Y5 @ X5 )
           => ( Q2 @ ( F2 @ X5 @ Y5 ) ) )
       => ( Q2 @ ( produc5622917954539892058al_a_c @ F2 @ P ) ) ) ) ).

% exE_realizer
thf(fact_523_exE__realizer,axiom,
    ! [P2: real > a > $o,P: product_prod_a_real,Q2: ( b > c ) > $o,F2: a > real > b > c] :
      ( ( P2 @ ( product_snd_a_real @ P ) @ ( product_fst_a_real @ P ) )
     => ( ! [X5: a,Y5: real] :
            ( ( P2 @ Y5 @ X5 )
           => ( Q2 @ ( F2 @ X5 @ Y5 ) ) )
       => ( Q2 @ ( produc7198824580026001574al_b_c @ F2 @ P ) ) ) ) ).

% exE_realizer
thf(fact_524_exI__realizer,axiom,
    ! [P2: b > real > $o,Y4: b,X4: real] :
      ( ( P2 @ Y4 @ X4 )
     => ( P2 @ ( product_snd_real_b @ ( product_Pair_real_b @ X4 @ Y4 ) ) @ ( product_fst_real_b @ ( product_Pair_real_b @ X4 @ Y4 ) ) ) ) ).

% exI_realizer
thf(fact_525_exI__realizer,axiom,
    ! [P2: a > b > $o,Y4: a,X4: b] :
      ( ( P2 @ Y4 @ X4 )
     => ( P2 @ ( product_snd_b_a @ ( product_Pair_b_a @ X4 @ Y4 ) ) @ ( product_fst_b_a @ ( product_Pair_b_a @ X4 @ Y4 ) ) ) ) ).

% exI_realizer
thf(fact_526_exI__realizer,axiom,
    ! [P2: real > a > $o,Y4: real,X4: a] :
      ( ( P2 @ Y4 @ X4 )
     => ( P2 @ ( product_snd_a_real @ ( product_Pair_a_real @ X4 @ Y4 ) ) @ ( product_fst_a_real @ ( product_Pair_a_real @ X4 @ Y4 ) ) ) ) ).

% exI_realizer
thf(fact_527_exI__realizer,axiom,
    ! [P2: real > b > $o,Y4: real,X4: b] :
      ( ( P2 @ Y4 @ X4 )
     => ( P2 @ ( product_snd_b_real @ ( product_Pair_b_real @ X4 @ Y4 ) ) @ ( product_fst_b_real @ ( product_Pair_b_real @ X4 @ Y4 ) ) ) ) ).

% exI_realizer
thf(fact_528_exI__realizer,axiom,
    ! [P2: real > product_prod_a_b > $o,Y4: real,X4: product_prod_a_b] :
      ( ( P2 @ Y4 @ X4 )
     => ( P2 @ ( produc7037151529651111887b_real @ ( produc9021675809588086653b_real @ X4 @ Y4 ) ) @ ( produc7266368915318857873b_real @ ( produc9021675809588086653b_real @ X4 @ Y4 ) ) ) ) ).

% exI_realizer
thf(fact_529_exI__realizer,axiom,
    ! [P2: real > real > $o,Y4: real,X4: real] :
      ( ( P2 @ Y4 @ X4 )
     => ( P2 @ ( produc3484788084999411615l_real @ ( produc4511245868158468465l_real @ X4 @ Y4 ) ) @ ( produc5828954698716094813l_real @ ( produc4511245868158468465l_real @ X4 @ Y4 ) ) ) ) ).

% exI_realizer
thf(fact_530_exI__realizer,axiom,
    ! [P2: real > nat > $o,Y4: real,X4: nat] :
      ( ( P2 @ Y4 @ X4 )
     => ( P2 @ ( product_snd_nat_real @ ( produc7837566107596912789t_real @ X4 @ Y4 ) ) @ ( product_fst_nat_real @ ( produc7837566107596912789t_real @ X4 @ Y4 ) ) ) ) ).

% exI_realizer
thf(fact_531_exI__realizer,axiom,
    ! [P2: a > real > $o,Y4: a,X4: real] :
      ( ( P2 @ Y4 @ X4 )
     => ( P2 @ ( product_snd_real_a @ ( product_Pair_real_a @ X4 @ Y4 ) ) @ ( product_fst_real_a @ ( product_Pair_real_a @ X4 @ Y4 ) ) ) ) ).

% exI_realizer
thf(fact_532_exI__realizer,axiom,
    ! [P2: product_prod_a_b > real > $o,Y4: product_prod_a_b,X4: real] :
      ( ( P2 @ Y4 @ X4 )
     => ( P2 @ ( produc4276089182416139253od_a_b @ ( produc6260613462353114019od_a_b @ X4 @ Y4 ) ) @ ( produc4505306568083885239od_a_b @ ( produc6260613462353114019od_a_b @ X4 @ Y4 ) ) ) ) ).

% exI_realizer
thf(fact_533_exI__realizer,axiom,
    ! [P2: b > a > $o,Y4: b,X4: a] :
      ( ( P2 @ Y4 @ X4 )
     => ( P2 @ ( product_snd_a_b @ ( product_Pair_a_b @ X4 @ Y4 ) ) @ ( product_fst_a_b @ ( product_Pair_a_b @ X4 @ Y4 ) ) ) ) ).

% exI_realizer
thf(fact_534_split__pairs,axiom,
    ! [A5: real,B5: b,X3: product_prod_real_b] :
      ( ( ( product_Pair_real_b @ A5 @ B5 )
        = X3 )
      = ( ( ( product_fst_real_b @ X3 )
          = A5 )
        & ( ( product_snd_real_b @ X3 )
          = B5 ) ) ) ).

% split_pairs
thf(fact_535_split__pairs,axiom,
    ! [A5: b,B5: a,X3: product_prod_b_a] :
      ( ( ( product_Pair_b_a @ A5 @ B5 )
        = X3 )
      = ( ( ( product_fst_b_a @ X3 )
          = A5 )
        & ( ( product_snd_b_a @ X3 )
          = B5 ) ) ) ).

% split_pairs
thf(fact_536_split__pairs,axiom,
    ! [A5: a,B5: real,X3: product_prod_a_real] :
      ( ( ( product_Pair_a_real @ A5 @ B5 )
        = X3 )
      = ( ( ( product_fst_a_real @ X3 )
          = A5 )
        & ( ( product_snd_a_real @ X3 )
          = B5 ) ) ) ).

% split_pairs
thf(fact_537_split__pairs,axiom,
    ! [A5: b,B5: real,X3: product_prod_b_real] :
      ( ( ( product_Pair_b_real @ A5 @ B5 )
        = X3 )
      = ( ( ( product_fst_b_real @ X3 )
          = A5 )
        & ( ( product_snd_b_real @ X3 )
          = B5 ) ) ) ).

% split_pairs
thf(fact_538_split__pairs,axiom,
    ! [A5: product_prod_a_b,B5: real,X3: produc7929879615859924995b_real] :
      ( ( ( produc9021675809588086653b_real @ A5 @ B5 )
        = X3 )
      = ( ( ( produc7266368915318857873b_real @ X3 )
          = A5 )
        & ( ( produc7037151529651111887b_real @ X3 )
          = B5 ) ) ) ).

% split_pairs
thf(fact_539_split__pairs,axiom,
    ! [A5: real,B5: real,X3: produc2422161461964618553l_real] :
      ( ( ( produc4511245868158468465l_real @ A5 @ B5 )
        = X3 )
      = ( ( ( produc5828954698716094813l_real @ X3 )
          = A5 )
        & ( ( produc3484788084999411615l_real @ X3 )
          = B5 ) ) ) ).

% split_pairs
thf(fact_540_split__pairs,axiom,
    ! [A5: nat,B5: real,X3: produc7716430852924023517t_real] :
      ( ( ( produc7837566107596912789t_real @ A5 @ B5 )
        = X3 )
      = ( ( ( product_fst_nat_real @ X3 )
          = A5 )
        & ( ( product_snd_nat_real @ X3 )
          = B5 ) ) ) ).

% split_pairs
thf(fact_541_split__pairs,axiom,
    ! [A5: real,B5: a,X3: product_prod_real_a] :
      ( ( ( product_Pair_real_a @ A5 @ B5 )
        = X3 )
      = ( ( ( product_fst_real_a @ X3 )
          = A5 )
        & ( ( product_snd_real_a @ X3 )
          = B5 ) ) ) ).

% split_pairs
thf(fact_542_split__pairs,axiom,
    ! [A5: real,B5: product_prod_a_b,X3: produc1405624045518934769od_a_b] :
      ( ( ( produc6260613462353114019od_a_b @ A5 @ B5 )
        = X3 )
      = ( ( ( produc4505306568083885239od_a_b @ X3 )
          = A5 )
        & ( ( produc4276089182416139253od_a_b @ X3 )
          = B5 ) ) ) ).

% split_pairs
thf(fact_543_split__pairs,axiom,
    ! [A5: a,B5: b,X3: product_prod_a_b] :
      ( ( ( product_Pair_a_b @ A5 @ B5 )
        = X3 )
      = ( ( ( product_fst_a_b @ X3 )
          = A5 )
        & ( ( product_snd_a_b @ X3 )
          = B5 ) ) ) ).

% split_pairs
thf(fact_544_conjI__realizer,axiom,
    ! [P2: real > $o,P: real,Q2: b > $o,Q: b] :
      ( ( P2 @ P )
     => ( ( Q2 @ Q )
       => ( ( P2 @ ( product_fst_real_b @ ( product_Pair_real_b @ P @ Q ) ) )
          & ( Q2 @ ( product_snd_real_b @ ( product_Pair_real_b @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_545_conjI__realizer,axiom,
    ! [P2: b > $o,P: b,Q2: a > $o,Q: a] :
      ( ( P2 @ P )
     => ( ( Q2 @ Q )
       => ( ( P2 @ ( product_fst_b_a @ ( product_Pair_b_a @ P @ Q ) ) )
          & ( Q2 @ ( product_snd_b_a @ ( product_Pair_b_a @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_546_conjI__realizer,axiom,
    ! [P2: a > $o,P: a,Q2: real > $o,Q: real] :
      ( ( P2 @ P )
     => ( ( Q2 @ Q )
       => ( ( P2 @ ( product_fst_a_real @ ( product_Pair_a_real @ P @ Q ) ) )
          & ( Q2 @ ( product_snd_a_real @ ( product_Pair_a_real @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_547_conjI__realizer,axiom,
    ! [P2: b > $o,P: b,Q2: real > $o,Q: real] :
      ( ( P2 @ P )
     => ( ( Q2 @ Q )
       => ( ( P2 @ ( product_fst_b_real @ ( product_Pair_b_real @ P @ Q ) ) )
          & ( Q2 @ ( product_snd_b_real @ ( product_Pair_b_real @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_548_conjI__realizer,axiom,
    ! [P2: product_prod_a_b > $o,P: product_prod_a_b,Q2: real > $o,Q: real] :
      ( ( P2 @ P )
     => ( ( Q2 @ Q )
       => ( ( P2 @ ( produc7266368915318857873b_real @ ( produc9021675809588086653b_real @ P @ Q ) ) )
          & ( Q2 @ ( produc7037151529651111887b_real @ ( produc9021675809588086653b_real @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_549_conjI__realizer,axiom,
    ! [P2: real > $o,P: real,Q2: real > $o,Q: real] :
      ( ( P2 @ P )
     => ( ( Q2 @ Q )
       => ( ( P2 @ ( produc5828954698716094813l_real @ ( produc4511245868158468465l_real @ P @ Q ) ) )
          & ( Q2 @ ( produc3484788084999411615l_real @ ( produc4511245868158468465l_real @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_550_conjI__realizer,axiom,
    ! [P2: nat > $o,P: nat,Q2: real > $o,Q: real] :
      ( ( P2 @ P )
     => ( ( Q2 @ Q )
       => ( ( P2 @ ( product_fst_nat_real @ ( produc7837566107596912789t_real @ P @ Q ) ) )
          & ( Q2 @ ( product_snd_nat_real @ ( produc7837566107596912789t_real @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_551_conjI__realizer,axiom,
    ! [P2: real > $o,P: real,Q2: a > $o,Q: a] :
      ( ( P2 @ P )
     => ( ( Q2 @ Q )
       => ( ( P2 @ ( product_fst_real_a @ ( product_Pair_real_a @ P @ Q ) ) )
          & ( Q2 @ ( product_snd_real_a @ ( product_Pair_real_a @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_552_conjI__realizer,axiom,
    ! [P2: real > $o,P: real,Q2: product_prod_a_b > $o,Q: product_prod_a_b] :
      ( ( P2 @ P )
     => ( ( Q2 @ Q )
       => ( ( P2 @ ( produc4505306568083885239od_a_b @ ( produc6260613462353114019od_a_b @ P @ Q ) ) )
          & ( Q2 @ ( produc4276089182416139253od_a_b @ ( produc6260613462353114019od_a_b @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_553_conjI__realizer,axiom,
    ! [P2: a > $o,P: a,Q2: b > $o,Q: b] :
      ( ( P2 @ P )
     => ( ( Q2 @ Q )
       => ( ( P2 @ ( product_fst_a_b @ ( product_Pair_a_b @ P @ Q ) ) )
          & ( Q2 @ ( product_snd_a_b @ ( product_Pair_a_b @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_554_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: real > b > $o,X4: real,Y4: b,A: product_prod_real_b] :
      ( ( P2 @ X4 @ Y4 )
     => ( ( A
          = ( product_Pair_real_b @ X4 @ Y4 ) )
       => ( P2 @ ( product_fst_real_b @ A ) @ ( product_snd_real_b @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_555_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: b > a > $o,X4: b,Y4: a,A: product_prod_b_a] :
      ( ( P2 @ X4 @ Y4 )
     => ( ( A
          = ( product_Pair_b_a @ X4 @ Y4 ) )
       => ( P2 @ ( product_fst_b_a @ A ) @ ( product_snd_b_a @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_556_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: a > real > $o,X4: a,Y4: real,A: product_prod_a_real] :
      ( ( P2 @ X4 @ Y4 )
     => ( ( A
          = ( product_Pair_a_real @ X4 @ Y4 ) )
       => ( P2 @ ( product_fst_a_real @ A ) @ ( product_snd_a_real @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_557_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: b > real > $o,X4: b,Y4: real,A: product_prod_b_real] :
      ( ( P2 @ X4 @ Y4 )
     => ( ( A
          = ( product_Pair_b_real @ X4 @ Y4 ) )
       => ( P2 @ ( product_fst_b_real @ A ) @ ( product_snd_b_real @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_558_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: product_prod_a_b > real > $o,X4: product_prod_a_b,Y4: real,A: produc7929879615859924995b_real] :
      ( ( P2 @ X4 @ Y4 )
     => ( ( A
          = ( produc9021675809588086653b_real @ X4 @ Y4 ) )
       => ( P2 @ ( produc7266368915318857873b_real @ A ) @ ( produc7037151529651111887b_real @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_559_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: real > real > $o,X4: real,Y4: real,A: produc2422161461964618553l_real] :
      ( ( P2 @ X4 @ Y4 )
     => ( ( A
          = ( produc4511245868158468465l_real @ X4 @ Y4 ) )
       => ( P2 @ ( produc5828954698716094813l_real @ A ) @ ( produc3484788084999411615l_real @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_560_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: nat > real > $o,X4: nat,Y4: real,A: produc7716430852924023517t_real] :
      ( ( P2 @ X4 @ Y4 )
     => ( ( A
          = ( produc7837566107596912789t_real @ X4 @ Y4 ) )
       => ( P2 @ ( product_fst_nat_real @ A ) @ ( product_snd_nat_real @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_561_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: real > a > $o,X4: real,Y4: a,A: product_prod_real_a] :
      ( ( P2 @ X4 @ Y4 )
     => ( ( A
          = ( product_Pair_real_a @ X4 @ Y4 ) )
       => ( P2 @ ( product_fst_real_a @ A ) @ ( product_snd_real_a @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_562_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: real > product_prod_a_b > $o,X4: real,Y4: product_prod_a_b,A: produc1405624045518934769od_a_b] :
      ( ( P2 @ X4 @ Y4 )
     => ( ( A
          = ( produc6260613462353114019od_a_b @ X4 @ Y4 ) )
       => ( P2 @ ( produc4505306568083885239od_a_b @ A ) @ ( produc4276089182416139253od_a_b @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_563_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: a > b > $o,X4: a,Y4: b,A: product_prod_a_b] :
      ( ( P2 @ X4 @ Y4 )
     => ( ( A
          = ( product_Pair_a_b @ X4 @ Y4 ) )
       => ( P2 @ ( product_fst_a_b @ A ) @ ( product_snd_a_b @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_564_exE__realizer_H,axiom,
    ! [P2: real > real > $o,P: produc2422161461964618553l_real] :
      ( ( P2 @ ( produc3484788084999411615l_real @ P ) @ ( produc5828954698716094813l_real @ P ) )
     => ~ ! [X5: real,Y5: real] :
            ~ ( P2 @ Y5 @ X5 ) ) ).

% exE_realizer'
thf(fact_565_exE__realizer_H,axiom,
    ! [P2: real > nat > $o,P: produc7716430852924023517t_real] :
      ( ( P2 @ ( product_snd_nat_real @ P ) @ ( product_fst_nat_real @ P ) )
     => ~ ! [X5: nat,Y5: real] :
            ~ ( P2 @ Y5 @ X5 ) ) ).

% exE_realizer'
thf(fact_566_exE__realizer_H,axiom,
    ! [P2: a > real > $o,P: product_prod_real_a] :
      ( ( P2 @ ( product_snd_real_a @ P ) @ ( product_fst_real_a @ P ) )
     => ~ ! [X5: real,Y5: a] :
            ~ ( P2 @ Y5 @ X5 ) ) ).

% exE_realizer'
thf(fact_567_exE__realizer_H,axiom,
    ! [P2: product_prod_a_b > real > $o,P: produc1405624045518934769od_a_b] :
      ( ( P2 @ ( produc4276089182416139253od_a_b @ P ) @ ( produc4505306568083885239od_a_b @ P ) )
     => ~ ! [X5: real,Y5: product_prod_a_b] :
            ~ ( P2 @ Y5 @ X5 ) ) ).

% exE_realizer'
thf(fact_568_exE__realizer_H,axiom,
    ! [P2: b > a > $o,P: product_prod_a_b] :
      ( ( P2 @ ( product_snd_a_b @ P ) @ ( product_fst_a_b @ P ) )
     => ~ ! [X5: a,Y5: b] :
            ~ ( P2 @ Y5 @ X5 ) ) ).

% exE_realizer'
thf(fact_569_sndI,axiom,
    ! [X4: product_prod_real_a,Y4: real,Z3: a] :
      ( ( X4
        = ( product_Pair_real_a @ Y4 @ Z3 ) )
     => ( ( product_snd_real_a @ X4 )
        = Z3 ) ) ).

% sndI
thf(fact_570_sndI,axiom,
    ! [X4: product_prod_real_b,Y4: real,Z3: b] :
      ( ( X4
        = ( product_Pair_real_b @ Y4 @ Z3 ) )
     => ( ( product_snd_real_b @ X4 )
        = Z3 ) ) ).

% sndI
thf(fact_571_sndI,axiom,
    ! [X4: product_prod_b_a,Y4: b,Z3: a] :
      ( ( X4
        = ( product_Pair_b_a @ Y4 @ Z3 ) )
     => ( ( product_snd_b_a @ X4 )
        = Z3 ) ) ).

% sndI
thf(fact_572_sndI,axiom,
    ! [X4: product_prod_a_real,Y4: a,Z3: real] :
      ( ( X4
        = ( product_Pair_a_real @ Y4 @ Z3 ) )
     => ( ( product_snd_a_real @ X4 )
        = Z3 ) ) ).

% sndI
thf(fact_573_sndI,axiom,
    ! [X4: product_prod_b_real,Y4: b,Z3: real] :
      ( ( X4
        = ( product_Pair_b_real @ Y4 @ Z3 ) )
     => ( ( product_snd_b_real @ X4 )
        = Z3 ) ) ).

% sndI
thf(fact_574_sndI,axiom,
    ! [X4: produc7929879615859924995b_real,Y4: product_prod_a_b,Z3: real] :
      ( ( X4
        = ( produc9021675809588086653b_real @ Y4 @ Z3 ) )
     => ( ( produc7037151529651111887b_real @ X4 )
        = Z3 ) ) ).

% sndI
thf(fact_575_sndI,axiom,
    ! [X4: produc1405624045518934769od_a_b,Y4: real,Z3: product_prod_a_b] :
      ( ( X4
        = ( produc6260613462353114019od_a_b @ Y4 @ Z3 ) )
     => ( ( produc4276089182416139253od_a_b @ X4 )
        = Z3 ) ) ).

% sndI
thf(fact_576_sndI,axiom,
    ! [X4: product_prod_a_b,Y4: a,Z3: b] :
      ( ( X4
        = ( product_Pair_a_b @ Y4 @ Z3 ) )
     => ( ( product_snd_a_b @ X4 )
        = Z3 ) ) ).

% sndI
thf(fact_577_eq__snd__iff,axiom,
    ! [B: a,P: product_prod_real_a] :
      ( ( B
        = ( product_snd_real_a @ P ) )
      = ( ? [A4: real] :
            ( P
            = ( product_Pair_real_a @ A4 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_578_eq__snd__iff,axiom,
    ! [B: b,P: product_prod_real_b] :
      ( ( B
        = ( product_snd_real_b @ P ) )
      = ( ? [A4: real] :
            ( P
            = ( product_Pair_real_b @ A4 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_579_eq__snd__iff,axiom,
    ! [B: a,P: product_prod_b_a] :
      ( ( B
        = ( product_snd_b_a @ P ) )
      = ( ? [A4: b] :
            ( P
            = ( product_Pair_b_a @ A4 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_580_eq__snd__iff,axiom,
    ! [B: real,P: product_prod_a_real] :
      ( ( B
        = ( product_snd_a_real @ P ) )
      = ( ? [A4: a] :
            ( P
            = ( product_Pair_a_real @ A4 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_581_eq__snd__iff,axiom,
    ! [B: real,P: product_prod_b_real] :
      ( ( B
        = ( product_snd_b_real @ P ) )
      = ( ? [A4: b] :
            ( P
            = ( product_Pair_b_real @ A4 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_582_eq__snd__iff,axiom,
    ! [B: real,P: produc7929879615859924995b_real] :
      ( ( B
        = ( produc7037151529651111887b_real @ P ) )
      = ( ? [A4: product_prod_a_b] :
            ( P
            = ( produc9021675809588086653b_real @ A4 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_583_eq__snd__iff,axiom,
    ! [B: product_prod_a_b,P: produc1405624045518934769od_a_b] :
      ( ( B
        = ( produc4276089182416139253od_a_b @ P ) )
      = ( ? [A4: real] :
            ( P
            = ( produc6260613462353114019od_a_b @ A4 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_584_eq__snd__iff,axiom,
    ! [B: b,P: product_prod_a_b] :
      ( ( B
        = ( product_snd_a_b @ P ) )
      = ( ? [A4: a] :
            ( P
            = ( product_Pair_a_b @ A4 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_585_fstI,axiom,
    ! [X4: product_prod_real_b,Y4: real,Z3: b] :
      ( ( X4
        = ( product_Pair_real_b @ Y4 @ Z3 ) )
     => ( ( product_fst_real_b @ X4 )
        = Y4 ) ) ).

% fstI
thf(fact_586_fstI,axiom,
    ! [X4: product_prod_b_a,Y4: b,Z3: a] :
      ( ( X4
        = ( product_Pair_b_a @ Y4 @ Z3 ) )
     => ( ( product_fst_b_a @ X4 )
        = Y4 ) ) ).

% fstI
thf(fact_587_fstI,axiom,
    ! [X4: product_prod_a_real,Y4: a,Z3: real] :
      ( ( X4
        = ( product_Pair_a_real @ Y4 @ Z3 ) )
     => ( ( product_fst_a_real @ X4 )
        = Y4 ) ) ).

% fstI
thf(fact_588_fstI,axiom,
    ! [X4: product_prod_b_real,Y4: b,Z3: real] :
      ( ( X4
        = ( product_Pair_b_real @ Y4 @ Z3 ) )
     => ( ( product_fst_b_real @ X4 )
        = Y4 ) ) ).

% fstI
thf(fact_589_fstI,axiom,
    ! [X4: produc7929879615859924995b_real,Y4: product_prod_a_b,Z3: real] :
      ( ( X4
        = ( produc9021675809588086653b_real @ Y4 @ Z3 ) )
     => ( ( produc7266368915318857873b_real @ X4 )
        = Y4 ) ) ).

% fstI
thf(fact_590_fstI,axiom,
    ! [X4: produc1405624045518934769od_a_b,Y4: real,Z3: product_prod_a_b] :
      ( ( X4
        = ( produc6260613462353114019od_a_b @ Y4 @ Z3 ) )
     => ( ( produc4505306568083885239od_a_b @ X4 )
        = Y4 ) ) ).

% fstI
thf(fact_591_fstI,axiom,
    ! [X4: product_prod_a_b,Y4: a,Z3: b] :
      ( ( X4
        = ( product_Pair_a_b @ Y4 @ Z3 ) )
     => ( ( product_fst_a_b @ X4 )
        = Y4 ) ) ).

% fstI
thf(fact_592_fstI,axiom,
    ! [X4: produc2422161461964618553l_real,Y4: real,Z3: real] :
      ( ( X4
        = ( produc4511245868158468465l_real @ Y4 @ Z3 ) )
     => ( ( produc5828954698716094813l_real @ X4 )
        = Y4 ) ) ).

% fstI
thf(fact_593_fstI,axiom,
    ! [X4: produc7716430852924023517t_real,Y4: nat,Z3: real] :
      ( ( X4
        = ( produc7837566107596912789t_real @ Y4 @ Z3 ) )
     => ( ( product_fst_nat_real @ X4 )
        = Y4 ) ) ).

% fstI
thf(fact_594_fstI,axiom,
    ! [X4: product_prod_real_a,Y4: real,Z3: a] :
      ( ( X4
        = ( product_Pair_real_a @ Y4 @ Z3 ) )
     => ( ( product_fst_real_a @ X4 )
        = Y4 ) ) ).

% fstI
thf(fact_595_eq__fst__iff,axiom,
    ! [A: real,P: product_prod_real_b] :
      ( ( A
        = ( product_fst_real_b @ P ) )
      = ( ? [B4: b] :
            ( P
            = ( product_Pair_real_b @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_596_eq__fst__iff,axiom,
    ! [A: b,P: product_prod_b_a] :
      ( ( A
        = ( product_fst_b_a @ P ) )
      = ( ? [B4: a] :
            ( P
            = ( product_Pair_b_a @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_597_eq__fst__iff,axiom,
    ! [A: a,P: product_prod_a_real] :
      ( ( A
        = ( product_fst_a_real @ P ) )
      = ( ? [B4: real] :
            ( P
            = ( product_Pair_a_real @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_598_eq__fst__iff,axiom,
    ! [A: b,P: product_prod_b_real] :
      ( ( A
        = ( product_fst_b_real @ P ) )
      = ( ? [B4: real] :
            ( P
            = ( product_Pair_b_real @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_599_eq__fst__iff,axiom,
    ! [A: product_prod_a_b,P: produc7929879615859924995b_real] :
      ( ( A
        = ( produc7266368915318857873b_real @ P ) )
      = ( ? [B4: real] :
            ( P
            = ( produc9021675809588086653b_real @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_600_eq__fst__iff,axiom,
    ! [A: real,P: produc1405624045518934769od_a_b] :
      ( ( A
        = ( produc4505306568083885239od_a_b @ P ) )
      = ( ? [B4: product_prod_a_b] :
            ( P
            = ( produc6260613462353114019od_a_b @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_601_eq__fst__iff,axiom,
    ! [A: a,P: product_prod_a_b] :
      ( ( A
        = ( product_fst_a_b @ P ) )
      = ( ? [B4: b] :
            ( P
            = ( product_Pair_a_b @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_602_eq__fst__iff,axiom,
    ! [A: real,P: produc2422161461964618553l_real] :
      ( ( A
        = ( produc5828954698716094813l_real @ P ) )
      = ( ? [B4: real] :
            ( P
            = ( produc4511245868158468465l_real @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_603_eq__fst__iff,axiom,
    ! [A: nat,P: produc7716430852924023517t_real] :
      ( ( A
        = ( product_fst_nat_real @ P ) )
      = ( ? [B4: real] :
            ( P
            = ( produc7837566107596912789t_real @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_604_eq__fst__iff,axiom,
    ! [A: real,P: product_prod_real_a] :
      ( ( A
        = ( product_fst_real_a @ P ) )
      = ( ? [B4: a] :
            ( P
            = ( product_Pair_real_a @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_605_rewriteL__comp__comp,axiom,
    ! [F2: $o > $o,G2: real > $o,L2: real > $o,H: $o > real] :
      ( ( ( comp_o_o_real @ F2 @ G2 )
        = L2 )
     => ( ( comp_o_o_o @ F2 @ ( comp_real_o_o @ G2 @ H ) )
        = ( comp_real_o_o @ L2 @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_606_rewriteL__comp__comp,axiom,
    ! [F2: nat > nat,G2: real > nat,L2: real > nat,H: nat > real] :
      ( ( ( comp_nat_nat_real @ F2 @ G2 )
        = L2 )
     => ( ( comp_nat_nat_nat @ F2 @ ( comp_real_nat_nat @ G2 @ H ) )
        = ( comp_real_nat_nat @ L2 @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_607_rewriteL__comp__comp,axiom,
    ! [F2: real > $o,G2: real > real,L2: real > $o,H: $o > real] :
      ( ( ( comp_real_o_real @ F2 @ G2 )
        = L2 )
     => ( ( comp_real_o_o @ F2 @ ( comp_real_real_o @ G2 @ H ) )
        = ( comp_real_o_o @ L2 @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_608_rewriteL__comp__comp,axiom,
    ! [F2: real > nat,G2: real > real,L2: real > nat,H: nat > real] :
      ( ( ( comp_real_nat_real @ F2 @ G2 )
        = L2 )
     => ( ( comp_real_nat_nat @ F2 @ ( comp_real_real_nat @ G2 @ H ) )
        = ( comp_real_nat_nat @ L2 @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_609_rewriteL__comp__comp,axiom,
    ! [F2: real > real,G2: real > real,L2: real > real,H: real > real] :
      ( ( ( comp_real_real_real @ F2 @ G2 )
        = L2 )
     => ( ( comp_real_real_real @ F2 @ ( comp_real_real_real @ G2 @ H ) )
        = ( comp_real_real_real @ L2 @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_610_rewriteL__comp__comp,axiom,
    ! [F2: real > $o,G2: $o > real,L2: $o > $o,H: $o > $o] :
      ( ( ( comp_real_o_o @ F2 @ G2 )
        = L2 )
     => ( ( comp_real_o_o @ F2 @ ( comp_o_real_o @ G2 @ H ) )
        = ( comp_o_o_o @ L2 @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_611_rewriteL__comp__comp,axiom,
    ! [F2: real > nat,G2: nat > real,L2: nat > nat,H: nat > nat] :
      ( ( ( comp_real_nat_nat @ F2 @ G2 )
        = L2 )
     => ( ( comp_real_nat_nat @ F2 @ ( comp_nat_real_nat @ G2 @ H ) )
        = ( comp_nat_nat_nat @ L2 @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_612_rewriteL__comp__comp,axiom,
    ! [F2: real > produc7716430852924023517t_real,G2: real > real,L2: real > produc7716430852924023517t_real,H: produc7716430852924023517t_real > real] :
      ( ( ( comp_r4030900867926482106l_real @ F2 @ G2 )
        = L2 )
     => ( ( comp_r4825950202331181903t_real @ F2 @ ( comp_r8349034141028359008t_real @ G2 @ H ) )
        = ( comp_r4825950202331181903t_real @ L2 @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_613_rewriteL__comp__comp,axiom,
    ! [F2: produc7716430852924023517t_real > produc7716430852924023517t_real,G2: real > produc7716430852924023517t_real,L2: real > produc7716430852924023517t_real,H: produc7716430852924023517t_real > real] :
      ( ( ( comp_P6455894728016498639l_real @ F2 @ G2 )
        = L2 )
     => ( ( comp_P5614709513016865274t_real @ F2 @ ( comp_r4825950202331181903t_real @ G2 @ H ) )
        = ( comp_r4825950202331181903t_real @ L2 @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_614_rewriteL__comp__comp,axiom,
    ! [F2: real > produc7716430852924023517t_real,G2: produc7716430852924023517t_real > real,L2: produc7716430852924023517t_real > produc7716430852924023517t_real,H: produc7716430852924023517t_real > produc7716430852924023517t_real] :
      ( ( ( comp_r4825950202331181903t_real @ F2 @ G2 )
        = L2 )
     => ( ( comp_r4825950202331181903t_real @ F2 @ ( comp_P1550655964263599733t_real @ G2 @ H ) )
        = ( comp_P5614709513016865274t_real @ L2 @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_615_rewriteR__comp__comp,axiom,
    ! [G2: $o > real,H: $o > $o,R2: $o > real,F2: real > $o] :
      ( ( ( comp_o_real_o @ G2 @ H )
        = R2 )
     => ( ( comp_o_o_o @ ( comp_real_o_o @ F2 @ G2 ) @ H )
        = ( comp_real_o_o @ F2 @ R2 ) ) ) ).

% rewriteR_comp_comp
thf(fact_616_rewriteR__comp__comp,axiom,
    ! [G2: nat > real,H: nat > nat,R2: nat > real,F2: real > nat] :
      ( ( ( comp_nat_real_nat @ G2 @ H )
        = R2 )
     => ( ( comp_nat_nat_nat @ ( comp_real_nat_nat @ F2 @ G2 ) @ H )
        = ( comp_real_nat_nat @ F2 @ R2 ) ) ) ).

% rewriteR_comp_comp
thf(fact_617_rewriteR__comp__comp,axiom,
    ! [G2: real > real,H: $o > real,R2: $o > real,F2: real > $o] :
      ( ( ( comp_real_real_o @ G2 @ H )
        = R2 )
     => ( ( comp_real_o_o @ ( comp_real_o_real @ F2 @ G2 ) @ H )
        = ( comp_real_o_o @ F2 @ R2 ) ) ) ).

% rewriteR_comp_comp
thf(fact_618_rewriteR__comp__comp,axiom,
    ! [G2: real > real,H: nat > real,R2: nat > real,F2: real > nat] :
      ( ( ( comp_real_real_nat @ G2 @ H )
        = R2 )
     => ( ( comp_real_nat_nat @ ( comp_real_nat_real @ F2 @ G2 ) @ H )
        = ( comp_real_nat_nat @ F2 @ R2 ) ) ) ).

% rewriteR_comp_comp
thf(fact_619_rewriteR__comp__comp,axiom,
    ! [G2: real > real,H: real > real,R2: real > real,F2: real > real] :
      ( ( ( comp_real_real_real @ G2 @ H )
        = R2 )
     => ( ( comp_real_real_real @ ( comp_real_real_real @ F2 @ G2 ) @ H )
        = ( comp_real_real_real @ F2 @ R2 ) ) ) ).

% rewriteR_comp_comp
thf(fact_620_rewriteR__comp__comp,axiom,
    ! [G2: real > $o,H: $o > real,R2: $o > $o,F2: $o > $o] :
      ( ( ( comp_real_o_o @ G2 @ H )
        = R2 )
     => ( ( comp_real_o_o @ ( comp_o_o_real @ F2 @ G2 ) @ H )
        = ( comp_o_o_o @ F2 @ R2 ) ) ) ).

% rewriteR_comp_comp
thf(fact_621_rewriteR__comp__comp,axiom,
    ! [G2: real > nat,H: nat > real,R2: nat > nat,F2: nat > nat] :
      ( ( ( comp_real_nat_nat @ G2 @ H )
        = R2 )
     => ( ( comp_real_nat_nat @ ( comp_nat_nat_real @ F2 @ G2 ) @ H )
        = ( comp_nat_nat_nat @ F2 @ R2 ) ) ) ).

% rewriteR_comp_comp
thf(fact_622_rewriteR__comp__comp,axiom,
    ! [G2: real > real,H: produc7716430852924023517t_real > real,R2: produc7716430852924023517t_real > real,F2: real > produc7716430852924023517t_real] :
      ( ( ( comp_r8349034141028359008t_real @ G2 @ H )
        = R2 )
     => ( ( comp_r4825950202331181903t_real @ ( comp_r4030900867926482106l_real @ F2 @ G2 ) @ H )
        = ( comp_r4825950202331181903t_real @ F2 @ R2 ) ) ) ).

% rewriteR_comp_comp
thf(fact_623_rewriteR__comp__comp,axiom,
    ! [G2: produc7716430852924023517t_real > real,H: produc7716430852924023517t_real > produc7716430852924023517t_real,R2: produc7716430852924023517t_real > real,F2: real > produc7716430852924023517t_real] :
      ( ( ( comp_P1550655964263599733t_real @ G2 @ H )
        = R2 )
     => ( ( comp_P5614709513016865274t_real @ ( comp_r4825950202331181903t_real @ F2 @ G2 ) @ H )
        = ( comp_r4825950202331181903t_real @ F2 @ R2 ) ) ) ).

% rewriteR_comp_comp
thf(fact_624_rewriteR__comp__comp,axiom,
    ! [G2: real > produc7716430852924023517t_real,H: produc7716430852924023517t_real > real,R2: produc7716430852924023517t_real > produc7716430852924023517t_real,F2: produc7716430852924023517t_real > produc7716430852924023517t_real] :
      ( ( ( comp_r4825950202331181903t_real @ G2 @ H )
        = R2 )
     => ( ( comp_r4825950202331181903t_real @ ( comp_P6455894728016498639l_real @ F2 @ G2 ) @ H )
        = ( comp_P5614709513016865274t_real @ F2 @ R2 ) ) ) ).

% rewriteR_comp_comp
thf(fact_625_rewriteL__comp__comp2,axiom,
    ! [F2: $o > $o,G2: real > $o,L1: real > $o,L22: real > real,H: $o > real,R2: $o > real] :
      ( ( ( comp_o_o_real @ F2 @ G2 )
        = ( comp_real_o_real @ L1 @ L22 ) )
     => ( ( ( comp_real_real_o @ L22 @ H )
          = R2 )
       => ( ( comp_o_o_o @ F2 @ ( comp_real_o_o @ G2 @ H ) )
          = ( comp_real_o_o @ L1 @ R2 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_626_rewriteL__comp__comp2,axiom,
    ! [F2: nat > nat,G2: real > nat,L1: real > nat,L22: real > real,H: nat > real,R2: nat > real] :
      ( ( ( comp_nat_nat_real @ F2 @ G2 )
        = ( comp_real_nat_real @ L1 @ L22 ) )
     => ( ( ( comp_real_real_nat @ L22 @ H )
          = R2 )
       => ( ( comp_nat_nat_nat @ F2 @ ( comp_real_nat_nat @ G2 @ H ) )
          = ( comp_real_nat_nat @ L1 @ R2 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_627_rewriteL__comp__comp2,axiom,
    ! [F2: real > $o,G2: real > real,L1: $o > $o,L22: real > $o,H: $o > real,R2: $o > $o] :
      ( ( ( comp_real_o_real @ F2 @ G2 )
        = ( comp_o_o_real @ L1 @ L22 ) )
     => ( ( ( comp_real_o_o @ L22 @ H )
          = R2 )
       => ( ( comp_real_o_o @ F2 @ ( comp_real_real_o @ G2 @ H ) )
          = ( comp_o_o_o @ L1 @ R2 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_628_rewriteL__comp__comp2,axiom,
    ! [F2: real > nat,G2: real > real,L1: nat > nat,L22: real > nat,H: nat > real,R2: nat > nat] :
      ( ( ( comp_real_nat_real @ F2 @ G2 )
        = ( comp_nat_nat_real @ L1 @ L22 ) )
     => ( ( ( comp_real_nat_nat @ L22 @ H )
          = R2 )
       => ( ( comp_real_nat_nat @ F2 @ ( comp_real_real_nat @ G2 @ H ) )
          = ( comp_nat_nat_nat @ L1 @ R2 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_629_rewriteL__comp__comp2,axiom,
    ! [F2: $o > real,G2: real > $o,L1: real > real,L22: real > real,H: $o > real,R2: $o > real] :
      ( ( ( comp_o_real_real @ F2 @ G2 )
        = ( comp_real_real_real @ L1 @ L22 ) )
     => ( ( ( comp_real_real_o @ L22 @ H )
          = R2 )
       => ( ( comp_o_real_o @ F2 @ ( comp_real_o_o @ G2 @ H ) )
          = ( comp_real_real_o @ L1 @ R2 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_630_rewriteL__comp__comp2,axiom,
    ! [F2: nat > real,G2: real > nat,L1: real > real,L22: real > real,H: nat > real,R2: nat > real] :
      ( ( ( comp_nat_real_real @ F2 @ G2 )
        = ( comp_real_real_real @ L1 @ L22 ) )
     => ( ( ( comp_real_real_nat @ L22 @ H )
          = R2 )
       => ( ( comp_nat_real_nat @ F2 @ ( comp_real_nat_nat @ G2 @ H ) )
          = ( comp_real_real_nat @ L1 @ R2 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_631_rewriteL__comp__comp2,axiom,
    ! [F2: real > real,G2: real > real,L1: $o > real,L22: real > $o,H: $o > real,R2: $o > $o] :
      ( ( ( comp_real_real_real @ F2 @ G2 )
        = ( comp_o_real_real @ L1 @ L22 ) )
     => ( ( ( comp_real_o_o @ L22 @ H )
          = R2 )
       => ( ( comp_real_real_o @ F2 @ ( comp_real_real_o @ G2 @ H ) )
          = ( comp_o_real_o @ L1 @ R2 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_632_rewriteL__comp__comp2,axiom,
    ! [F2: real > real,G2: real > real,L1: nat > real,L22: real > nat,H: nat > real,R2: nat > nat] :
      ( ( ( comp_real_real_real @ F2 @ G2 )
        = ( comp_nat_real_real @ L1 @ L22 ) )
     => ( ( ( comp_real_nat_nat @ L22 @ H )
          = R2 )
       => ( ( comp_real_real_nat @ F2 @ ( comp_real_real_nat @ G2 @ H ) )
          = ( comp_nat_real_nat @ L1 @ R2 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_633_rewriteL__comp__comp2,axiom,
    ! [F2: real > real,G2: real > real,L1: real > real,L22: real > real,H: real > real,R2: real > real] :
      ( ( ( comp_real_real_real @ F2 @ G2 )
        = ( comp_real_real_real @ L1 @ L22 ) )
     => ( ( ( comp_real_real_real @ L22 @ H )
          = R2 )
       => ( ( comp_real_real_real @ F2 @ ( comp_real_real_real @ G2 @ H ) )
          = ( comp_real_real_real @ L1 @ R2 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_634_rewriteL__comp__comp2,axiom,
    ! [F2: real > $o,G2: $o > real,L1: real > $o,L22: $o > real,H: $o > $o,R2: $o > real] :
      ( ( ( comp_real_o_o @ F2 @ G2 )
        = ( comp_real_o_o @ L1 @ L22 ) )
     => ( ( ( comp_o_real_o @ L22 @ H )
          = R2 )
       => ( ( comp_real_o_o @ F2 @ ( comp_o_real_o @ G2 @ H ) )
          = ( comp_real_o_o @ L1 @ R2 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_635_rewriteR__comp__comp2,axiom,
    ! [G2: $o > real,H: $o > $o,R1: real > real,R22: $o > real,F2: real > $o,L2: real > $o] :
      ( ( ( comp_o_real_o @ G2 @ H )
        = ( comp_real_real_o @ R1 @ R22 ) )
     => ( ( ( comp_real_o_real @ F2 @ R1 )
          = L2 )
       => ( ( comp_o_o_o @ ( comp_real_o_o @ F2 @ G2 ) @ H )
          = ( comp_real_o_o @ L2 @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_636_rewriteR__comp__comp2,axiom,
    ! [G2: nat > real,H: nat > nat,R1: real > real,R22: nat > real,F2: real > nat,L2: real > nat] :
      ( ( ( comp_nat_real_nat @ G2 @ H )
        = ( comp_real_real_nat @ R1 @ R22 ) )
     => ( ( ( comp_real_nat_real @ F2 @ R1 )
          = L2 )
       => ( ( comp_nat_nat_nat @ ( comp_real_nat_nat @ F2 @ G2 ) @ H )
          = ( comp_real_nat_nat @ L2 @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_637_rewriteR__comp__comp2,axiom,
    ! [G2: real > real,H: $o > real,R1: $o > real,R22: $o > $o,F2: real > $o,L2: $o > $o] :
      ( ( ( comp_real_real_o @ G2 @ H )
        = ( comp_o_real_o @ R1 @ R22 ) )
     => ( ( ( comp_real_o_o @ F2 @ R1 )
          = L2 )
       => ( ( comp_real_o_o @ ( comp_real_o_real @ F2 @ G2 ) @ H )
          = ( comp_o_o_o @ L2 @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_638_rewriteR__comp__comp2,axiom,
    ! [G2: real > real,H: nat > real,R1: nat > real,R22: nat > nat,F2: real > nat,L2: nat > nat] :
      ( ( ( comp_real_real_nat @ G2 @ H )
        = ( comp_nat_real_nat @ R1 @ R22 ) )
     => ( ( ( comp_real_nat_nat @ F2 @ R1 )
          = L2 )
       => ( ( comp_real_nat_nat @ ( comp_real_nat_real @ F2 @ G2 ) @ H )
          = ( comp_nat_nat_nat @ L2 @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_639_rewriteR__comp__comp2,axiom,
    ! [G2: $o > real,H: real > $o,R1: real > real,R22: real > real,F2: real > $o,L2: real > $o] :
      ( ( ( comp_o_real_real @ G2 @ H )
        = ( comp_real_real_real @ R1 @ R22 ) )
     => ( ( ( comp_real_o_real @ F2 @ R1 )
          = L2 )
       => ( ( comp_o_o_real @ ( comp_real_o_o @ F2 @ G2 ) @ H )
          = ( comp_real_o_real @ L2 @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_640_rewriteR__comp__comp2,axiom,
    ! [G2: nat > real,H: real > nat,R1: real > real,R22: real > real,F2: real > nat,L2: real > nat] :
      ( ( ( comp_nat_real_real @ G2 @ H )
        = ( comp_real_real_real @ R1 @ R22 ) )
     => ( ( ( comp_real_nat_real @ F2 @ R1 )
          = L2 )
       => ( ( comp_nat_nat_real @ ( comp_real_nat_nat @ F2 @ G2 ) @ H )
          = ( comp_real_nat_real @ L2 @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_641_rewriteR__comp__comp2,axiom,
    ! [G2: real > real,H: real > real,R1: $o > real,R22: real > $o,F2: real > $o,L2: $o > $o] :
      ( ( ( comp_real_real_real @ G2 @ H )
        = ( comp_o_real_real @ R1 @ R22 ) )
     => ( ( ( comp_real_o_o @ F2 @ R1 )
          = L2 )
       => ( ( comp_real_o_real @ ( comp_real_o_real @ F2 @ G2 ) @ H )
          = ( comp_o_o_real @ L2 @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_642_rewriteR__comp__comp2,axiom,
    ! [G2: real > real,H: real > real,R1: nat > real,R22: real > nat,F2: real > nat,L2: nat > nat] :
      ( ( ( comp_real_real_real @ G2 @ H )
        = ( comp_nat_real_real @ R1 @ R22 ) )
     => ( ( ( comp_real_nat_nat @ F2 @ R1 )
          = L2 )
       => ( ( comp_real_nat_real @ ( comp_real_nat_real @ F2 @ G2 ) @ H )
          = ( comp_nat_nat_real @ L2 @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_643_rewriteR__comp__comp2,axiom,
    ! [G2: real > real,H: real > real,R1: real > real,R22: real > real,F2: real > real,L2: real > real] :
      ( ( ( comp_real_real_real @ G2 @ H )
        = ( comp_real_real_real @ R1 @ R22 ) )
     => ( ( ( comp_real_real_real @ F2 @ R1 )
          = L2 )
       => ( ( comp_real_real_real @ ( comp_real_real_real @ F2 @ G2 ) @ H )
          = ( comp_real_real_real @ L2 @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_644_rewriteR__comp__comp2,axiom,
    ! [G2: real > $o,H: $o > real,R1: real > $o,R22: $o > real,F2: $o > $o,L2: real > $o] :
      ( ( ( comp_real_o_o @ G2 @ H )
        = ( comp_real_o_o @ R1 @ R22 ) )
     => ( ( ( comp_o_o_real @ F2 @ R1 )
          = L2 )
       => ( ( comp_real_o_o @ ( comp_o_o_real @ F2 @ G2 ) @ H )
          = ( comp_real_o_o @ L2 @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_645_comp__apply__eq,axiom,
    ! [F2: real > produc7716430852924023517t_real,G2: produc7716430852924023517t_real > real,X4: produc7716430852924023517t_real,H: real > produc7716430852924023517t_real,K2: produc7716430852924023517t_real > real] :
      ( ( ( F2 @ ( G2 @ X4 ) )
        = ( H @ ( K2 @ X4 ) ) )
     => ( ( comp_r4825950202331181903t_real @ F2 @ G2 @ X4 )
        = ( comp_r4825950202331181903t_real @ H @ K2 @ X4 ) ) ) ).

% comp_apply_eq
thf(fact_646_comp__apply__eq,axiom,
    ! [F2: real > real,G2: real > real,X4: real,H: real > real,K2: real > real] :
      ( ( ( F2 @ ( G2 @ X4 ) )
        = ( H @ ( K2 @ X4 ) ) )
     => ( ( comp_real_real_real @ F2 @ G2 @ X4 )
        = ( comp_real_real_real @ H @ K2 @ X4 ) ) ) ).

% comp_apply_eq
thf(fact_647_comp__apply__eq,axiom,
    ! [F2: real > $o,G2: $o > real,X4: $o,H: real > $o,K2: $o > real] :
      ( ( ( F2 @ ( G2 @ X4 ) )
        = ( H @ ( K2 @ X4 ) ) )
     => ( ( comp_real_o_o @ F2 @ G2 @ X4 )
        = ( comp_real_o_o @ H @ K2 @ X4 ) ) ) ).

% comp_apply_eq
thf(fact_648_comp__apply__eq,axiom,
    ! [F2: real > nat,G2: nat > real,X4: nat,H: real > nat,K2: nat > real] :
      ( ( ( F2 @ ( G2 @ X4 ) )
        = ( H @ ( K2 @ X4 ) ) )
     => ( ( comp_real_nat_nat @ F2 @ G2 @ X4 )
        = ( comp_real_nat_nat @ H @ K2 @ X4 ) ) ) ).

% comp_apply_eq
thf(fact_649_comp__apply__eq,axiom,
    ! [F2: ( a > b > c ) > product_prod_a_b > c,G2: real > a > b > c,X4: real,H: ( a > b > c ) > product_prod_a_b > c,K2: real > a > b > c] :
      ( ( ( F2 @ ( G2 @ X4 ) )
        = ( H @ ( K2 @ X4 ) ) )
     => ( ( comp_a6364899482013671645c_real @ F2 @ G2 @ X4 )
        = ( comp_a6364899482013671645c_real @ H @ K2 @ X4 ) ) ) ).

% comp_apply_eq
thf(fact_650_qbs__morphism__comp,axiom,
    ! [F2: $o > $o,X3: quasi_borel_o,Y3: quasi_borel_o,G2: $o > real,Z: quasi_borel_real] :
      ( ( member_o_o @ F2 @ ( qbs_morphism_o_o @ X3 @ Y3 ) )
     => ( ( member_o_real @ G2 @ ( qbs_morphism_o_real @ Y3 @ Z ) )
       => ( member_o_real @ ( comp_o_real_o @ G2 @ F2 ) @ ( qbs_morphism_o_real @ X3 @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_651_qbs__morphism__comp,axiom,
    ! [F2: real > real,X3: quasi_borel_real,Y3: quasi_borel_real,G2: real > real,Z: quasi_borel_real] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
     => ( ( member_real_real @ G2 @ ( qbs_mo5229770564518008146l_real @ Y3 @ Z ) )
       => ( member_real_real @ ( comp_real_real_real @ G2 @ F2 ) @ ( qbs_mo5229770564518008146l_real @ X3 @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_652_qbs__morphism__comp,axiom,
    ! [F2: real > real,X3: quasi_borel_real,Y3: quasi_borel_real,G2: real > $o,Z: quasi_borel_o] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
     => ( ( member_real_o @ G2 @ ( qbs_morphism_real_o @ Y3 @ Z ) )
       => ( member_real_o @ ( comp_real_o_real @ G2 @ F2 ) @ ( qbs_morphism_real_o @ X3 @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_653_qbs__morphism__comp,axiom,
    ! [F2: real > $o,X3: quasi_borel_real,Y3: quasi_borel_o,G2: $o > $o,Z: quasi_borel_o] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
     => ( ( member_o_o @ G2 @ ( qbs_morphism_o_o @ Y3 @ Z ) )
       => ( member_real_o @ ( comp_o_o_real @ G2 @ F2 ) @ ( qbs_morphism_real_o @ X3 @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_654_qbs__morphism__comp,axiom,
    ! [F2: real > $o,X3: quasi_borel_real,Y3: quasi_borel_o,G2: $o > real,Z: quasi_borel_real] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
     => ( ( member_o_real @ G2 @ ( qbs_morphism_o_real @ Y3 @ Z ) )
       => ( member_real_real @ ( comp_o_real_real @ G2 @ F2 ) @ ( qbs_mo5229770564518008146l_real @ X3 @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_655_qbs__morphism__comp,axiom,
    ! [F2: $o > real,X3: quasi_borel_o,Y3: quasi_borel_real,G2: real > real,Z: quasi_borel_real] :
      ( ( member_o_real @ F2 @ ( qbs_morphism_o_real @ X3 @ Y3 ) )
     => ( ( member_real_real @ G2 @ ( qbs_mo5229770564518008146l_real @ Y3 @ Z ) )
       => ( member_o_real @ ( comp_real_real_o @ G2 @ F2 ) @ ( qbs_morphism_o_real @ X3 @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_656_qbs__morphism__comp,axiom,
    ! [F2: $o > real,X3: quasi_borel_o,Y3: quasi_borel_real,G2: real > $o,Z: quasi_borel_o] :
      ( ( member_o_real @ F2 @ ( qbs_morphism_o_real @ X3 @ Y3 ) )
     => ( ( member_real_o @ G2 @ ( qbs_morphism_real_o @ Y3 @ Z ) )
       => ( member_o_o @ ( comp_real_o_o @ G2 @ F2 ) @ ( qbs_morphism_o_o @ X3 @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_657_qbs__morphism__comp,axiom,
    ! [F2: real > $o,X3: quasi_borel_real,Y3: quasi_borel_o,G2: $o > nat,Z: quasi_borel_nat] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
     => ( ( member_o_nat @ G2 @ ( qbs_morphism_o_nat @ Y3 @ Z ) )
       => ( member_real_nat @ ( comp_o_nat_real @ G2 @ F2 ) @ ( qbs_mo6567951568834356598al_nat @ X3 @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_658_qbs__morphism__comp,axiom,
    ! [F2: nat > $o,X3: quasi_borel_nat,Y3: quasi_borel_o,G2: $o > real,Z: quasi_borel_real] :
      ( ( member_nat_o @ F2 @ ( qbs_morphism_nat_o @ X3 @ Y3 ) )
     => ( ( member_o_real @ G2 @ ( qbs_morphism_o_real @ Y3 @ Z ) )
       => ( member_nat_real @ ( comp_o_real_nat @ G2 @ F2 ) @ ( qbs_mo2000642995705457910t_real @ X3 @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_659_qbs__morphism__comp,axiom,
    ! [F2: $o > real,X3: quasi_borel_o,Y3: quasi_borel_real,G2: real > nat,Z: quasi_borel_nat] :
      ( ( member_o_real @ F2 @ ( qbs_morphism_o_real @ X3 @ Y3 ) )
     => ( ( member_real_nat @ G2 @ ( qbs_mo6567951568834356598al_nat @ Y3 @ Z ) )
       => ( member_o_nat @ ( comp_real_nat_o @ G2 @ F2 ) @ ( qbs_morphism_o_nat @ X3 @ Z ) ) ) ) ).

% qbs_morphism_comp
thf(fact_660_case__prod__comp,axiom,
    ! [F2: ( a > b > c ) > product_prod_a_b > c,G2: real > a > b > c,X4: produc1405624045518934769od_a_b] :
      ( ( produc8366947261062197552_a_b_c @ ( comp_a6364899482013671645c_real @ F2 @ G2 ) @ X4 )
      = ( F2 @ ( G2 @ ( produc4505306568083885239od_a_b @ X4 ) ) @ ( produc4276089182416139253od_a_b @ X4 ) ) ) ).

% case_prod_comp
thf(fact_661_qbs__morphism__pair__iff,axiom,
    ! [F2: real > product_prod_real_o,X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_o] :
      ( ( member6586820919158520515real_o @ F2 @ ( qbs_mo6498981662437225095real_o @ X3 @ ( binary4057238779996960701real_o @ Y3 @ Z ) ) )
      = ( ( member_real_real @ ( comp_P7324324619018053534l_real @ product_fst_real_o @ F2 ) @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
        & ( member_real_o @ ( comp_P4035609806083913856o_real @ product_snd_real_o @ F2 ) @ ( qbs_morphism_real_o @ X3 @ Z ) ) ) ) ).

% qbs_morphism_pair_iff
thf(fact_662_qbs__morphism__pair__iff,axiom,
    ! [F2: real > product_prod_o_real,X3: quasi_borel_real,Y3: quasi_borel_o,Z: quasi_borel_real] :
      ( ( member8223553389164786773o_real @ F2 @ ( qbs_mo3903038352199750937o_real @ X3 @ ( binary2548174404955791127o_real @ Y3 @ Z ) ) )
      = ( ( member_real_o @ ( comp_P958736042193659502o_real @ product_fst_o_real @ F2 ) @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
        & ( member_real_real @ ( comp_P4165359869975341104l_real @ product_snd_o_real @ F2 ) @ ( qbs_mo5229770564518008146l_real @ X3 @ Z ) ) ) ) ).

% qbs_morphism_pair_iff
thf(fact_663_qbs__morphism__pair__iff,axiom,
    ! [F2: real > product_prod_o_o,X3: quasi_borel_real,Y3: quasi_borel_o,Z: quasi_borel_o] :
      ( ( member8624048055576332635od_o_o @ F2 @ ( qbs_mo8591899500417447169od_o_o @ X3 @ ( binary9159730317414444269bs_o_o @ Y3 @ Z ) ) )
      = ( ( member_real_o @ ( comp_P7609422216084732352o_real @ product_fst_o_o @ F2 ) @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
        & ( member_real_o @ ( comp_P7609422216084732352o_real @ product_snd_o_o @ F2 ) @ ( qbs_morphism_real_o @ X3 @ Z ) ) ) ) ).

% qbs_morphism_pair_iff
thf(fact_664_qbs__morphism__pair__iff,axiom,
    ! [F2: real > produc3741383161447143261al_nat,X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_nat] :
      ( ( member4159480375084375953al_nat @ F2 @ ( qbs_mo8849718567295897911al_nat @ X3 @ ( binary7505510235992378091al_nat @ Y3 @ Z ) ) )
      = ( ( member_real_real @ ( comp_P2062867634480536980l_real @ product_fst_real_nat @ F2 ) @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
        & ( member_real_nat @ ( comp_P6248124061026825784t_real @ product_snd_real_nat @ F2 ) @ ( qbs_mo6567951568834356598al_nat @ X3 @ Z ) ) ) ) ).

% qbs_morphism_pair_iff
thf(fact_665_qbs__morphism__pair__iff,axiom,
    ! [F2: real > product_prod_o_nat,X3: quasi_borel_real,Y3: quasi_borel_o,Z: quasi_borel_nat] :
      ( ( member7334495436961965817_o_nat @ F2 @ ( qbs_mo7100413126075687229_o_nat @ X3 @ ( binary4578070153795289531_o_nat @ Y3 @ Z ) ) )
      = ( ( member_real_o @ ( comp_P2340352180389457098o_real @ product_fst_o_nat @ F2 ) @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
        & ( member_real_nat @ ( comp_P1507898882101401464t_real @ product_snd_o_nat @ F2 ) @ ( qbs_mo6567951568834356598al_nat @ X3 @ Z ) ) ) ) ).

% qbs_morphism_pair_iff
thf(fact_666_qbs__morphism__pair__iff,axiom,
    ! [F2: real > product_prod_nat_o,X3: quasi_borel_real,Y3: quasi_borel_nat,Z: quasi_borel_o] :
      ( ( member8382098559140269471_nat_o @ F2 @ ( qbs_mo1385575613276404451_nat_o @ X3 @ ( binary7680741514903474841_nat_o @ Y3 @ Z ) ) )
      = ( ( member_real_nat @ ( comp_P789980896094113310t_real @ product_fst_nat_o @ F2 ) @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) )
        & ( member_real_o @ ( comp_P1872995966849966244o_real @ product_snd_nat_o @ F2 ) @ ( qbs_morphism_real_o @ X3 @ Z ) ) ) ) ).

% qbs_morphism_pair_iff
thf(fact_667_qbs__morphism__pair__iff,axiom,
    ! [F2: real > product_prod_nat_nat,X3: quasi_borel_real,Y3: quasi_borel_nat,Z: quasi_borel_nat] :
      ( ( member278708040391457717at_nat @ F2 @ ( qbs_mo4077890138368776155at_nat @ X3 @ ( binary6297550310575005455at_nat @ Y3 @ Z ) ) )
      = ( ( member_real_nat @ ( comp_P543440408108907612t_real @ product_fst_nat_nat @ F2 ) @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) )
        & ( member_real_nat @ ( comp_P543440408108907612t_real @ product_snd_nat_nat @ F2 ) @ ( qbs_mo6567951568834356598al_nat @ X3 @ Z ) ) ) ) ).

% qbs_morphism_pair_iff
thf(fact_668_qbs__morphism__pair__iff,axiom,
    ! [F2: real > product_prod_real_a,X3: quasi_borel_real,Y3: quasi_borel_real,Z: quasi_borel_a] :
      ( ( member1006887528422719913real_a @ F2 @ ( qbs_mo1948987420364309741real_a @ X3 @ ( binary5762279046363823267real_a @ Y3 @ Z ) ) )
      = ( ( member_real_real @ ( comp_P3002741825051030916l_real @ product_fst_real_a @ F2 ) @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
        & ( member_real_a @ ( comp_P7874914735527052288a_real @ product_snd_real_a @ F2 ) @ ( qbs_morphism_real_a @ X3 @ Z ) ) ) ) ).

% qbs_morphism_pair_iff
thf(fact_669_qbs__morphism__pair__iff,axiom,
    ! [F2: $o > product_prod_real_a,X3: quasi_borel_o,Y3: quasi_borel_real,Z: quasi_borel_a] :
      ( ( member4948893057617750905real_a @ F2 @ ( qbs_mo4240396302186037607real_a @ X3 @ ( binary5762279046363823267real_a @ Y3 @ Z ) ) )
      = ( ( member_o_real @ ( comp_P3046350667264871104real_o @ product_fst_real_a @ F2 ) @ ( qbs_morphism_o_real @ X3 @ Y3 ) )
        & ( member_o_a @ ( comp_P4879073787575347012_a_a_o @ product_snd_real_a @ F2 ) @ ( qbs_morphism_o_a @ X3 @ Z ) ) ) ) ).

% qbs_morphism_pair_iff
thf(fact_670_qbs__morphism__pair__iff,axiom,
    ! [F2: nat > product_prod_real_a,X3: quasi_borel_nat,Y3: quasi_borel_real,Z: quasi_borel_a] :
      ( ( member3792249494800367565real_a @ F2 @ ( qbs_mo2610884258138134673real_a @ X3 @ ( binary5762279046363823267real_a @ Y3 @ Z ) ) )
      = ( ( member_nat_real @ ( comp_P4702048683463605928al_nat @ product_fst_real_a @ F2 ) @ ( qbs_mo2000642995705457910t_real @ X3 @ Y3 ) )
        & ( member_nat_a @ ( comp_P8403799777262422820_a_nat @ product_snd_real_a @ F2 ) @ ( qbs_morphism_nat_a @ X3 @ Z ) ) ) ) ).

% qbs_morphism_pair_iff
thf(fact_671_compose__const_I2_J,axiom,
    ! [A: produc7716430852924023517t_real,G2: produc7716430852924023517t_real > real] :
      ( ( comp_r4825950202331181903t_real
        @ ^ [X2: real] : A
        @ G2 )
      = ( ^ [X2: produc7716430852924023517t_real] : A ) ) ).

% compose_const(2)
thf(fact_672_compose__const_I2_J,axiom,
    ! [A: real,G2: real > real] :
      ( ( comp_real_real_real
        @ ^ [X2: real] : A
        @ G2 )
      = ( ^ [X2: real] : A ) ) ).

% compose_const(2)
thf(fact_673_compose__const_I2_J,axiom,
    ! [A: $o,G2: $o > real] :
      ( ( comp_real_o_o
        @ ^ [X2: real] : A
        @ G2 )
      = ( ^ [X2: $o] : A ) ) ).

% compose_const(2)
thf(fact_674_compose__const_I2_J,axiom,
    ! [A: nat,G2: nat > real] :
      ( ( comp_real_nat_nat
        @ ^ [X2: real] : A
        @ G2 )
      = ( ^ [X2: nat] : A ) ) ).

% compose_const(2)
thf(fact_675_compose__const_I2_J,axiom,
    ! [A: product_prod_a_b > c,G2: real > a > b > c] :
      ( ( comp_a6364899482013671645c_real
        @ ^ [X2: a > b > c] : A
        @ G2 )
      = ( ^ [X2: real] : A ) ) ).

% compose_const(2)
thf(fact_676_K__record__comp,axiom,
    ! [C: produc7716430852924023517t_real,F2: produc7716430852924023517t_real > real] :
      ( ( comp_r4825950202331181903t_real
        @ ^ [X2: real] : C
        @ F2 )
      = ( ^ [X2: produc7716430852924023517t_real] : C ) ) ).

% K_record_comp
thf(fact_677_K__record__comp,axiom,
    ! [C: real,F2: real > real] :
      ( ( comp_real_real_real
        @ ^ [X2: real] : C
        @ F2 )
      = ( ^ [X2: real] : C ) ) ).

% K_record_comp
thf(fact_678_K__record__comp,axiom,
    ! [C: $o,F2: $o > real] :
      ( ( comp_real_o_o
        @ ^ [X2: real] : C
        @ F2 )
      = ( ^ [X2: $o] : C ) ) ).

% K_record_comp
thf(fact_679_K__record__comp,axiom,
    ! [C: nat,F2: nat > real] :
      ( ( comp_real_nat_nat
        @ ^ [X2: real] : C
        @ F2 )
      = ( ^ [X2: nat] : C ) ) ).

% K_record_comp
thf(fact_680_K__record__comp,axiom,
    ! [C: product_prod_a_b > c,F2: real > a > b > c] :
      ( ( comp_a6364899482013671645c_real
        @ ^ [X2: a > b > c] : C
        @ F2 )
      = ( ^ [X2: real] : C ) ) ).

% K_record_comp
thf(fact_681_qbs__exp__morphismI,axiom,
    ! [X3: quasi_borel_o,Y3: quasi_borel_b,F2: $o > b > c,Z: quasi_borel_c] :
      ( ! [Alpha: real > $o,Beta: real > product_prod_real_b] :
          ( ( member_real_o @ Alpha @ ( qbs_Mx_o @ X3 ) )
         => ( ( member1077921568469065898real_b @ Beta @ ( binary2731563775470309561real_b @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ Y3 ) )
           => ( member_real_c @ ( comp_P4571499527812350529c_real @ ( produc2835462372567216025al_b_c @ ( comp_o_b_c_real @ F2 @ Alpha ) ) @ Beta ) @ ( qbs_Mx_c @ Z ) ) ) )
     => ( member_o_b_c @ F2 @ ( qbs_morphism_o_b_c @ X3 @ ( exponent_exp_qbs_b_c @ Y3 @ Z ) ) ) ) ).

% qbs_exp_morphismI
thf(fact_682_qbs__exp__morphismI,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_b,F2: nat > b > c,Z: quasi_borel_c] :
      ( ! [Alpha: real > nat,Beta: real > product_prod_real_b] :
          ( ( member_real_nat @ Alpha @ ( qbs_Mx_nat @ X3 ) )
         => ( ( member1077921568469065898real_b @ Beta @ ( binary2731563775470309561real_b @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ Y3 ) )
           => ( member_real_c @ ( comp_P4571499527812350529c_real @ ( produc2835462372567216025al_b_c @ ( comp_nat_b_c_real @ F2 @ Alpha ) ) @ Beta ) @ ( qbs_Mx_c @ Z ) ) ) )
     => ( member_nat_b_c @ F2 @ ( qbs_morphism_nat_b_c @ X3 @ ( exponent_exp_qbs_b_c @ Y3 @ Z ) ) ) ) ).

% qbs_exp_morphismI
thf(fact_683_qbs__exp__morphismI,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_b,F2: real > b > c,Z: quasi_borel_c] :
      ( ! [Alpha: real > real,Beta: real > product_prod_real_b] :
          ( ( member_real_real @ Alpha @ ( qbs_Mx_real @ X3 ) )
         => ( ( member1077921568469065898real_b @ Beta @ ( binary2731563775470309561real_b @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ Y3 ) )
           => ( member_real_c @ ( comp_P4571499527812350529c_real @ ( produc2835462372567216025al_b_c @ ( comp_real_b_c_real @ F2 @ Alpha ) ) @ Beta ) @ ( qbs_Mx_c @ Z ) ) ) )
     => ( member_real_b_c @ F2 @ ( qbs_mo6398413456135019852al_b_c @ X3 @ ( exponent_exp_qbs_b_c @ Y3 @ Z ) ) ) ) ).

% qbs_exp_morphismI
thf(fact_684_qbs__exp__morphismI,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b,F2: a > b > c,Z: quasi_borel_c] :
      ( ! [Alpha: real > a,Beta: real > product_prod_real_b] :
          ( ( member_real_a @ Alpha @ ( qbs_Mx_a @ X3 ) )
         => ( ( member1077921568469065898real_b @ Beta @ ( binary2731563775470309561real_b @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ Y3 ) )
           => ( member_real_c @ ( comp_P4571499527812350529c_real @ ( produc2835462372567216025al_b_c @ ( comp_a_b_c_real @ F2 @ Alpha ) ) @ Beta ) @ ( qbs_Mx_c @ Z ) ) ) )
     => ( member_a_b_c @ F2 @ ( qbs_morphism_a_b_c @ X3 @ ( exponent_exp_qbs_b_c @ Y3 @ Z ) ) ) ) ).

% qbs_exp_morphismI
thf(fact_685_qbs__exp__morphismI,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_a,F2: real > a > c,Z: quasi_borel_c] :
      ( ! [Alpha: real > real,Beta: real > product_prod_real_a] :
          ( ( member_real_real @ Alpha @ ( qbs_Mx_real @ X3 ) )
         => ( ( member1006887528422719913real_a @ Beta @ ( binary2731563775470309560real_a @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ Y3 ) )
           => ( member_real_c @ ( comp_P620607892193762050c_real @ ( produc5622917954539892058al_a_c @ ( comp_real_a_c_real @ F2 @ Alpha ) ) @ Beta ) @ ( qbs_Mx_c @ Z ) ) ) )
     => ( member_real_a_c @ F2 @ ( qbs_mo9185869038107695885al_a_c @ X3 @ ( exponent_exp_qbs_a_c @ Y3 @ Z ) ) ) ) ).

% qbs_exp_morphismI
thf(fact_686_qbs__exp__morphismI,axiom,
    ! [X3: quasi_borel_o,Y3: quasi_borel_a,F2: $o > a > c,Z: quasi_borel_c] :
      ( ! [Alpha: real > $o,Beta: real > product_prod_real_a] :
          ( ( member_real_o @ Alpha @ ( qbs_Mx_o @ X3 ) )
         => ( ( member1006887528422719913real_a @ Beta @ ( binary2731563775470309560real_a @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ Y3 ) )
           => ( member_real_c @ ( comp_P620607892193762050c_real @ ( produc5622917954539892058al_a_c @ ( comp_o_a_c_real @ F2 @ Alpha ) ) @ Beta ) @ ( qbs_Mx_c @ Z ) ) ) )
     => ( member_o_a_c @ F2 @ ( qbs_morphism_o_a_c @ X3 @ ( exponent_exp_qbs_a_c @ Y3 @ Z ) ) ) ) ).

% qbs_exp_morphismI
thf(fact_687_qbs__exp__morphismI,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_a,F2: nat > a > c,Z: quasi_borel_c] :
      ( ! [Alpha: real > nat,Beta: real > product_prod_real_a] :
          ( ( member_real_nat @ Alpha @ ( qbs_Mx_nat @ X3 ) )
         => ( ( member1006887528422719913real_a @ Beta @ ( binary2731563775470309560real_a @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ Y3 ) )
           => ( member_real_c @ ( comp_P620607892193762050c_real @ ( produc5622917954539892058al_a_c @ ( comp_nat_a_c_real @ F2 @ Alpha ) ) @ Beta ) @ ( qbs_Mx_c @ Z ) ) ) )
     => ( member_nat_a_c @ F2 @ ( qbs_morphism_nat_a_c @ X3 @ ( exponent_exp_qbs_a_c @ Y3 @ Z ) ) ) ) ).

% qbs_exp_morphismI
thf(fact_688_qbs__exp__morphismI,axiom,
    ! [X3: quasi_borel_o,Y3: quasi_borel_a,F2: $o > a > b > c,Z: quasi_borel_b_c] :
      ( ! [Alpha: real > $o,Beta: real > product_prod_real_a] :
          ( ( member_real_o @ Alpha @ ( qbs_Mx_o @ X3 ) )
         => ( ( member1006887528422719913real_a @ Beta @ ( binary2731563775470309560real_a @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ Y3 ) )
           => ( member_real_b_c @ ( comp_P5170362070794227966c_real @ ( produc8409101302566321868_a_b_c @ ( comp_o_a_b_c_real @ F2 @ Alpha ) ) @ Beta ) @ ( qbs_Mx_b_c @ Z ) ) ) )
     => ( member_o_a_b_c @ F2 @ ( qbs_morphism_o_a_b_c @ X3 @ ( expone6081388564108922123_a_b_c @ Y3 @ Z ) ) ) ) ).

% qbs_exp_morphismI
thf(fact_689_qbs__exp__morphismI,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_a,F2: nat > a > b > c,Z: quasi_borel_b_c] :
      ( ! [Alpha: real > nat,Beta: real > product_prod_real_a] :
          ( ( member_real_nat @ Alpha @ ( qbs_Mx_nat @ X3 ) )
         => ( ( member1006887528422719913real_a @ Beta @ ( binary2731563775470309560real_a @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ Y3 ) )
           => ( member_real_b_c @ ( comp_P5170362070794227966c_real @ ( produc8409101302566321868_a_b_c @ ( comp_nat_a_b_c_real @ F2 @ Alpha ) ) @ Beta ) @ ( qbs_Mx_b_c @ Z ) ) ) )
     => ( member_nat_a_b_c @ F2 @ ( qbs_mo7229212818010124491_a_b_c @ X3 @ ( expone6081388564108922123_a_b_c @ Y3 @ Z ) ) ) ) ).

% qbs_exp_morphismI
thf(fact_690_qbs__exp__morphismI,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_a,F2: real > a > b > c,Z: quasi_borel_b_c] :
      ( ! [Alpha: real > real,Beta: real > product_prod_real_a] :
          ( ( member_real_real @ Alpha @ ( qbs_Mx_real @ X3 ) )
         => ( ( member1006887528422719913real_a @ Beta @ ( binary2731563775470309560real_a @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ Y3 ) )
           => ( member_real_b_c @ ( comp_P5170362070794227966c_real @ ( produc8409101302566321868_a_b_c @ ( comp_real_a_b_c_real @ F2 @ Alpha ) ) @ Beta ) @ ( qbs_Mx_b_c @ Z ) ) ) )
     => ( member_real_a_b_c @ F2 @ ( qbs_mo534596117765811055_a_b_c @ X3 @ ( expone6081388564108922123_a_b_c @ Y3 @ Z ) ) ) ) ).

% qbs_exp_morphismI
thf(fact_691_comp__apply,axiom,
    ( comp_r4825950202331181903t_real
    = ( ^ [F: real > produc7716430852924023517t_real,G: produc7716430852924023517t_real > real,X2: produc7716430852924023517t_real] : ( F @ ( G @ X2 ) ) ) ) ).

% comp_apply
thf(fact_692_comp__apply,axiom,
    ( comp_real_real_real
    = ( ^ [F: real > real,G: real > real,X2: real] : ( F @ ( G @ X2 ) ) ) ) ).

% comp_apply
thf(fact_693_comp__apply,axiom,
    ( comp_real_o_o
    = ( ^ [F: real > $o,G: $o > real,X2: $o] : ( F @ ( G @ X2 ) ) ) ) ).

% comp_apply
thf(fact_694_comp__apply,axiom,
    ( comp_real_nat_nat
    = ( ^ [F: real > nat,G: nat > real,X2: nat] : ( F @ ( G @ X2 ) ) ) ) ).

% comp_apply
thf(fact_695_comp__apply,axiom,
    ( comp_a6364899482013671645c_real
    = ( ^ [F: ( a > b > c ) > product_prod_a_b > c,G: real > a > b > c,X2: real] : ( F @ ( G @ X2 ) ) ) ) ).

% comp_apply
thf(fact_696_split__cong,axiom,
    ! [Q: product_prod_real_a,F2: real > a > b > c,G2: real > a > b > c,P: product_prod_real_a] :
      ( ! [X5: real,Y5: a] :
          ( ( ( product_Pair_real_a @ X5 @ Y5 )
            = Q )
         => ( ( F2 @ X5 @ Y5 )
            = ( G2 @ X5 @ Y5 ) ) )
     => ( ( P = Q )
       => ( ( produc8409101302566321868_a_b_c @ F2 @ P )
          = ( produc8409101302566321868_a_b_c @ G2 @ Q ) ) ) ) ).

% split_cong
thf(fact_697_split__cong,axiom,
    ! [Q: produc1405624045518934769od_a_b,F2: real > product_prod_a_b > c,G2: real > product_prod_a_b > c,P: produc1405624045518934769od_a_b] :
      ( ! [X5: real,Y5: product_prod_a_b] :
          ( ( ( produc6260613462353114019od_a_b @ X5 @ Y5 )
            = Q )
         => ( ( F2 @ X5 @ Y5 )
            = ( G2 @ X5 @ Y5 ) ) )
     => ( ( P = Q )
       => ( ( produc8366947261062197552_a_b_c @ F2 @ P )
          = ( produc8366947261062197552_a_b_c @ G2 @ Q ) ) ) ) ).

% split_cong
thf(fact_698_split__cong,axiom,
    ! [Q: product_prod_a_b,F2: a > b > c,G2: a > b > c,P: product_prod_a_b] :
      ( ! [X5: a,Y5: b] :
          ( ( ( product_Pair_a_b @ X5 @ Y5 )
            = Q )
         => ( ( F2 @ X5 @ Y5 )
            = ( G2 @ X5 @ Y5 ) ) )
     => ( ( P = Q )
       => ( ( produc6028431345588019475_a_b_c @ F2 @ P )
          = ( produc6028431345588019475_a_b_c @ G2 @ Q ) ) ) ) ).

% split_cong
thf(fact_699_split__cong,axiom,
    ! [Q: product_prod_real_b,F2: real > b > c,G2: real > b > c,P: product_prod_real_b] :
      ( ! [X5: real,Y5: b] :
          ( ( ( product_Pair_real_b @ X5 @ Y5 )
            = Q )
         => ( ( F2 @ X5 @ Y5 )
            = ( G2 @ X5 @ Y5 ) ) )
     => ( ( P = Q )
       => ( ( produc2835462372567216025al_b_c @ F2 @ P )
          = ( produc2835462372567216025al_b_c @ G2 @ Q ) ) ) ) ).

% split_cong
thf(fact_700_split__cong,axiom,
    ! [Q: product_prod_real_a,F2: real > a > c,G2: real > a > c,P: product_prod_real_a] :
      ( ! [X5: real,Y5: a] :
          ( ( ( product_Pair_real_a @ X5 @ Y5 )
            = Q )
         => ( ( F2 @ X5 @ Y5 )
            = ( G2 @ X5 @ Y5 ) ) )
     => ( ( P = Q )
       => ( ( produc5622917954539892058al_a_c @ F2 @ P )
          = ( produc5622917954539892058al_a_c @ G2 @ Q ) ) ) ) ).

% split_cong
thf(fact_701_split__cong,axiom,
    ! [Q: product_prod_a_real,F2: a > real > b > c,G2: a > real > b > c,P: product_prod_a_real] :
      ( ! [X5: a,Y5: real] :
          ( ( ( product_Pair_a_real @ X5 @ Y5 )
            = Q )
         => ( ( F2 @ X5 @ Y5 )
            = ( G2 @ X5 @ Y5 ) ) )
     => ( ( P = Q )
       => ( ( produc7198824580026001574al_b_c @ F2 @ P )
          = ( produc7198824580026001574al_b_c @ G2 @ Q ) ) ) ) ).

% split_cong
thf(fact_702_qbs__eval__morphism,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_c] : ( member6416298619526509074_c_b_c @ expone4424288639908565227al_b_c @ ( qbs_mo4465056886186108344_c_b_c @ ( binary247682643360736042_b_c_b @ ( exponent_exp_qbs_b_c @ X3 @ Y3 ) @ X3 ) @ Y3 ) ) ).

% qbs_eval_morphism
thf(fact_703_qbs__eval__morphism,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b_c] : ( member4815647094349763600_a_b_c @ expone857715690683330810_a_b_c @ ( qbs_mo2739576739718418430_a_b_c @ ( binary188420029494746134_b_c_a @ ( expone6081388564108922123_a_b_c @ X3 @ Y3 ) @ X3 ) @ Y3 ) ) ).

% qbs_eval_morphism
thf(fact_704_exp__qbs__def,axiom,
    ( expone1656787320005700680_a_b_c
    = ( ^ [X: quasi_7706945541993221175real_a,Y: quasi_borel_b_c] : ( quasi_1052261562784621898_a_b_c @ ( produc6088510557483919976_a_b_c @ ( qbs_mo8653977514671865831_a_b_c @ X @ Y ) @ ( expone4204337439263262707_a_b_c @ X @ Y ) ) ) ) ) ).

% exp_qbs_def
thf(fact_705_exp__qbs__def,axiom,
    ( expone4174669362753510615al_nat
    = ( ^ [X: quasi_borel_real,Y: quasi_borel_nat] : ( quasi_7050651594119414233al_nat @ ( produc4583020555951415302al_nat @ ( qbs_mo6567951568834356598al_nat @ X @ Y ) @ ( expone3954210144133575042al_nat @ X @ Y ) ) ) ) ) ).

% exp_qbs_def
thf(fact_706_exp__qbs__def,axiom,
    ( expone5053526631941837485al_b_c
    = ( ^ [X: quasi_borel_real,Y: quasi_borel_b_c] : ( quasi_1614826383807741615al_b_c @ ( produc1926322370929056946al_b_c @ ( qbs_mo6398413456135019852al_b_c @ X @ Y ) @ ( expone303615731128029528al_b_c @ X @ Y ) ) ) ) ) ).

% exp_qbs_def
thf(fact_707_exp__qbs__def,axiom,
    ( expone6779206709035782606_a_b_c
    = ( ^ [X: quasi_borel_real,Y: quasi_borel_a_b_c] : ( quasi_8296237299518586338_a_b_c @ ( produc7100086208523987490_a_b_c @ ( qbs_mo534596117765811055_a_b_c @ X @ Y ) @ ( expone1129265718773867619_a_b_c @ X @ Y ) ) ) ) ) ).

% exp_qbs_def
thf(fact_708_exp__qbs__def,axiom,
    ( expone8830732826479387735t_real
    = ( ^ [X: quasi_borel_nat,Y: quasi_borel_real] : ( quasi_1802327248741518681t_real @ ( produc9006861556841674502t_real @ ( qbs_mo2000642995705457910t_real @ X @ Y ) @ ( expone8610273607859452162t_real @ X @ Y ) ) ) ) ) ).

% exp_qbs_def
thf(fact_709_exp__qbs__def,axiom,
    ( expone6081388564108922123_a_b_c
    = ( ^ [X: quasi_borel_a,Y: quasi_borel_b_c] : ( quasi_5610574512630110679_a_b_c @ ( produc8215486259843092578_a_b_c @ ( qbs_morphism_a_b_c @ X @ Y ) @ ( expone5572123575668448672_a_b_c @ X @ Y ) ) ) ) ) ).

% exp_qbs_def
thf(fact_710_exp__qbs__def,axiom,
    ( exponent_exp_qbs_b_c
    = ( ^ [X: quasi_borel_b,Y: quasi_borel_c] : ( quasi_6207043359997831396el_b_c @ ( produc1420289723773840796al_b_c @ ( qbs_morphism_b_c @ X @ Y ) @ ( expone4235142314707039685Mx_b_c @ X @ Y ) ) ) ) ) ).

% exp_qbs_def
thf(fact_711_exp__qbs__def,axiom,
    ( expone8870078507744808369_a_b_c
    = ( ^ [X: quasi_8309430206217406798od_a_b,Y: quasi_borel_c] : ( quasi_3086123867576815227_a_b_c @ ( produc5052459688918616138_a_b_c @ ( qbs_mo2296058654870477648_a_b_c @ X @ Y ) @ ( expone95873867685489500_a_b_c @ X @ Y ) ) ) ) ) ).

% exp_qbs_def
thf(fact_712_exp__qbs__correct,axiom,
    ! [X3: quasi_7706945541993221175real_a,Y3: quasi_borel_b_c] :
      ( ( quasi_8648868249187627029_a_b_c @ ( expone1656787320005700680_a_b_c @ X3 @ Y3 ) )
      = ( produc6088510557483919976_a_b_c @ ( qbs_mo8653977514671865831_a_b_c @ X3 @ Y3 ) @ ( expone4204337439263262707_a_b_c @ X3 @ Y3 ) ) ) ).

% exp_qbs_correct
thf(fact_713_exp__qbs__correct,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_nat] :
      ( ( quasi_4171214832242746788al_nat @ ( expone4174669362753510615al_nat @ X3 @ Y3 ) )
      = ( produc4583020555951415302al_nat @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) @ ( expone3954210144133575042al_nat @ X3 @ Y3 ) ) ) ).

% exp_qbs_correct
thf(fact_714_exp__qbs__correct,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_b_c] :
      ( ( quasi_5254293591698803834al_b_c @ ( expone5053526631941837485al_b_c @ X3 @ Y3 ) )
      = ( produc1926322370929056946al_b_c @ ( qbs_mo6398413456135019852al_b_c @ X3 @ Y3 ) @ ( expone303615731128029528al_b_c @ X3 @ Y3 ) ) ) ).

% exp_qbs_correct
thf(fact_715_exp__qbs__correct,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_a_b_c] :
      ( ( quasi_6700461205876095319_a_b_c @ ( expone6779206709035782606_a_b_c @ X3 @ Y3 ) )
      = ( produc7100086208523987490_a_b_c @ ( qbs_mo534596117765811055_a_b_c @ X3 @ Y3 ) @ ( expone1129265718773867619_a_b_c @ X3 @ Y3 ) ) ) ).

% exp_qbs_correct
thf(fact_716_exp__qbs__correct,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real] :
      ( ( quasi_8146262523719627044t_real @ ( expone8830732826479387735t_real @ X3 @ Y3 ) )
      = ( produc9006861556841674502t_real @ ( qbs_mo2000642995705457910t_real @ X3 @ Y3 ) @ ( expone8610273607859452162t_real @ X3 @ Y3 ) ) ) ).

% exp_qbs_correct
thf(fact_717_exp__qbs__correct,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b_c] :
      ( ( quasi_4142501723813778252_a_b_c @ ( expone6081388564108922123_a_b_c @ X3 @ Y3 ) )
      = ( produc8215486259843092578_a_b_c @ ( qbs_morphism_a_b_c @ X3 @ Y3 ) @ ( expone5572123575668448672_a_b_c @ X3 @ Y3 ) ) ) ).

% exp_qbs_correct
thf(fact_718_exp__qbs__correct,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_c] :
      ( ( quasi_5923488038834321583el_b_c @ ( exponent_exp_qbs_b_c @ X3 @ Y3 ) )
      = ( produc1420289723773840796al_b_c @ ( qbs_morphism_b_c @ X3 @ Y3 ) @ ( expone4235142314707039685Mx_b_c @ X3 @ Y3 ) ) ) ).

% exp_qbs_correct
thf(fact_719_exp__qbs__correct,axiom,
    ! [X3: quasi_8309430206217406798od_a_b,Y3: quasi_borel_c] :
      ( ( quasi_6543333519567149894_a_b_c @ ( expone8870078507744808369_a_b_c @ X3 @ Y3 ) )
      = ( produc5052459688918616138_a_b_c @ ( qbs_mo2296058654870477648_a_b_c @ X3 @ Y3 ) @ ( expone95873867685489500_a_b_c @ X3 @ Y3 ) ) ) ).

% exp_qbs_correct
thf(fact_720__092_060open_062_I_092_060lambda_062_Ix_M_Ay_J_O_A_Icase__prod_A_092_060circ_062_Ak_J_Ax_Ay_J_A_092_060circ_062_A_092_060alpha_062_A_061_A_I_092_060lambda_062_Ir_M_Ay_J_O_Ak_A_Ifst_A_I_092_060alpha_062_Ar_J_J_A_Ifst_A_Isnd_A_I_092_060alpha_062_Ar_J_J_J_Ay_J_A_092_060circ_062_A_I_092_060lambda_062r_O_A_Ir_M_Asnd_A_Isnd_A_I_092_060alpha_062_Ar_J_J_J_J_092_060close_062,axiom,
    ( ( comp_P7067203313445288664c_real @ ( produc8366947261062197552_a_b_c @ ( comp_a6364899482013671645c_real @ produc6028431345588019475_a_b_c @ k ) ) @ alpha )
    = ( comp_P4571499527812350529c_real
      @ ( produc2835462372567216025al_b_c
        @ ^ [R: real] : ( k @ ( produc4505306568083885239od_a_b @ ( alpha @ R ) ) @ ( product_fst_a_b @ ( produc4276089182416139253od_a_b @ ( alpha @ R ) ) ) ) )
      @ ^ [R: real] : ( product_Pair_real_b @ R @ ( product_snd_a_b @ ( produc4276089182416139253od_a_b @ ( alpha @ R ) ) ) ) ) ) ).

% \<open>(\<lambda>(x, y). (case_prod \<circ> k) x y) \<circ> \<alpha> = (\<lambda>(r, y). k (fst (\<alpha> r)) (fst (snd (\<alpha> r))) y) \<circ> (\<lambda>r. (r, snd (snd (\<alpha> r))))\<close>
thf(fact_721_pair__qbs__Mx,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_a] :
      ( ( qbs_Mx2044252498660063120real_a @ ( binary5762279046363823267real_a @ X3 @ Y3 ) )
      = ( binary2731563775470309560real_a @ X3 @ Y3 ) ) ).

% pair_qbs_Mx
thf(fact_722_pair__qbs__Mx,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b] :
      ( ( qbs_Mx8952202186341960991od_a_b @ ( binary3918968219557196014bs_a_b @ X3 @ Y3 ) )
      = ( binary5811906450663726489Mx_a_b @ X3 @ Y3 ) ) ).

% pair_qbs_Mx
thf(fact_723_pair__qbs__Mx,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real] :
      ( ( qbs_Mx6884344600386557780t_real @ ( binary2938201662863479403t_real @ X3 @ Y3 ) )
      = ( binary1593783336058016534t_real @ X3 @ Y3 ) ) ).

% pair_qbs_Mx
thf(fact_724_pair__qbs__Mx,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_real] :
      ( ( qbs_Mx2863504943393711152l_real @ ( binary210465342804807751l_real @ X3 @ Y3 ) )
      = ( binary6833691656172727154l_real @ X3 @ Y3 ) ) ).

% pair_qbs_Mx
thf(fact_725_pair__qbs__Mx,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_b] :
      ( ( qbs_Mx2044252502963291921real_b @ ( binary5762279046363823268real_b @ X3 @ Y3 ) )
      = ( binary2731563775470309561real_b @ X3 @ Y3 ) ) ).

% pair_qbs_Mx
thf(fact_726_pair__qbs__Mx,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_real] :
      ( ( qbs_Mx7123204611580856611b_real @ ( binary1505106857224228350b_real @ X3 @ Y3 ) )
      = ( binary7697763623185490451b_real @ X3 @ Y3 ) ) ).

% pair_qbs_Mx
thf(fact_727_pair__qbs__Mx,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_a] :
      ( ( qbs_Mx6164746600066056157od_b_a @ ( binary1131512637584519980bs_b_a @ X3 @ Y3 ) )
      = ( binary3024450868691050455Mx_b_a @ X3 @ Y3 ) ) ).

% pair_qbs_Mx
thf(fact_728_pair__qbs__Mx,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_real] :
      ( ( qbs_Mx1526985996392725922a_real @ ( binary5132260278890873469a_real @ X3 @ Y3 ) )
      = ( binary2101545007997359762a_real @ X3 @ Y3 ) ) ).

% pair_qbs_Mx
thf(fact_729_pair__qbs__Mx,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_8309430206217406798od_a_b] :
      ( ( qbs_Mx1525208361947520314od_a_b @ ( binary7782493704384473421od_a_b @ X3 @ Y3 ) )
      = ( binary1851749123906691170od_a_b @ X3 @ Y3 ) ) ).

% pair_qbs_Mx
thf(fact_730_exp__qbs__Mx,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b_c] :
      ( ( qbs_Mx_a_b_c @ ( expone6081388564108922123_a_b_c @ X3 @ Y3 ) )
      = ( expone5572123575668448672_a_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_Mx
thf(fact_731_exp__qbs__Mx,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_c] :
      ( ( qbs_Mx_b_c @ ( exponent_exp_qbs_b_c @ X3 @ Y3 ) )
      = ( expone4235142314707039685Mx_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_Mx
thf(fact_732_exp__qbs__Mx,axiom,
    ! [X3: quasi_8309430206217406798od_a_b,Y3: quasi_borel_c] :
      ( ( qbs_Mx6669678912392177926_a_b_c @ ( expone8870078507744808369_a_b_c @ X3 @ Y3 ) )
      = ( expone95873867685489500_a_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_Mx
thf(fact_733_fst__diag__fst,axiom,
    ( ( comp_P6892385181472540974od_a_b @ product_fst_a_a
      @ ( comp_a1036870397537576092od_a_b
        @ ^ [X2: a] : ( product_Pair_a_a @ X2 @ X2 )
        @ product_fst_a_b ) )
    = product_fst_a_b ) ).

% fst_diag_fst
thf(fact_734_fst__diag__fst,axiom,
    ( ( comp_P4902882437973770541t_real @ product_fst_nat_nat
      @ ( comp_n8665336278051121359t_real
        @ ^ [X2: nat] : ( product_Pair_nat_nat @ X2 @ X2 )
        @ product_fst_nat_real ) )
    = product_fst_nat_real ) ).

% fst_diag_fst
thf(fact_735_fst__diag__fst,axiom,
    ( ( comp_P544700997026044725od_a_b @ produc5828954698716094813l_real
      @ ( comp_r9147466637321353051od_a_b
        @ ^ [X2: real] : ( produc4511245868158468465l_real @ X2 @ X2 )
        @ produc4505306568083885239od_a_b ) )
    = produc4505306568083885239od_a_b ) ).

% fst_diag_fst
thf(fact_736_fst__diag__fst,axiom,
    ( ( comp_P3276979369905350645l_real @ produc5828954698716094813l_real
      @ ( comp_r97482993418849103l_real
        @ ^ [X2: real] : ( produc4511245868158468465l_real @ X2 @ X2 )
        @ produc5828954698716094813l_real ) )
    = produc5828954698716094813l_real ) ).

% fst_diag_fst
thf(fact_737_fst__diag__fst,axiom,
    ( ( comp_P1589298742348195979real_a @ produc5828954698716094813l_real
      @ ( comp_r5571647577339959985real_a
        @ ^ [X2: real] : ( produc4511245868158468465l_real @ X2 @ X2 )
        @ product_fst_real_a ) )
    = product_fst_real_a ) ).

% fst_diag_fst
thf(fact_738_snd__diag__snd,axiom,
    ( ( comp_P8163392464686388501od_a_b @ produc8875788424405714885od_a_b
      @ ( comp_P1447306808648735059od_a_b
        @ ^ [X2: product_prod_a_b] : ( produc6550459592057863831od_a_b @ X2 @ X2 )
        @ produc4276089182416139253od_a_b ) )
    = produc4276089182416139253od_a_b ) ).

% snd_diag_snd
thf(fact_739_snd__diag__snd,axiom,
    ( ( comp_P5715990135234274861od_a_b @ product_snd_b_b
      @ ( comp_b6573281471806798941od_a_b
        @ ^ [X2: b] : ( product_Pair_b_b @ X2 @ X2 )
        @ product_snd_a_b ) )
    = product_snd_a_b ) ).

% snd_diag_snd
thf(fact_740_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha2: real > real,X3: quasi_borel_real,R2: real] :
      ( ( member_real_real @ Alpha2 @ ( qbs_Mx_real @ X3 ) )
     => ( member_real @ ( Alpha2 @ R2 ) @ ( qbs_space_real @ X3 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_741_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha2: real > $o,X3: quasi_borel_o,R2: real] :
      ( ( member_real_o @ Alpha2 @ ( qbs_Mx_o @ X3 ) )
     => ( member_o @ ( Alpha2 @ R2 ) @ ( qbs_space_o @ X3 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_742_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha2: real > nat,X3: quasi_borel_nat,R2: real] :
      ( ( member_real_nat @ Alpha2 @ ( qbs_Mx_nat @ X3 ) )
     => ( member_nat @ ( Alpha2 @ R2 ) @ ( qbs_space_nat @ X3 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_743_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha2: real > real > real,X3: quasi_1840791737016710247l_real,R2: real] :
      ( ( member8878224140454985689l_real @ Alpha2 @ ( qbs_Mx_real_real @ X3 ) )
     => ( member_real_real @ ( Alpha2 @ R2 ) @ ( qbs_space_real_real @ X3 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_744_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha2: real > real > $o,X3: quasi_borel_real_o,R2: real] :
      ( ( member_real_real_o @ Alpha2 @ ( qbs_Mx_real_o @ X3 ) )
     => ( member_real_o @ ( Alpha2 @ R2 ) @ ( qbs_space_real_o @ X3 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_745_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha2: real > real > nat,X3: quasi_borel_real_nat,R2: real] :
      ( ( member_real_real_nat @ Alpha2 @ ( qbs_Mx_real_nat @ X3 ) )
     => ( member_real_nat @ ( Alpha2 @ R2 ) @ ( qbs_space_real_nat @ X3 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_746_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha2: real > $o > real,X3: quasi_borel_o_real,R2: real] :
      ( ( member_real_o_real @ Alpha2 @ ( qbs_Mx_o_real @ X3 ) )
     => ( member_o_real @ ( Alpha2 @ R2 ) @ ( qbs_space_o_real @ X3 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_747_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha2: real > nat > real,X3: quasi_borel_nat_real,R2: real] :
      ( ( member_real_nat_real @ Alpha2 @ ( qbs_Mx_nat_real @ X3 ) )
     => ( member_nat_real @ ( Alpha2 @ R2 ) @ ( qbs_space_nat_real @ X3 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_748_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha2: real > b > c,X3: quasi_borel_b_c,R2: real] :
      ( ( member_real_b_c @ Alpha2 @ ( qbs_Mx_b_c @ X3 ) )
     => ( member_b_c @ ( Alpha2 @ R2 ) @ ( qbs_space_b_c @ X3 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_749_qbs__Mx__to__X_I2_J,axiom,
    ! [Alpha2: real > product_prod_a_b > c,X3: quasi_4437365610616121517_a_b_c,R2: real] :
      ( ( member3234269468440695583_a_b_c @ Alpha2 @ ( qbs_Mx6669678912392177926_a_b_c @ X3 ) )
     => ( member1080921174361771732_a_b_c @ ( Alpha2 @ R2 ) @ ( qbs_sp1497204993120353415_a_b_c @ X3 ) ) ) ).

% qbs_Mx_to_X(2)
thf(fact_750_qbs__closed2__dest,axiom,
    ! [X4: real,X3: quasi_borel_real] :
      ( ( member_real @ X4 @ ( qbs_space_real @ X3 ) )
     => ( member_real_real
        @ ^ [R: real] : X4
        @ ( qbs_Mx_real @ X3 ) ) ) ).

% qbs_closed2_dest
thf(fact_751_qbs__closed2__dest,axiom,
    ! [X4: $o,X3: quasi_borel_o] :
      ( ( member_o @ X4 @ ( qbs_space_o @ X3 ) )
     => ( member_real_o
        @ ^ [R: real] : X4
        @ ( qbs_Mx_o @ X3 ) ) ) ).

% qbs_closed2_dest
thf(fact_752_qbs__closed2__dest,axiom,
    ! [X4: nat,X3: quasi_borel_nat] :
      ( ( member_nat @ X4 @ ( qbs_space_nat @ X3 ) )
     => ( member_real_nat
        @ ^ [R: real] : X4
        @ ( qbs_Mx_nat @ X3 ) ) ) ).

% qbs_closed2_dest
thf(fact_753_qbs__closed2__dest,axiom,
    ! [X4: b > c,X3: quasi_borel_b_c] :
      ( ( member_b_c @ X4 @ ( qbs_space_b_c @ X3 ) )
     => ( member_real_b_c
        @ ^ [R: real] : X4
        @ ( qbs_Mx_b_c @ X3 ) ) ) ).

% qbs_closed2_dest
thf(fact_754_qbs__closed2__dest,axiom,
    ! [X4: real > real,X3: quasi_1840791737016710247l_real] :
      ( ( member_real_real @ X4 @ ( qbs_space_real_real @ X3 ) )
     => ( member8878224140454985689l_real
        @ ^ [R: real] : X4
        @ ( qbs_Mx_real_real @ X3 ) ) ) ).

% qbs_closed2_dest
thf(fact_755_qbs__closed2__dest,axiom,
    ! [X4: real > $o,X3: quasi_borel_real_o] :
      ( ( member_real_o @ X4 @ ( qbs_space_real_o @ X3 ) )
     => ( member_real_real_o
        @ ^ [R: real] : X4
        @ ( qbs_Mx_real_o @ X3 ) ) ) ).

% qbs_closed2_dest
thf(fact_756_qbs__closed2__dest,axiom,
    ! [X4: real > nat,X3: quasi_borel_real_nat] :
      ( ( member_real_nat @ X4 @ ( qbs_space_real_nat @ X3 ) )
     => ( member_real_real_nat
        @ ^ [R: real] : X4
        @ ( qbs_Mx_real_nat @ X3 ) ) ) ).

% qbs_closed2_dest
thf(fact_757_qbs__closed2__dest,axiom,
    ! [X4: $o > real,X3: quasi_borel_o_real] :
      ( ( member_o_real @ X4 @ ( qbs_space_o_real @ X3 ) )
     => ( member_real_o_real
        @ ^ [R: real] : X4
        @ ( qbs_Mx_o_real @ X3 ) ) ) ).

% qbs_closed2_dest
thf(fact_758_qbs__closed2__dest,axiom,
    ! [X4: nat > real,X3: quasi_borel_nat_real] :
      ( ( member_nat_real @ X4 @ ( qbs_space_nat_real @ X3 ) )
     => ( member_real_nat_real
        @ ^ [R: real] : X4
        @ ( qbs_Mx_nat_real @ X3 ) ) ) ).

% qbs_closed2_dest
thf(fact_759_qbs__closed2__dest,axiom,
    ! [X4: product_prod_a_b > c,X3: quasi_4437365610616121517_a_b_c] :
      ( ( member1080921174361771732_a_b_c @ X4 @ ( qbs_sp1497204993120353415_a_b_c @ X3 ) )
     => ( member3234269468440695583_a_b_c
        @ ^ [R: real] : X4
        @ ( qbs_Mx6669678912392177926_a_b_c @ X3 ) ) ) ).

% qbs_closed2_dest
thf(fact_760_fst__diag__snd,axiom,
    ( ( comp_P8163392464686388501od_a_b @ produc5013601669340818563od_a_b
      @ ( comp_P1447306808648735059od_a_b
        @ ^ [X2: product_prod_a_b] : ( produc6550459592057863831od_a_b @ X2 @ X2 )
        @ produc4276089182416139253od_a_b ) )
    = produc4276089182416139253od_a_b ) ).

% fst_diag_snd
thf(fact_761_fst__diag__snd,axiom,
    ( ( comp_P5715990135234274861od_a_b @ product_fst_b_b
      @ ( comp_b6573281471806798941od_a_b
        @ ^ [X2: b] : ( product_Pair_b_b @ X2 @ X2 )
        @ product_snd_a_b ) )
    = product_snd_a_b ) ).

% fst_diag_snd
thf(fact_762_snd__diag__fst,axiom,
    ( ( comp_P544700997026044725od_a_b @ produc3484788084999411615l_real
      @ ( comp_r9147466637321353051od_a_b
        @ ^ [X2: real] : ( produc4511245868158468465l_real @ X2 @ X2 )
        @ produc4505306568083885239od_a_b ) )
    = produc4505306568083885239od_a_b ) ).

% snd_diag_fst
thf(fact_763_snd__diag__fst,axiom,
    ( ( comp_P6892385181472540974od_a_b @ product_snd_a_a
      @ ( comp_a1036870397537576092od_a_b
        @ ^ [X2: a] : ( product_Pair_a_a @ X2 @ X2 )
        @ product_fst_a_b ) )
    = product_fst_a_b ) ).

% snd_diag_fst
thf(fact_764_snd__diag__fst,axiom,
    ( ( comp_P3276979369905350645l_real @ produc3484788084999411615l_real
      @ ( comp_r97482993418849103l_real
        @ ^ [X2: real] : ( produc4511245868158468465l_real @ X2 @ X2 )
        @ produc5828954698716094813l_real ) )
    = produc5828954698716094813l_real ) ).

% snd_diag_fst
thf(fact_765_snd__diag__fst,axiom,
    ( ( comp_P4902882437973770541t_real @ product_snd_nat_nat
      @ ( comp_n8665336278051121359t_real
        @ ^ [X2: nat] : ( product_Pair_nat_nat @ X2 @ X2 )
        @ product_fst_nat_real ) )
    = product_fst_nat_real ) ).

% snd_diag_fst
thf(fact_766_snd__diag__fst,axiom,
    ( ( comp_P1589298742348195979real_a @ produc3484788084999411615l_real
      @ ( comp_r5571647577339959985real_a
        @ ^ [X2: real] : ( produc4511245868158468465l_real @ X2 @ X2 )
        @ product_fst_real_a ) )
    = product_fst_real_a ) ).

% snd_diag_fst
thf(fact_767_qbs__morphismE_I3_J,axiom,
    ! [F2: $o > $o,X3: quasi_borel_o,Y3: quasi_borel_o,Alpha2: real > $o] :
      ( ( member_o_o @ F2 @ ( qbs_morphism_o_o @ X3 @ Y3 ) )
     => ( ( member_real_o @ Alpha2 @ ( qbs_Mx_o @ X3 ) )
       => ( member_real_o @ ( comp_o_o_real @ F2 @ Alpha2 ) @ ( qbs_Mx_o @ Y3 ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_768_qbs__morphismE_I3_J,axiom,
    ! [F2: $o > nat,X3: quasi_borel_o,Y3: quasi_borel_nat,Alpha2: real > $o] :
      ( ( member_o_nat @ F2 @ ( qbs_morphism_o_nat @ X3 @ Y3 ) )
     => ( ( member_real_o @ Alpha2 @ ( qbs_Mx_o @ X3 ) )
       => ( member_real_nat @ ( comp_o_nat_real @ F2 @ Alpha2 ) @ ( qbs_Mx_nat @ Y3 ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_769_qbs__morphismE_I3_J,axiom,
    ! [F2: nat > $o,X3: quasi_borel_nat,Y3: quasi_borel_o,Alpha2: real > nat] :
      ( ( member_nat_o @ F2 @ ( qbs_morphism_nat_o @ X3 @ Y3 ) )
     => ( ( member_real_nat @ Alpha2 @ ( qbs_Mx_nat @ X3 ) )
       => ( member_real_o @ ( comp_nat_o_real @ F2 @ Alpha2 ) @ ( qbs_Mx_o @ Y3 ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_770_qbs__morphismE_I3_J,axiom,
    ! [F2: nat > nat,X3: quasi_borel_nat,Y3: quasi_borel_nat,Alpha2: real > nat] :
      ( ( member_nat_nat @ F2 @ ( qbs_morphism_nat_nat @ X3 @ Y3 ) )
     => ( ( member_real_nat @ Alpha2 @ ( qbs_Mx_nat @ X3 ) )
       => ( member_real_nat @ ( comp_nat_nat_real @ F2 @ Alpha2 ) @ ( qbs_Mx_nat @ Y3 ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_771_qbs__morphismE_I3_J,axiom,
    ! [F2: real > real,X3: quasi_borel_real,Y3: quasi_borel_real,Alpha2: real > real] :
      ( ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) )
     => ( ( member_real_real @ Alpha2 @ ( qbs_Mx_real @ X3 ) )
       => ( member_real_real @ ( comp_real_real_real @ F2 @ Alpha2 ) @ ( qbs_Mx_real @ Y3 ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_772_qbs__morphismE_I3_J,axiom,
    ! [F2: real > $o,X3: quasi_borel_real,Y3: quasi_borel_o,Alpha2: real > real] :
      ( ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) )
     => ( ( member_real_real @ Alpha2 @ ( qbs_Mx_real @ X3 ) )
       => ( member_real_o @ ( comp_real_o_real @ F2 @ Alpha2 ) @ ( qbs_Mx_o @ Y3 ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_773_qbs__morphismE_I3_J,axiom,
    ! [F2: $o > real,X3: quasi_borel_o,Y3: quasi_borel_real,Alpha2: real > $o] :
      ( ( member_o_real @ F2 @ ( qbs_morphism_o_real @ X3 @ Y3 ) )
     => ( ( member_real_o @ Alpha2 @ ( qbs_Mx_o @ X3 ) )
       => ( member_real_real @ ( comp_o_real_real @ F2 @ Alpha2 ) @ ( qbs_Mx_real @ Y3 ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_774_qbs__morphismE_I3_J,axiom,
    ! [F2: real > nat,X3: quasi_borel_real,Y3: quasi_borel_nat,Alpha2: real > real] :
      ( ( member_real_nat @ F2 @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) )
     => ( ( member_real_real @ Alpha2 @ ( qbs_Mx_real @ X3 ) )
       => ( member_real_nat @ ( comp_real_nat_real @ F2 @ Alpha2 ) @ ( qbs_Mx_nat @ Y3 ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_775_qbs__morphismE_I3_J,axiom,
    ! [F2: nat > real,X3: quasi_borel_nat,Y3: quasi_borel_real,Alpha2: real > nat] :
      ( ( member_nat_real @ F2 @ ( qbs_mo2000642995705457910t_real @ X3 @ Y3 ) )
     => ( ( member_real_nat @ Alpha2 @ ( qbs_Mx_nat @ X3 ) )
       => ( member_real_real @ ( comp_nat_real_real @ F2 @ Alpha2 ) @ ( qbs_Mx_real @ Y3 ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_776_qbs__morphismE_I3_J,axiom,
    ! [F2: $o > b > c,X3: quasi_borel_o,Y3: quasi_borel_b_c,Alpha2: real > $o] :
      ( ( member_o_b_c @ F2 @ ( qbs_morphism_o_b_c @ X3 @ Y3 ) )
     => ( ( member_real_o @ Alpha2 @ ( qbs_Mx_o @ X3 ) )
       => ( member_real_b_c @ ( comp_o_b_c_real @ F2 @ Alpha2 ) @ ( qbs_Mx_b_c @ Y3 ) ) ) ) ).

% qbs_morphismE(3)
thf(fact_777_qbs__morphismI,axiom,
    ! [X3: quasi_borel_real,F2: real > real,Y3: quasi_borel_real] :
      ( ! [Alpha: real > real] :
          ( ( member_real_real @ Alpha @ ( qbs_Mx_real @ X3 ) )
         => ( member_real_real @ ( comp_real_real_real @ F2 @ Alpha ) @ ( qbs_Mx_real @ Y3 ) ) )
     => ( member_real_real @ F2 @ ( qbs_mo5229770564518008146l_real @ X3 @ Y3 ) ) ) ).

% qbs_morphismI
thf(fact_778_qbs__morphismI,axiom,
    ! [X3: quasi_borel_real,F2: real > $o,Y3: quasi_borel_o] :
      ( ! [Alpha: real > real] :
          ( ( member_real_real @ Alpha @ ( qbs_Mx_real @ X3 ) )
         => ( member_real_o @ ( comp_real_o_real @ F2 @ Alpha ) @ ( qbs_Mx_o @ Y3 ) ) )
     => ( member_real_o @ F2 @ ( qbs_morphism_real_o @ X3 @ Y3 ) ) ) ).

% qbs_morphismI
thf(fact_779_qbs__morphismI,axiom,
    ! [X3: quasi_borel_o,F2: $o > real,Y3: quasi_borel_real] :
      ( ! [Alpha: real > $o] :
          ( ( member_real_o @ Alpha @ ( qbs_Mx_o @ X3 ) )
         => ( member_real_real @ ( comp_o_real_real @ F2 @ Alpha ) @ ( qbs_Mx_real @ Y3 ) ) )
     => ( member_o_real @ F2 @ ( qbs_morphism_o_real @ X3 @ Y3 ) ) ) ).

% qbs_morphismI
thf(fact_780_qbs__morphismI,axiom,
    ! [X3: quasi_borel_o,F2: $o > $o,Y3: quasi_borel_o] :
      ( ! [Alpha: real > $o] :
          ( ( member_real_o @ Alpha @ ( qbs_Mx_o @ X3 ) )
         => ( member_real_o @ ( comp_o_o_real @ F2 @ Alpha ) @ ( qbs_Mx_o @ Y3 ) ) )
     => ( member_o_o @ F2 @ ( qbs_morphism_o_o @ X3 @ Y3 ) ) ) ).

% qbs_morphismI
thf(fact_781_qbs__morphismI,axiom,
    ! [X3: quasi_borel_o,F2: $o > nat,Y3: quasi_borel_nat] :
      ( ! [Alpha: real > $o] :
          ( ( member_real_o @ Alpha @ ( qbs_Mx_o @ X3 ) )
         => ( member_real_nat @ ( comp_o_nat_real @ F2 @ Alpha ) @ ( qbs_Mx_nat @ Y3 ) ) )
     => ( member_o_nat @ F2 @ ( qbs_morphism_o_nat @ X3 @ Y3 ) ) ) ).

% qbs_morphismI
thf(fact_782_qbs__morphismI,axiom,
    ! [X3: quasi_borel_nat,F2: nat > $o,Y3: quasi_borel_o] :
      ( ! [Alpha: real > nat] :
          ( ( member_real_nat @ Alpha @ ( qbs_Mx_nat @ X3 ) )
         => ( member_real_o @ ( comp_nat_o_real @ F2 @ Alpha ) @ ( qbs_Mx_o @ Y3 ) ) )
     => ( member_nat_o @ F2 @ ( qbs_morphism_nat_o @ X3 @ Y3 ) ) ) ).

% qbs_morphismI
thf(fact_783_qbs__morphismI,axiom,
    ! [X3: quasi_borel_nat,F2: nat > nat,Y3: quasi_borel_nat] :
      ( ! [Alpha: real > nat] :
          ( ( member_real_nat @ Alpha @ ( qbs_Mx_nat @ X3 ) )
         => ( member_real_nat @ ( comp_nat_nat_real @ F2 @ Alpha ) @ ( qbs_Mx_nat @ Y3 ) ) )
     => ( member_nat_nat @ F2 @ ( qbs_morphism_nat_nat @ X3 @ Y3 ) ) ) ).

% qbs_morphismI
thf(fact_784_qbs__morphismI,axiom,
    ! [X3: quasi_borel_real,F2: real > nat,Y3: quasi_borel_nat] :
      ( ! [Alpha: real > real] :
          ( ( member_real_real @ Alpha @ ( qbs_Mx_real @ X3 ) )
         => ( member_real_nat @ ( comp_real_nat_real @ F2 @ Alpha ) @ ( qbs_Mx_nat @ Y3 ) ) )
     => ( member_real_nat @ F2 @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) ) ) ).

% qbs_morphismI
thf(fact_785_qbs__morphismI,axiom,
    ! [X3: quasi_borel_nat,F2: nat > real,Y3: quasi_borel_real] :
      ( ! [Alpha: real > nat] :
          ( ( member_real_nat @ Alpha @ ( qbs_Mx_nat @ X3 ) )
         => ( member_real_real @ ( comp_nat_real_real @ F2 @ Alpha ) @ ( qbs_Mx_real @ Y3 ) ) )
     => ( member_nat_real @ F2 @ ( qbs_mo2000642995705457910t_real @ X3 @ Y3 ) ) ) ).

% qbs_morphismI
thf(fact_786_qbs__morphismI,axiom,
    ! [X3: quasi_8309430206217406798od_a_b,F2: product_prod_a_b > c,Y3: quasi_borel_c] :
      ( ! [Alpha: real > product_prod_a_b] :
          ( ( member4641211897452655452od_a_b @ Alpha @ ( qbs_Mx8952202186341960991od_a_b @ X3 ) )
         => ( member_real_c @ ( comp_P3807720206163042279c_real @ F2 @ Alpha ) @ ( qbs_Mx_c @ Y3 ) ) )
     => ( member1080921174361771732_a_b_c @ F2 @ ( qbs_mo2296058654870477648_a_b_c @ X3 @ Y3 ) ) ) ).

% qbs_morphismI
thf(fact_787_comp__def,axiom,
    ( comp_r4825950202331181903t_real
    = ( ^ [F: real > produc7716430852924023517t_real,G: produc7716430852924023517t_real > real,X2: produc7716430852924023517t_real] : ( F @ ( G @ X2 ) ) ) ) ).

% comp_def
thf(fact_788_comp__def,axiom,
    ( comp_real_real_real
    = ( ^ [F: real > real,G: real > real,X2: real] : ( F @ ( G @ X2 ) ) ) ) ).

% comp_def
thf(fact_789_comp__def,axiom,
    ( comp_real_o_o
    = ( ^ [F: real > $o,G: $o > real,X2: $o] : ( F @ ( G @ X2 ) ) ) ) ).

% comp_def
thf(fact_790_comp__def,axiom,
    ( comp_real_nat_nat
    = ( ^ [F: real > nat,G: nat > real,X2: nat] : ( F @ ( G @ X2 ) ) ) ) ).

% comp_def
thf(fact_791_comp__def,axiom,
    ( comp_a6364899482013671645c_real
    = ( ^ [F: ( a > b > c ) > product_prod_a_b > c,G: real > a > b > c,X2: real] : ( F @ ( G @ X2 ) ) ) ) ).

% comp_def
thf(fact_792_comp__assoc,axiom,
    ! [F2: real > $o,G2: $o > real,H: $o > $o] :
      ( ( comp_o_o_o @ ( comp_real_o_o @ F2 @ G2 ) @ H )
      = ( comp_real_o_o @ F2 @ ( comp_o_real_o @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_793_comp__assoc,axiom,
    ! [F2: real > nat,G2: nat > real,H: nat > nat] :
      ( ( comp_nat_nat_nat @ ( comp_real_nat_nat @ F2 @ G2 ) @ H )
      = ( comp_real_nat_nat @ F2 @ ( comp_nat_real_nat @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_794_comp__assoc,axiom,
    ! [F2: real > real,G2: real > real,H: real > real] :
      ( ( comp_real_real_real @ ( comp_real_real_real @ F2 @ G2 ) @ H )
      = ( comp_real_real_real @ F2 @ ( comp_real_real_real @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_795_comp__assoc,axiom,
    ! [F2: $o > $o,G2: real > $o,H: $o > real] :
      ( ( comp_real_o_o @ ( comp_o_o_real @ F2 @ G2 ) @ H )
      = ( comp_o_o_o @ F2 @ ( comp_real_o_o @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_796_comp__assoc,axiom,
    ! [F2: real > $o,G2: real > real,H: $o > real] :
      ( ( comp_real_o_o @ ( comp_real_o_real @ F2 @ G2 ) @ H )
      = ( comp_real_o_o @ F2 @ ( comp_real_real_o @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_797_comp__assoc,axiom,
    ! [F2: nat > nat,G2: real > nat,H: nat > real] :
      ( ( comp_real_nat_nat @ ( comp_nat_nat_real @ F2 @ G2 ) @ H )
      = ( comp_nat_nat_nat @ F2 @ ( comp_real_nat_nat @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_798_comp__assoc,axiom,
    ! [F2: real > nat,G2: real > real,H: nat > real] :
      ( ( comp_real_nat_nat @ ( comp_real_nat_real @ F2 @ G2 ) @ H )
      = ( comp_real_nat_nat @ F2 @ ( comp_real_real_nat @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_799_comp__assoc,axiom,
    ! [F2: real > produc7716430852924023517t_real,G2: real > real,H: produc7716430852924023517t_real > real] :
      ( ( comp_r4825950202331181903t_real @ ( comp_r4030900867926482106l_real @ F2 @ G2 ) @ H )
      = ( comp_r4825950202331181903t_real @ F2 @ ( comp_r8349034141028359008t_real @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_800_comp__assoc,axiom,
    ! [F2: real > produc7716430852924023517t_real,G2: produc7716430852924023517t_real > real,H: produc7716430852924023517t_real > produc7716430852924023517t_real] :
      ( ( comp_P5614709513016865274t_real @ ( comp_r4825950202331181903t_real @ F2 @ G2 ) @ H )
      = ( comp_r4825950202331181903t_real @ F2 @ ( comp_P1550655964263599733t_real @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_801_comp__assoc,axiom,
    ! [F2: produc7716430852924023517t_real > produc7716430852924023517t_real,G2: real > produc7716430852924023517t_real,H: produc7716430852924023517t_real > real] :
      ( ( comp_r4825950202331181903t_real @ ( comp_P6455894728016498639l_real @ F2 @ G2 ) @ H )
      = ( comp_P5614709513016865274t_real @ F2 @ ( comp_r4825950202331181903t_real @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_802_comp__eq__dest,axiom,
    ! [A: real > produc7716430852924023517t_real,B: produc7716430852924023517t_real > real,C: real > produc7716430852924023517t_real,D: produc7716430852924023517t_real > real,V: produc7716430852924023517t_real] :
      ( ( ( comp_r4825950202331181903t_real @ A @ B )
        = ( comp_r4825950202331181903t_real @ C @ D ) )
     => ( ( A @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_803_comp__eq__dest,axiom,
    ! [A: real > real,B: real > real,C: real > real,D: real > real,V: real] :
      ( ( ( comp_real_real_real @ A @ B )
        = ( comp_real_real_real @ C @ D ) )
     => ( ( A @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_804_comp__eq__dest,axiom,
    ! [A: real > $o,B: $o > real,C: real > $o,D: $o > real,V: $o] :
      ( ( ( comp_real_o_o @ A @ B )
        = ( comp_real_o_o @ C @ D ) )
     => ( ( A @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_805_comp__eq__dest,axiom,
    ! [A: real > nat,B: nat > real,C: real > nat,D: nat > real,V: nat] :
      ( ( ( comp_real_nat_nat @ A @ B )
        = ( comp_real_nat_nat @ C @ D ) )
     => ( ( A @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_806_comp__eq__dest,axiom,
    ! [A: ( a > b > c ) > product_prod_a_b > c,B: real > a > b > c,C: ( a > b > c ) > product_prod_a_b > c,D: real > a > b > c,V: real] :
      ( ( ( comp_a6364899482013671645c_real @ A @ B )
        = ( comp_a6364899482013671645c_real @ C @ D ) )
     => ( ( A @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_807_comp__eq__elim,axiom,
    ! [A: real > produc7716430852924023517t_real,B: produc7716430852924023517t_real > real,C: real > produc7716430852924023517t_real,D: produc7716430852924023517t_real > real] :
      ( ( ( comp_r4825950202331181903t_real @ A @ B )
        = ( comp_r4825950202331181903t_real @ C @ D ) )
     => ! [V2: produc7716430852924023517t_real] :
          ( ( A @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_808_comp__eq__elim,axiom,
    ! [A: real > real,B: real > real,C: real > real,D: real > real] :
      ( ( ( comp_real_real_real @ A @ B )
        = ( comp_real_real_real @ C @ D ) )
     => ! [V2: real] :
          ( ( A @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_809_comp__eq__elim,axiom,
    ! [A: real > $o,B: $o > real,C: real > $o,D: $o > real] :
      ( ( ( comp_real_o_o @ A @ B )
        = ( comp_real_o_o @ C @ D ) )
     => ! [V2: $o] :
          ( ( A @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_810_comp__eq__elim,axiom,
    ! [A: real > nat,B: nat > real,C: real > nat,D: nat > real] :
      ( ( ( comp_real_nat_nat @ A @ B )
        = ( comp_real_nat_nat @ C @ D ) )
     => ! [V2: nat] :
          ( ( A @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_811_comp__eq__elim,axiom,
    ! [A: ( a > b > c ) > product_prod_a_b > c,B: real > a > b > c,C: ( a > b > c ) > product_prod_a_b > c,D: real > a > b > c] :
      ( ( ( comp_a6364899482013671645c_real @ A @ B )
        = ( comp_a6364899482013671645c_real @ C @ D ) )
     => ! [V2: real] :
          ( ( A @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_812_comp__cong,axiom,
    ! [F2: real > produc7716430852924023517t_real,G2: produc7716430852924023517t_real > real,X4: produc7716430852924023517t_real,F3: real > produc7716430852924023517t_real,G3: produc7716430852924023517t_real > real,X6: produc7716430852924023517t_real] :
      ( ( ( F2 @ ( G2 @ X4 ) )
        = ( F3 @ ( G3 @ X6 ) ) )
     => ( ( comp_r4825950202331181903t_real @ F2 @ G2 @ X4 )
        = ( comp_r4825950202331181903t_real @ F3 @ G3 @ X6 ) ) ) ).

% comp_cong
thf(fact_813_comp__cong,axiom,
    ! [F2: real > real,G2: real > real,X4: real,F3: real > real,G3: real > real,X6: real] :
      ( ( ( F2 @ ( G2 @ X4 ) )
        = ( F3 @ ( G3 @ X6 ) ) )
     => ( ( comp_real_real_real @ F2 @ G2 @ X4 )
        = ( comp_real_real_real @ F3 @ G3 @ X6 ) ) ) ).

% comp_cong
thf(fact_814_comp__cong,axiom,
    ! [F2: real > $o,G2: $o > real,X4: $o,F3: real > $o,G3: $o > real,X6: $o] :
      ( ( ( F2 @ ( G2 @ X4 ) )
        = ( F3 @ ( G3 @ X6 ) ) )
     => ( ( comp_real_o_o @ F2 @ G2 @ X4 )
        = ( comp_real_o_o @ F3 @ G3 @ X6 ) ) ) ).

% comp_cong
thf(fact_815_comp__cong,axiom,
    ! [F2: real > nat,G2: nat > real,X4: nat,F3: real > nat,G3: nat > real,X6: nat] :
      ( ( ( F2 @ ( G2 @ X4 ) )
        = ( F3 @ ( G3 @ X6 ) ) )
     => ( ( comp_real_nat_nat @ F2 @ G2 @ X4 )
        = ( comp_real_nat_nat @ F3 @ G3 @ X6 ) ) ) ).

% comp_cong
thf(fact_816_comp__cong,axiom,
    ! [F2: ( a > b > c ) > product_prod_a_b > c,G2: real > a > b > c,X4: real,F3: ( a > b > c ) > product_prod_a_b > c,G3: real > a > b > c,X6: real] :
      ( ( ( F2 @ ( G2 @ X4 ) )
        = ( F3 @ ( G3 @ X6 ) ) )
     => ( ( comp_a6364899482013671645c_real @ F2 @ G2 @ X4 )
        = ( comp_a6364899482013671645c_real @ F3 @ G3 @ X6 ) ) ) ).

% comp_cong
thf(fact_817_comp__eq__dest__lhs,axiom,
    ! [A: real > produc7716430852924023517t_real,B: produc7716430852924023517t_real > real,C: produc7716430852924023517t_real > produc7716430852924023517t_real,V: produc7716430852924023517t_real] :
      ( ( ( comp_r4825950202331181903t_real @ A @ B )
        = C )
     => ( ( A @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_818_comp__eq__dest__lhs,axiom,
    ! [A: real > real,B: real > real,C: real > real,V: real] :
      ( ( ( comp_real_real_real @ A @ B )
        = C )
     => ( ( A @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_819_comp__eq__dest__lhs,axiom,
    ! [A: real > $o,B: $o > real,C: $o > $o,V: $o] :
      ( ( ( comp_real_o_o @ A @ B )
        = C )
     => ( ( A @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_820_comp__eq__dest__lhs,axiom,
    ! [A: real > nat,B: nat > real,C: nat > nat,V: nat] :
      ( ( ( comp_real_nat_nat @ A @ B )
        = C )
     => ( ( A @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_821_comp__eq__dest__lhs,axiom,
    ! [A: ( a > b > c ) > product_prod_a_b > c,B: real > a > b > c,C: real > product_prod_a_b > c,V: real] :
      ( ( ( comp_a6364899482013671645c_real @ A @ B )
        = C )
     => ( ( A @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_822_fst__snd__flip,axiom,
    ( product_fst_a_real
    = ( comp_P8403000611219577773a_real @ product_snd_real_a
      @ ( produc7204482282939075911real_a
        @ ^ [X2: a,Y2: real] : ( product_Pair_real_a @ Y2 @ X2 ) ) ) ) ).

% fst_snd_flip
thf(fact_823_fst__snd__flip,axiom,
    ( product_fst_b_real
    = ( comp_P488263325884094958b_real @ product_snd_real_b
      @ ( produc6367669841173908169real_b
        @ ^ [X2: b,Y2: real] : ( product_Pair_real_b @ Y2 @ X2 ) ) ) ) ).

% fst_snd_flip
thf(fact_824_fst__snd__flip,axiom,
    ( product_fst_real_b
    = ( comp_P6914732054928830003real_b @ product_snd_b_real
      @ ( produc6781195011795835521b_real
        @ ^ [X2: real,Y2: b] : ( product_Pair_b_real @ Y2 @ X2 ) ) ) ) ).

% fst_snd_flip
thf(fact_825_fst__snd__flip,axiom,
    ( produc4505306568083885239od_a_b
    = ( comp_P7740967659496281733od_a_b @ produc7037151529651111887b_real
      @ ( produc4394725342292598227b_real
        @ ^ [X2: real,Y2: product_prod_a_b] : ( produc9021675809588086653b_real @ Y2 @ X2 ) ) ) ) ).

% fst_snd_flip
thf(fact_826_fst__snd__flip,axiom,
    ( product_fst_a_b
    = ( comp_P1375487287417587949od_a_b @ product_snd_b_a
      @ ( produc6204743795672244857od_b_a
        @ ^ [X2: a,Y2: b] : ( product_Pair_b_a @ Y2 @ X2 ) ) ) ) ).

% fst_snd_flip
thf(fact_827_fst__snd__flip,axiom,
    ( produc5828954698716094813l_real
    = ( comp_P3276979369905350645l_real @ produc3484788084999411615l_real
      @ ( produc3818700948422621747l_real
        @ ^ [X2: real,Y2: real] : ( produc4511245868158468465l_real @ Y2 @ X2 ) ) ) ) ).

% fst_snd_flip
thf(fact_828_fst__snd__flip,axiom,
    ( product_fst_nat_real
    = ( comp_P4280070858310468689t_real @ product_snd_real_nat
      @ ( produc4028160848036898611al_nat
        @ ^ [X2: nat,Y2: real] : ( produc3181502643871035669al_nat @ Y2 @ X2 ) ) ) ) ).

% fst_snd_flip
thf(fact_829_fst__snd__flip,axiom,
    ( product_fst_real_a
    = ( comp_P3982218943028520241real_a @ product_snd_a_real
      @ ( produc6468399846837644415a_real
        @ ^ [X2: real,Y2: a] : ( product_Pair_a_real @ Y2 @ X2 ) ) ) ) ).

% fst_snd_flip
thf(fact_830_fst__snd__flip,axiom,
    ( produc7266368915318857873b_real
    = ( comp_P8173869841510096599b_real @ produc4276089182416139253od_a_b
      @ ( produc7563370495284026267od_a_b
        @ ^ [X2: product_prod_a_b,Y2: real] : ( produc6260613462353114019od_a_b @ Y2 @ X2 ) ) ) ) ).

% fst_snd_flip
thf(fact_831_fst__snd__flip,axiom,
    ( product_fst_b_a
    = ( comp_P8445432443013323052od_b_a @ product_snd_a_b
      @ ( produc4348216232050026237od_a_b
        @ ^ [X2: b,Y2: a] : ( product_Pair_a_b @ Y2 @ X2 ) ) ) ) ).

% fst_snd_flip
thf(fact_832_snd__fst__flip,axiom,
    ( product_snd_b_real
    = ( comp_P8514091664527323699b_real @ product_fst_real_b
      @ ( produc6367669841173908169real_b
        @ ^ [X2: b,Y2: real] : ( product_Pair_real_b @ Y2 @ X2 ) ) ) ) ).

% snd_fst_flip
thf(fact_833_snd__fst__flip,axiom,
    ( product_snd_real_a
    = ( comp_P3994435691685055241real_a @ product_fst_a_real
      @ ( produc6468399846837644415a_real
        @ ^ [X2: real,Y2: a] : ( product_Pair_a_real @ Y2 @ X2 ) ) ) ) ).

% snd_fst_flip
thf(fact_834_snd__fst__flip,axiom,
    ( product_snd_real_b
    = ( comp_P3883066875231310154real_b @ product_fst_b_real
      @ ( produc6781195011795835521b_real
        @ ^ [X2: real,Y2: b] : ( product_Pair_b_real @ Y2 @ X2 ) ) ) ) ).

% snd_fst_flip
thf(fact_835_snd__fst__flip,axiom,
    ( produc7037151529651111887b_real
    = ( comp_P7154842541956054149b_real @ produc4505306568083885239od_a_b
      @ ( produc7563370495284026267od_a_b
        @ ^ [X2: product_prod_a_b,Y2: real] : ( produc6260613462353114019od_a_b @ Y2 @ X2 ) ) ) ) ).

% snd_fst_flip
thf(fact_836_snd__fst__flip,axiom,
    ( product_snd_b_a
    = ( comp_P9084872743345139181od_b_a @ product_fst_a_b
      @ ( produc4348216232050026237od_a_b
        @ ^ [X2: b,Y2: a] : ( product_Pair_a_b @ Y2 @ X2 ) ) ) ) ).

% snd_fst_flip
thf(fact_837_snd__fst__flip,axiom,
    ( produc3484788084999411615l_real
    = ( comp_P3276979369905350645l_real @ produc5828954698716094813l_real
      @ ( produc3818700948422621747l_real
        @ ^ [X2: real,Y2: real] : ( produc4511245868158468465l_real @ Y2 @ X2 ) ) ) ) ).

% snd_fst_flip
thf(fact_838_snd__fst__flip,axiom,
    ( product_snd_real_nat
    = ( comp_P5942511060023479633al_nat @ product_fst_nat_real
      @ ( produc3658697984569465395t_real
        @ ^ [X2: real,Y2: nat] : ( produc7837566107596912789t_real @ Y2 @ X2 ) ) ) ) ).

% snd_fst_flip
thf(fact_839_snd__fst__flip,axiom,
    ( product_snd_a_real
    = ( comp_P8768528715489323313a_real @ product_fst_real_a
      @ ( produc7204482282939075911real_a
        @ ^ [X2: a,Y2: real] : ( product_Pair_real_a @ Y2 @ X2 ) ) ) ) ).

% snd_fst_flip
thf(fact_840_snd__fst__flip,axiom,
    ( produc4276089182416139253od_a_b
    = ( comp_P1986170303150605363od_a_b @ produc7266368915318857873b_real
      @ ( produc4394725342292598227b_real
        @ ^ [X2: real,Y2: product_prod_a_b] : ( produc9021675809588086653b_real @ Y2 @ X2 ) ) ) ) ).

% snd_fst_flip
thf(fact_841_snd__fst__flip,axiom,
    ( product_snd_a_b
    = ( comp_P736046987085771820od_a_b @ product_fst_b_a
      @ ( produc6204743795672244857od_b_a
        @ ^ [X2: a,Y2: b] : ( product_Pair_b_a @ Y2 @ X2 ) ) ) ) ).

% snd_fst_flip
thf(fact_842_compose__const_I1_J,axiom,
    ! [F2: real > produc7716430852924023517t_real,A: real] :
      ( ( comp_r4825950202331181903t_real @ F2
        @ ^ [X2: produc7716430852924023517t_real] : A )
      = ( ^ [X2: produc7716430852924023517t_real] : ( F2 @ A ) ) ) ).

% compose_const(1)
thf(fact_843_compose__const_I1_J,axiom,
    ! [F2: real > real,A: real] :
      ( ( comp_real_real_real @ F2
        @ ^ [X2: real] : A )
      = ( ^ [X2: real] : ( F2 @ A ) ) ) ).

% compose_const(1)
thf(fact_844_compose__const_I1_J,axiom,
    ! [F2: real > $o,A: real] :
      ( ( comp_real_o_o @ F2
        @ ^ [X2: $o] : A )
      = ( ^ [X2: $o] : ( F2 @ A ) ) ) ).

% compose_const(1)
thf(fact_845_compose__const_I1_J,axiom,
    ! [F2: real > nat,A: real] :
      ( ( comp_real_nat_nat @ F2
        @ ^ [X2: nat] : A )
      = ( ^ [X2: nat] : ( F2 @ A ) ) ) ).

% compose_const(1)
thf(fact_846_compose__const_I1_J,axiom,
    ! [F2: ( a > b > c ) > product_prod_a_b > c,A: a > b > c] :
      ( ( comp_a6364899482013671645c_real @ F2
        @ ^ [X2: real] : A )
      = ( ^ [X2: real] : ( F2 @ A ) ) ) ).

% compose_const(1)
thf(fact_847_pair__qbs__morphismI,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_o,F2: product_prod_real_o > real,Z: quasi_borel_real] :
      ( ! [Alpha: real > real,Beta: real > $o] :
          ( ( member_real_real @ Alpha @ ( qbs_Mx_real @ X3 ) )
         => ( ( member_real_o @ Beta @ ( qbs_Mx_o @ Y3 ) )
           => ( member_real_real
              @ ( comp_P7324324619018053534l_real @ F2
                @ ^ [R: real] : ( product_Pair_real_o @ ( Alpha @ R ) @ ( Beta @ R ) ) )
              @ ( qbs_Mx_real @ Z ) ) ) )
     => ( member2397750512517714755o_real @ F2 @ ( qbs_mo2263107299321320071o_real @ ( binary4057238779996960701real_o @ X3 @ Y3 ) @ Z ) ) ) ).

% pair_qbs_morphismI
thf(fact_848_pair__qbs__morphismI,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_o,F2: product_prod_real_o > $o,Z: quasi_borel_o] :
      ( ! [Alpha: real > real,Beta: real > $o] :
          ( ( member_real_real @ Alpha @ ( qbs_Mx_real @ X3 ) )
         => ( ( member_real_o @ Beta @ ( qbs_Mx_o @ Y3 ) )
           => ( member_real_o
              @ ( comp_P4035609806083913856o_real @ F2
                @ ^ [R: real] : ( product_Pair_real_o @ ( Alpha @ R ) @ ( Beta @ R ) ) )
              @ ( qbs_Mx_o @ Z ) ) ) )
     => ( member6922346998996484951al_o_o @ F2 @ ( qbs_mo8478100829156377981al_o_o @ ( binary4057238779996960701real_o @ X3 @ Y3 ) @ Z ) ) ) ).

% pair_qbs_morphismI
thf(fact_849_pair__qbs__morphismI,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_o,F2: product_prod_real_o > nat,Z: quasi_borel_nat] :
      ( ! [Alpha: real > real,Beta: real > $o] :
          ( ( member_real_real @ Alpha @ ( qbs_Mx_real @ X3 ) )
         => ( ( member_real_o @ Beta @ ( qbs_Mx_o @ Y3 ) )
           => ( member_real_nat
              @ ( comp_P1518313335960462658t_real @ F2
                @ ^ [R: real] : ( product_Pair_real_o @ ( Alpha @ R ) @ ( Beta @ R ) ) )
              @ ( qbs_Mx_nat @ Z ) ) ) )
     => ( member643724537881924711_o_nat @ F2 @ ( qbs_mo2709815783427026219_o_nat @ ( binary4057238779996960701real_o @ X3 @ Y3 ) @ Z ) ) ) ).

% pair_qbs_morphismI
thf(fact_850_pair__qbs__morphismI,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_nat,F2: produc3741383161447143261al_nat > real,Z: quasi_borel_real] :
      ( ! [Alpha: real > real,Beta: real > nat] :
          ( ( member_real_real @ Alpha @ ( qbs_Mx_real @ X3 ) )
         => ( ( member_real_nat @ Beta @ ( qbs_Mx_nat @ Y3 ) )
           => ( member_real_real
              @ ( comp_P2062867634480536980l_real @ F2
                @ ^ [R: real] : ( produc3181502643871035669al_nat @ ( Alpha @ R ) @ ( Beta @ R ) ) )
              @ ( qbs_Mx_real @ Z ) ) ) )
     => ( member8170672204161627299t_real @ F2 @ ( qbs_mo2914239553347605137t_real @ ( binary7505510235992378091al_nat @ X3 @ Y3 ) @ Z ) ) ) ).

% pair_qbs_morphismI
thf(fact_851_pair__qbs__morphismI,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_nat,F2: produc3741383161447143261al_nat > $o,Z: quasi_borel_o] :
      ( ! [Alpha: real > real,Beta: real > nat] :
          ( ( member_real_real @ Alpha @ ( qbs_Mx_real @ X3 ) )
         => ( ( member_real_nat @ Beta @ ( qbs_Mx_nat @ Y3 ) )
           => ( member_real_o
              @ ( comp_P8584947193023372810o_real @ F2
                @ ^ [R: real] : ( produc3181502643871035669al_nat @ ( Alpha @ R ) @ ( Beta @ R ) ) )
              @ ( qbs_Mx_o @ Z ) ) ) )
     => ( member5336788418610354679_nat_o @ F2 @ ( qbs_mo6997016501208148467_nat_o @ ( binary7505510235992378091al_nat @ X3 @ Y3 ) @ Z ) ) ) ).

% pair_qbs_morphismI
thf(fact_852_pair__qbs__morphismI,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_nat,F2: produc3741383161447143261al_nat > nat,Z: quasi_borel_nat] :
      ( ! [Alpha: real > real,Beta: real > nat] :
          ( ( member_real_real @ Alpha @ ( qbs_Mx_real @ X3 ) )
         => ( ( member_real_nat @ Beta @ ( qbs_Mx_nat @ Y3 ) )
           => ( member_real_nat
              @ ( comp_P6248124061026825784t_real @ F2
                @ ^ [R: real] : ( produc3181502643871035669al_nat @ ( Alpha @ R ) @ ( Beta @ R ) ) )
              @ ( qbs_Mx_nat @ Z ) ) ) )
     => ( member6474720949954373063at_nat @ F2 @ ( qbs_mo5788368670921675317at_nat @ ( binary7505510235992378091al_nat @ X3 @ Y3 ) @ Z ) ) ) ).

% pair_qbs_morphismI
thf(fact_853_pair__qbs__morphismI,axiom,
    ! [X3: quasi_borel_o,Y3: quasi_borel_real,F2: product_prod_o_real > real,Z: quasi_borel_real] :
      ( ! [Alpha: real > $o,Beta: real > real] :
          ( ( member_real_o @ Alpha @ ( qbs_Mx_o @ X3 ) )
         => ( ( member_real_real @ Beta @ ( qbs_Mx_real @ Y3 ) )
           => ( member_real_real
              @ ( comp_P4165359869975341104l_real @ F2
                @ ^ [R: real] : ( product_Pair_o_real @ ( Alpha @ R ) @ ( Beta @ R ) ) )
              @ ( qbs_Mx_real @ Z ) ) ) )
     => ( member5412739015385547989l_real @ F2 @ ( qbs_mo5278095802189153305l_real @ ( binary2548174404955791127o_real @ X3 @ Y3 ) @ Z ) ) ) ).

% pair_qbs_morphismI
thf(fact_854_pair__qbs__morphismI,axiom,
    ! [X3: quasi_borel_o,Y3: quasi_borel_real,F2: product_prod_o_real > $o,Z: quasi_borel_o] :
      ( ! [Alpha: real > $o,Beta: real > real] :
          ( ( member_real_o @ Alpha @ ( qbs_Mx_o @ X3 ) )
         => ( ( member_real_real @ Beta @ ( qbs_Mx_real @ Y3 ) )
           => ( member_real_o
              @ ( comp_P958736042193659502o_real @ F2
                @ ^ [R: real] : ( product_Pair_o_real @ ( Alpha @ R ) @ ( Beta @ R ) ) )
              @ ( qbs_Mx_o @ Z ) ) ) )
     => ( member997378602583572549real_o @ F2 @ ( qbs_mo2553132432743465579real_o @ ( binary2548174404955791127o_real @ X3 @ Y3 ) @ Z ) ) ) ).

% pair_qbs_morphismI
thf(fact_855_pair__qbs__morphismI,axiom,
    ! [X3: quasi_borel_o,Y3: quasi_borel_real,F2: product_prod_o_real > nat,Z: quasi_borel_nat] :
      ( ! [Alpha: real > $o,Beta: real > real] :
          ( ( member_real_o @ Alpha @ ( qbs_Mx_o @ X3 ) )
         => ( ( member_real_real @ Beta @ ( qbs_Mx_real @ Y3 ) )
           => ( member_real_nat
              @ ( comp_P4275935158355168980t_real @ F2
                @ ^ [R: real] : ( product_Pair_o_real @ ( Alpha @ R ) @ ( Beta @ R ) ) )
              @ ( qbs_Mx_nat @ Z ) ) ) )
     => ( member1545846085724057337al_nat @ F2 @ ( qbs_mo3611937331269158845al_nat @ ( binary2548174404955791127o_real @ X3 @ Y3 ) @ Z ) ) ) ).

% pair_qbs_morphismI
thf(fact_856_pair__qbs__morphismI,axiom,
    ! [X3: quasi_borel_o,Y3: quasi_borel_o,F2: product_prod_o_o > real,Z: quasi_borel_real] :
      ( ! [Alpha: real > $o,Beta: real > $o] :
          ( ( member_real_o @ Alpha @ ( qbs_Mx_o @ X3 ) )
         => ( ( member_real_o @ Beta @ ( qbs_Mx_o @ Y3 ) )
           => ( member_real_real
              @ ( comp_P2546925240435627614l_real @ F2
                @ ^ [R: real] : ( product_Pair_o_o @ ( Alpha @ R ) @ ( Beta @ R ) ) )
              @ ( qbs_Mx_real @ Z ) ) ) )
     => ( member3592995702671057773o_real @ F2 @ ( qbs_mo6235628468027255387o_real @ ( binary9159730317414444269bs_o_o @ X3 @ Y3 ) @ Z ) ) ) ).

% pair_qbs_morphismI
thf(fact_857_pair__qbs__Mx__def,axiom,
    ( binary6447122689459668562real_o
    = ( ^ [X: quasi_borel_real,Y: quasi_borel_o] :
          ( collec1207520706270639105real_o
          @ ^ [F: real > product_prod_real_o] :
              ( ( member_real_real @ ( comp_P7324324619018053534l_real @ product_fst_real_o @ F ) @ ( qbs_Mx_real @ X ) )
              & ( member_real_o @ ( comp_P4035609806083913856o_real @ product_snd_real_o @ F ) @ ( qbs_Mx_o @ Y ) ) ) ) ) ) ).

% pair_qbs_Mx_def
thf(fact_858_pair__qbs__Mx__def,axiom,
    ( binary6161091909186915222al_nat
    = ( ^ [X: quasi_borel_real,Y: quasi_borel_nat] :
          ( collec2547682538869862867al_nat
          @ ^ [F: real > produc3741383161447143261al_nat] :
              ( ( member_real_real @ ( comp_P2062867634480536980l_real @ product_fst_real_nat @ F ) @ ( qbs_Mx_real @ X ) )
              & ( member_real_nat @ ( comp_P6248124061026825784t_real @ product_snd_real_nat @ F ) @ ( qbs_Mx_nat @ Y ) ) ) ) ) ) ).

% pair_qbs_Mx_def
thf(fact_859_pair__qbs__Mx__def,axiom,
    ( binary4938058314418498988o_real
    = ( ^ [X: quasi_borel_o,Y: quasi_borel_real] :
          ( collec2844253176276905363o_real
          @ ^ [F: real > product_prod_o_real] :
              ( ( member_real_o @ ( comp_P958736042193659502o_real @ product_fst_o_real @ F ) @ ( qbs_Mx_o @ X ) )
              & ( member_real_real @ ( comp_P4165359869975341104l_real @ product_snd_o_real @ F ) @ ( qbs_Mx_real @ Y ) ) ) ) ) ) ).

% pair_qbs_Mx_def
thf(fact_860_pair__qbs__Mx__def,axiom,
    ( binary3036577528634221720Mx_o_o
    = ( ^ [X: quasi_borel_o,Y: quasi_borel_o] :
          ( collec6547829330364130717od_o_o
          @ ^ [F: real > product_prod_o_o] :
              ( ( member_real_o @ ( comp_P7609422216084732352o_real @ product_fst_o_o @ F ) @ ( qbs_Mx_o @ X ) )
              & ( member_real_o @ ( comp_P7609422216084732352o_real @ product_snd_o_o @ F ) @ ( qbs_Mx_o @ Y ) ) ) ) ) ) ).

% pair_qbs_Mx_def
thf(fact_861_pair__qbs__Mx__def,axiom,
    ( binary7314765211898530512_o_nat
    = ( ^ [X: quasi_borel_o,Y: quasi_borel_nat] :
          ( collec2604536313836085047_o_nat
          @ ^ [F: real > product_prod_o_nat] :
              ( ( member_real_o @ ( comp_P2340352180389457098o_real @ product_fst_o_nat @ F ) @ ( qbs_Mx_o @ X ) )
              & ( member_real_nat @ ( comp_P1507898882101401464t_real @ product_snd_o_nat @ F ) @ ( qbs_Mx_nat @ Y ) ) ) ) ) ) ).

% pair_qbs_Mx_def
thf(fact_862_pair__qbs__Mx__def,axiom,
    ( binary1194064536151940014_nat_o
    = ( ^ [X: quasi_borel_nat,Y: quasi_borel_o] :
          ( collec3652139436014388701_nat_o
          @ ^ [F: real > product_prod_nat_o] :
              ( ( member_real_nat @ ( comp_P789980896094113310t_real @ product_fst_nat_o @ F ) @ ( qbs_Mx_nat @ X ) )
              & ( member_real_o @ ( comp_P1872995966849966244o_real @ product_snd_nat_o @ F ) @ ( qbs_Mx_o @ Y ) ) ) ) ) ) ).

% pair_qbs_Mx_def
thf(fact_863_pair__qbs__Mx__def,axiom,
    ( binary2255896570119324986at_nat
    = ( ^ [X: quasi_borel_nat,Y: quasi_borel_nat] :
          ( collec6846052195855388407at_nat
          @ ^ [F: real > product_prod_nat_nat] :
              ( ( member_real_nat @ ( comp_P543440408108907612t_real @ product_fst_nat_nat @ F ) @ ( qbs_Mx_nat @ X ) )
              & ( member_real_nat @ ( comp_P543440408108907612t_real @ product_snd_nat_nat @ F ) @ ( qbs_Mx_nat @ Y ) ) ) ) ) ) ).

% pair_qbs_Mx_def
thf(fact_864_pair__qbs__Mx__def,axiom,
    ( binary6833691656172727154l_real
    = ( ^ [X: quasi_borel_real,Y: quasi_borel_real] :
          ( collec4958669439909949999l_real
          @ ^ [F: real > produc2422161461964618553l_real] :
              ( ( member_real_real @ ( comp_P4894738870877013744l_real @ produc5828954698716094813l_real @ F ) @ ( qbs_Mx_real @ X ) )
              & ( member_real_real @ ( comp_P4894738870877013744l_real @ produc3484788084999411615l_real @ F ) @ ( qbs_Mx_real @ Y ) ) ) ) ) ) ).

% pair_qbs_Mx_def
thf(fact_865_pair__qbs__Mx__def,axiom,
    ( binary1593783336058016534t_real
    = ( ^ [X: quasi_borel_nat,Y: quasi_borel_real] :
          ( collec8581060436531035475t_real
          @ ^ [F: real > produc7716430852924023517t_real] :
              ( ( member_real_nat @ ( comp_P7294336520020869560t_real @ product_fst_nat_real @ F ) @ ( qbs_Mx_nat @ X ) )
              & ( member_real_real @ ( comp_P9198714165227464980l_real @ product_snd_nat_real @ F ) @ ( qbs_Mx_real @ Y ) ) ) ) ) ) ).

% pair_qbs_Mx_def
thf(fact_866_pair__qbs__Mx__def,axiom,
    ( binary2731563775470309560real_a
    = ( ^ [X: quasi_borel_real,Y: quasi_borel_a] :
          ( collec6938821005316324327real_a
          @ ^ [F: real > product_prod_real_a] :
              ( ( member_real_real @ ( comp_P3002741825051030916l_real @ product_fst_real_a @ F ) @ ( qbs_Mx_real @ X ) )
              & ( member_real_a @ ( comp_P7874914735527052288a_real @ product_snd_real_a @ F ) @ ( qbs_Mx_a @ Y ) ) ) ) ) ) ).

% pair_qbs_Mx_def
thf(fact_867_qbs__Mx__is__morphisms,axiom,
    ( qbs_Mx_nat
    = ( qbs_mo6567951568834356598al_nat @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) ) ) ).

% qbs_Mx_is_morphisms
thf(fact_868_qbs__Mx__is__morphisms,axiom,
    ( qbs_Mx_b_c
    = ( qbs_mo6398413456135019852al_b_c @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) ) ) ).

% qbs_Mx_is_morphisms
thf(fact_869_qbs__Mx__is__morphisms,axiom,
    ( qbs_Mx_a_b_c
    = ( qbs_mo534596117765811055_a_b_c @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) ) ) ).

% qbs_Mx_is_morphisms
thf(fact_870_internal__case__prod__def,axiom,
    produc3154363079305547638_a_b_c = produc8409101302566321868_a_b_c ).

% internal_case_prod_def
thf(fact_871_internal__case__prod__def,axiom,
    produc5508868222326971654_a_b_c = produc8366947261062197552_a_b_c ).

% internal_case_prod_def
thf(fact_872_internal__case__prod__def,axiom,
    produc318858384453529021_a_b_c = produc6028431345588019475_a_b_c ).

% internal_case_prod_def
thf(fact_873_internal__case__prod__def,axiom,
    produc4017796711748182383al_b_c = produc2835462372567216025al_b_c ).

% internal_case_prod_def
thf(fact_874_internal__case__prod__def,axiom,
    produc6805252293720858416al_a_c = produc5622917954539892058al_a_c ).

% internal_case_prod_def
thf(fact_875_internal__case__prod__def,axiom,
    produc1944086356765227344al_b_c = produc7198824580026001574al_b_c ).

% internal_case_prod_def
thf(fact_876_fun_Omap__ident,axiom,
    ! [T2: real > real] :
      ( ( comp_real_real_real
        @ ^ [X2: real] : X2
        @ T2 )
      = T2 ) ).

% fun.map_ident
thf(fact_877_exp__qbs__closed2,axiom,
    ! [X3: quasi_7706945541993221175real_a,Y3: quasi_borel_b_c] : ( qbs_cl105519000001097878_a_b_c @ ( qbs_mo8653977514671865831_a_b_c @ X3 @ Y3 ) @ ( expone4204337439263262707_a_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_closed2
thf(fact_878_exp__qbs__closed2,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_nat] : ( qbs_closed2_real_nat @ ( qbs_mo6567951568834356598al_nat @ X3 @ Y3 ) @ ( expone3954210144133575042al_nat @ X3 @ Y3 ) ) ).

% exp_qbs_closed2
thf(fact_879_exp__qbs__closed2,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_b_c] : ( qbs_closed2_real_b_c @ ( qbs_mo6398413456135019852al_b_c @ X3 @ Y3 ) @ ( expone303615731128029528al_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_closed2
thf(fact_880_exp__qbs__closed2,axiom,
    ! [X3: quasi_borel_real,Y3: quasi_borel_a_b_c] : ( qbs_cl8895268087018464150_a_b_c @ ( qbs_mo534596117765811055_a_b_c @ X3 @ Y3 ) @ ( expone1129265718773867619_a_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_closed2
thf(fact_881_exp__qbs__closed2,axiom,
    ! [X3: quasi_borel_nat,Y3: quasi_borel_real] : ( qbs_closed2_nat_real @ ( qbs_mo2000642995705457910t_real @ X3 @ Y3 ) @ ( expone8610273607859452162t_real @ X3 @ Y3 ) ) ).

% exp_qbs_closed2
thf(fact_882_exp__qbs__closed2,axiom,
    ! [X3: quasi_borel_a,Y3: quasi_borel_b_c] : ( qbs_closed2_a_b_c @ ( qbs_morphism_a_b_c @ X3 @ Y3 ) @ ( expone5572123575668448672_a_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_closed2
thf(fact_883_exp__qbs__closed2,axiom,
    ! [X3: quasi_borel_b,Y3: quasi_borel_c] : ( qbs_closed2_b_c @ ( qbs_morphism_b_c @ X3 @ Y3 ) @ ( expone4235142314707039685Mx_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_closed2
thf(fact_884_exp__qbs__closed2,axiom,
    ! [X3: quasi_8309430206217406798od_a_b,Y3: quasi_borel_c] : ( qbs_cl6162802224411288007_a_b_c @ ( qbs_mo2296058654870477648_a_b_c @ X3 @ Y3 ) @ ( expone95873867685489500_a_b_c @ X3 @ Y3 ) ) ).

% exp_qbs_closed2
thf(fact_885_qbs__closed2__def,axiom,
    ( qbs_closed2_real
    = ( ^ [X: set_real,Mx: set_real_real] :
        ! [X2: real] :
          ( ( member_real @ X2 @ X )
         => ( member_real_real
            @ ^ [R: real] : X2
            @ Mx ) ) ) ) ).

% qbs_closed2_def
thf(fact_886_qbs__closed2__def,axiom,
    ( qbs_closed2_o
    = ( ^ [X: set_o,Mx: set_real_o] :
        ! [X2: $o] :
          ( ( member_o @ X2 @ X )
         => ( member_real_o
            @ ^ [R: real] : X2
            @ Mx ) ) ) ) ).

% qbs_closed2_def
thf(fact_887_qbs__closed2__def,axiom,
    ( qbs_closed2_nat
    = ( ^ [X: set_nat,Mx: set_real_nat] :
        ! [X2: nat] :
          ( ( member_nat @ X2 @ X )
         => ( member_real_nat
            @ ^ [R: real] : X2
            @ Mx ) ) ) ) ).

% qbs_closed2_def
thf(fact_888_qbs__closed2__def,axiom,
    ( qbs_closed2_b_c
    = ( ^ [X: set_b_c,Mx: set_real_b_c] :
        ! [X2: b > c] :
          ( ( member_b_c @ X2 @ X )
         => ( member_real_b_c
            @ ^ [R: real] : X2
            @ Mx ) ) ) ) ).

% qbs_closed2_def
thf(fact_889_qbs__closed2__def,axiom,
    ( qbs_closed2_a_b_c
    = ( ^ [X: set_a_b_c,Mx: set_real_a_b_c] :
        ! [X2: a > b > c] :
          ( ( member_a_b_c @ X2 @ X )
         => ( member_real_a_b_c
            @ ^ [R: real] : X2
            @ Mx ) ) ) ) ).

% qbs_closed2_def
thf(fact_890_qbs__closed2I,axiom,
    ! [X3: set_real,Mx2: set_real_real] :
      ( ! [X5: real] :
          ( ( member_real @ X5 @ X3 )
         => ( member_real_real
            @ ^ [R: real] : X5
            @ Mx2 ) )
     => ( qbs_closed2_real @ X3 @ Mx2 ) ) ).

% qbs_closed2I
thf(fact_891_qbs__closed2I,axiom,
    ! [X3: set_o,Mx2: set_real_o] :
      ( ! [X5: $o] :
          ( ( member_o @ X5 @ X3 )
         => ( member_real_o
            @ ^ [R: real] : X5
            @ Mx2 ) )
     => ( qbs_closed2_o @ X3 @ Mx2 ) ) ).

% qbs_closed2I
thf(fact_892_qbs__closed2I,axiom,
    ! [X3: set_nat,Mx2: set_real_nat] :
      ( ! [X5: nat] :
          ( ( member_nat @ X5 @ X3 )
         => ( member_real_nat
            @ ^ [R: real] : X5
            @ Mx2 ) )
     => ( qbs_closed2_nat @ X3 @ Mx2 ) ) ).

% qbs_closed2I
thf(fact_893_qbs__closed2I,axiom,
    ! [X3: set_b_c,Mx2: set_real_b_c] :
      ( ! [X5: b > c] :
          ( ( member_b_c @ X5 @ X3 )
         => ( member_real_b_c
            @ ^ [R: real] : X5
            @ Mx2 ) )
     => ( qbs_closed2_b_c @ X3 @ Mx2 ) ) ).

% qbs_closed2I
thf(fact_894_qbs__closed2I,axiom,
    ! [X3: set_real_real,Mx2: set_real_real_real] :
      ( ! [X5: real > real] :
          ( ( member_real_real @ X5 @ X3 )
         => ( member8878224140454985689l_real
            @ ^ [R: real] : X5
            @ Mx2 ) )
     => ( qbs_cl2097862303545872641l_real @ X3 @ Mx2 ) ) ).

% qbs_closed2I
thf(fact_895_qbs__closed2I,axiom,
    ! [X3: set_real_o,Mx2: set_real_real_o] :
      ( ! [X5: real > $o] :
          ( ( member_real_o @ X5 @ X3 )
         => ( member_real_real_o
            @ ^ [R: real] : X5
            @ Mx2 ) )
     => ( qbs_closed2_real_o @ X3 @ Mx2 ) ) ).

% qbs_closed2I
thf(fact_896_qbs__closed2I,axiom,
    ! [X3: set_real_nat,Mx2: set_real_real_nat] :
      ( ! [X5: real > nat] :
          ( ( member_real_nat @ X5 @ X3 )
         => ( member_real_real_nat
            @ ^ [R: real] : X5
            @ Mx2 ) )
     => ( qbs_closed2_real_nat @ X3 @ Mx2 ) ) ).

% qbs_closed2I
thf(fact_897_qbs__closed2I,axiom,
    ! [X3: set_o_real,Mx2: set_real_o_real] :
      ( ! [X5: $o > real] :
          ( ( member_o_real @ X5 @ X3 )
         => ( member_real_o_real
            @ ^ [R: real] : X5
            @ Mx2 ) )
     => ( qbs_closed2_o_real @ X3 @ Mx2 ) ) ).

% qbs_closed2I
thf(fact_898_qbs__closed2I,axiom,
    ! [X3: set_nat_real,Mx2: set_real_nat_real] :
      ( ! [X5: nat > real] :
          ( ( member_nat_real @ X5 @ X3 )
         => ( member_real_nat_real
            @ ^ [R: real] : X5
            @ Mx2 ) )
     => ( qbs_closed2_nat_real @ X3 @ Mx2 ) ) ).

% qbs_closed2I
thf(fact_899_qbs__closed2I,axiom,
    ! [X3: set_Pr3745489628154206067_a_b_c,Mx2: set_re227179899959045694_a_b_c] :
      ( ! [X5: product_prod_a_b > c] :
          ( ( member1080921174361771732_a_b_c @ X5 @ X3 )
         => ( member3234269468440695583_a_b_c
            @ ^ [R: real] : X5
            @ Mx2 ) )
     => ( qbs_cl6162802224411288007_a_b_c @ X3 @ Mx2 ) ) ).

% qbs_closed2I
thf(fact_900_convol__o,axiom,
    ! [F2: real > produc7716430852924023517t_real,G2: real > produc7716430852924023517t_real,H: produc7716430852924023517t_real > real] :
      ( ( comp_r2188859771317388101t_real @ ( bNF_co3113411965631273301t_real @ F2 @ G2 ) @ H )
      = ( bNF_co2828654319395810420t_real @ ( comp_r4825950202331181903t_real @ F2 @ H ) @ ( comp_r4825950202331181903t_real @ G2 @ H ) ) ) ).

% convol_o
thf(fact_901_convol__o,axiom,
    ! [F2: real > real,G2: real > real,H: real > real] :
      ( ( comp_r4464757161866874646l_real @ ( bNF_co7388595451723801839l_real @ F2 @ G2 ) @ H )
      = ( bNF_co7388595451723801839l_real @ ( comp_real_real_real @ F2 @ H ) @ ( comp_real_real_real @ G2 @ H ) ) ) ).

% convol_o
thf(fact_902_convol__o,axiom,
    ! [F2: real > $o,G2: real > $o,H: $o > real] :
      ( ( comp_r7319636394165045824_o_o_o @ ( bNF_convol_real_o_o @ F2 @ G2 ) @ H )
      = ( bNF_convol_o_o_o @ ( comp_real_o_o @ F2 @ H ) @ ( comp_real_o_o @ G2 @ H ) ) ) ).

% convol_o
thf(fact_903_convol__o,axiom,
    ! [F2: real > nat,G2: real > nat,H: nat > real] :
      ( ( comp_r2274689946347734786at_nat @ ( bNF_co2503443643428117431at_nat @ F2 @ G2 ) @ H )
      = ( bNF_co805650143699787099at_nat @ ( comp_real_nat_nat @ F2 @ H ) @ ( comp_real_nat_nat @ G2 @ H ) ) ) ).

% convol_o
thf(fact_904_convol__o,axiom,
    ! [F2: ( a > b > c ) > product_prod_a_b > c,G2: ( a > b > c ) > product_prod_a_b > c,H: real > a > b > c] :
      ( ( comp_a5729825720005968533c_real @ ( bNF_co2532616626889521512_a_b_c @ F2 @ G2 ) @ H )
      = ( bNF_co3546090298090268817_a_b_c @ ( comp_a6364899482013671645c_real @ F2 @ H ) @ ( comp_a6364899482013671645c_real @ G2 @ H ) ) ) ).

% convol_o
thf(fact_905_convol__o,axiom,
    ! [F2: real > nat,G2: real > real,H: produc7716430852924023517t_real > real] :
      ( ( comp_r4825950202331181903t_real @ ( bNF_co3869861653827910419t_real @ F2 @ G2 ) @ H )
      = ( bNF_co3215693860977014834t_real @ ( comp_r2336473409123003196t_real @ F2 @ H ) @ ( comp_r8349034141028359008t_real @ G2 @ H ) ) ) ).

% convol_o
thf(fact_906_fun_Omap__comp,axiom,
    ! [G2: $o > $o,F2: real > $o,V: $o > real] :
      ( ( comp_o_o_o @ G2 @ ( comp_real_o_o @ F2 @ V ) )
      = ( comp_real_o_o @ ( comp_o_o_real @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_907_fun_Omap__comp,axiom,
    ! [G2: nat > nat,F2: real > nat,V: nat > real] :
      ( ( comp_nat_nat_nat @ G2 @ ( comp_real_nat_nat @ F2 @ V ) )
      = ( comp_real_nat_nat @ ( comp_nat_nat_real @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_908_fun_Omap__comp,axiom,
    ! [G2: real > real,F2: real > real,V: real > real] :
      ( ( comp_real_real_real @ G2 @ ( comp_real_real_real @ F2 @ V ) )
      = ( comp_real_real_real @ ( comp_real_real_real @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_909_fun_Omap__comp,axiom,
    ! [G2: real > $o,F2: $o > real,V: $o > $o] :
      ( ( comp_real_o_o @ G2 @ ( comp_o_real_o @ F2 @ V ) )
      = ( comp_o_o_o @ ( comp_real_o_o @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_910_fun_Omap__comp,axiom,
    ! [G2: real > $o,F2: real > real,V: $o > real] :
      ( ( comp_real_o_o @ G2 @ ( comp_real_real_o @ F2 @ V ) )
      = ( comp_real_o_o @ ( comp_real_o_real @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_911_fun_Omap__comp,axiom,
    ! [G2: real > nat,F2: nat > real,V: nat > nat] :
      ( ( comp_real_nat_nat @ G2 @ ( comp_nat_real_nat @ F2 @ V ) )
      = ( comp_nat_nat_nat @ ( comp_real_nat_nat @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_912_fun_Omap__comp,axiom,
    ! [G2: real > nat,F2: real > real,V: nat > real] :
      ( ( comp_real_nat_nat @ G2 @ ( comp_real_real_nat @ F2 @ V ) )
      = ( comp_real_nat_nat @ ( comp_real_nat_real @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_913_fun_Omap__comp,axiom,
    ! [G2: real > produc7716430852924023517t_real,F2: real > real,V: produc7716430852924023517t_real > real] :
      ( ( comp_r4825950202331181903t_real @ G2 @ ( comp_r8349034141028359008t_real @ F2 @ V ) )
      = ( comp_r4825950202331181903t_real @ ( comp_r4030900867926482106l_real @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_914_fun_Omap__comp,axiom,
    ! [G2: produc7716430852924023517t_real > produc7716430852924023517t_real,F2: real > produc7716430852924023517t_real,V: produc7716430852924023517t_real > real] :
      ( ( comp_P5614709513016865274t_real @ G2 @ ( comp_r4825950202331181903t_real @ F2 @ V ) )
      = ( comp_r4825950202331181903t_real @ ( comp_P6455894728016498639l_real @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_915_fun_Omap__comp,axiom,
    ! [G2: real > produc7716430852924023517t_real,F2: produc7716430852924023517t_real > real,V: produc7716430852924023517t_real > produc7716430852924023517t_real] :
      ( ( comp_r4825950202331181903t_real @ G2 @ ( comp_P1550655964263599733t_real @ F2 @ V ) )
      = ( comp_P5614709513016865274t_real @ ( comp_r4825950202331181903t_real @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_916_real_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: real > b > c,Y3: sigma_measure_b_c] :
      ( ( member_real_b_c @ K2 @ ( sigma_219859910464686500al_b_c @ borel_5078946678739801102l_real @ Y3 ) )
     => ( member_real_b_c @ K2 @ ( qbs_mo6398413456135019852al_b_c @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur1405370791648741458bs_b_c @ Y3 ) ) ) ) ).

% real.qbs_morphism_measurable_intro
thf(fact_917_real_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: real > a > b > c,Y3: sigma_measure_a_b_c] :
      ( ( member_real_a_b_c @ K2 @ ( sigma_8538461840762587415_a_b_c @ borel_5078946678739801102l_real @ Y3 ) )
     => ( member_real_a_b_c @ K2 @ ( qbs_mo534596117765811055_a_b_c @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur1184878058648827625_a_b_c @ Y3 ) ) ) ) ).

% real.qbs_morphism_measurable_intro
thf(fact_918_real_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: real > produc2422161461964618553l_real,Y3: sigma_2308072346491277622l_real] :
      ( ( member9086635009091248365l_real @ K2 @ ( sigma_7998147297565726139l_real @ borel_5078946678739801102l_real @ Y3 ) )
     => ( member9086635009091248365l_real @ K2 @ ( qbs_mo6845038431372961811l_real @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur3029786804310284173l_real @ Y3 ) ) ) ) ).

% real.qbs_morphism_measurable_intro
thf(fact_919_real_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: real > produc7716430852924023517t_real,Y3: sigma_5310753476256395226t_real] :
      ( ( member969486235890772753t_real @ K2 @ ( sigma_2975298441655967327t_real @ borel_5078946678739801102l_real @ Y3 ) )
     => ( member969486235890772753t_real @ K2 @ ( qbs_mo3601394221918002359t_real @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur2011440102552004913t_real @ Y3 ) ) ) ) ).

% real.qbs_morphism_measurable_intro
thf(fact_920_real_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: real > real,Y3: sigma_measure_real] :
      ( ( member_real_real @ K2 @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ Y3 ) )
     => ( member_real_real @ K2 @ ( qbs_mo5229770564518008146l_real @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur6875533127466166616s_real @ Y3 ) ) ) ) ).

% real.qbs_morphism_measurable_intro
thf(fact_921_real_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: real > $o,Y3: sigma_measure_o] :
      ( ( member_real_o @ K2 @ ( sigma_3939073009482781210real_o @ borel_5078946678739801102l_real @ Y3 ) )
     => ( member_real_o @ K2 @ ( qbs_morphism_real_o @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur2705496967258476524_qbs_o @ Y3 ) ) ) ) ).

% real.qbs_morphism_measurable_intro
thf(fact_922_real_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: real > nat,Y3: sigma_measure_nat] :
      ( ( member_real_nat @ K2 @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ Y3 ) )
     => ( member_real_nat @ K2 @ ( qbs_mo6567951568834356598al_nat @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur4416158800429964412bs_nat @ Y3 ) ) ) ) ).

% real.qbs_morphism_measurable_intro
thf(fact_923_snd__sndOp,axiom,
    ! [P2: real > real > $o,Q2: real > product_prod_a_b > $o] :
      ( produc4276089182416139253od_a_b
      = ( comp_P1649614271169106373od_a_b @ produc4276089182416139253od_a_b @ ( bNF_sn4495111618435390810od_a_b @ P2 @ Q2 ) ) ) ).

% snd_sndOp
thf(fact_924_snd__sndOp,axiom,
    ! [P2: a > a > $o,Q2: a > b > $o] :
      ( product_snd_a_b
      = ( comp_P2009515992434452078od_a_b @ product_snd_a_b @ ( bNF_sndOp_a_a_b @ P2 @ Q2 ) ) ) ).

% snd_sndOp
thf(fact_925_fst__fstOp,axiom,
    ! [P2: a > b > $o,Q2: b > b > $o] :
      ( product_fst_a_b
      = ( comp_P2648956292766268207od_a_b @ product_fst_a_b @ ( bNF_fstOp_a_b_b @ P2 @ Q2 ) ) ) ).

% fst_fstOp
thf(fact_926_fst__fstOp,axiom,
    ! [P2: real > real > $o,Q2: real > real > $o] :
      ( produc5828954698716094813l_real
      = ( comp_P3276979369905350645l_real @ produc5828954698716094813l_real @ ( bNF_fs3847565544535062584l_real @ P2 @ Q2 ) ) ) ).

% fst_fstOp
thf(fact_927_fst__fstOp,axiom,
    ! [P2: real > a > $o,Q2: a > real > $o] :
      ( produc5828954698716094813l_real
      = ( comp_P549788833721629281l_real @ product_fst_real_a @ ( bNF_fs5479770303754431564a_real @ P2 @ Q2 ) ) ) ).

% fst_fstOp
thf(fact_928_fst__fstOp,axiom,
    ! [P2: nat > real > $o,Q2: real > real > $o] :
      ( product_fst_nat_real
      = ( comp_P694186714645584081t_real @ product_fst_nat_real @ ( bNF_fs3113317720638777948l_real @ P2 @ Q2 ) ) ) ).

% fst_fstOp
thf(fact_929_fst__fstOp,axiom,
    ! [P2: real > real > $o,Q2: real > a > $o] :
      ( product_fst_real_a
      = ( comp_P1589298742348195979real_a @ produc5828954698716094813l_real @ ( bNF_fs6109789071227381362real_a @ P2 @ Q2 ) ) ) ).

% fst_fstOp
thf(fact_930_fst__fstOp,axiom,
    ! [P2: real > a > $o,Q2: a > a > $o] :
      ( product_fst_real_a
      = ( comp_P62423180901884703real_a @ product_fst_real_a @ ( bNF_fstOp_real_a_a @ P2 @ Q2 ) ) ) ).

% fst_fstOp
thf(fact_931_fst__fstOp,axiom,
    ! [P2: real > real > $o,Q2: real > product_prod_a_b > $o] :
      ( produc4505306568083885239od_a_b
      = ( comp_P544700997026044725od_a_b @ produc5828954698716094813l_real @ ( bNF_fs1652773232771623964od_a_b @ P2 @ Q2 ) ) ) ).

% fst_fstOp
thf(fact_932_fst__fstOp,axiom,
    ! [P2: real > a > $o,Q2: a > product_prod_a_b > $o] :
      ( produc4505306568083885239od_a_b
      = ( comp_P7339791398657499593od_a_b @ product_fst_real_a @ ( bNF_fs5697544725373665032od_a_b @ P2 @ Q2 ) ) ) ).

% fst_fstOp
thf(fact_933_fst__fstOp,axiom,
    ! [P2: real > product_prod_a_b > $o,Q2: product_prod_a_b > real > $o] :
      ( produc5828954698716094813l_real
      = ( comp_P5152745405570707767l_real @ produc4505306568083885239od_a_b @ ( bNF_fs4413835580006596598b_real @ P2 @ Q2 ) ) ) ).

% fst_fstOp
thf(fact_934_fst__fstOp,axiom,
    ! [P2: real > product_prod_a_b > $o,Q2: product_prod_a_b > a > $o] :
      ( product_fst_real_a
      = ( comp_P6767852656780618441real_a @ produc4505306568083885239od_a_b @ ( bNF_fs1099215190774911796_a_b_a @ P2 @ Q2 ) ) ) ).

% fst_fstOp
thf(fact_935_snd__comp__apsnd,axiom,
    ! [F2: real > produc7716430852924023517t_real] :
      ( ( comp_P5382238685994250021t_real @ produc1253116029013359366t_real @ ( produc4373565763360480515al_nat @ F2 ) )
      = ( comp_r4825950202331181903t_real @ F2 @ product_snd_nat_real ) ) ).

% snd_comp_apsnd
thf(fact_936_snd__comp__apsnd,axiom,
    ! [F2: product_prod_a_b > product_prod_a_b] :
      ( ( comp_P1649614271169106373od_a_b @ produc4276089182416139253od_a_b @ ( produc2010715641590200234b_real @ F2 ) )
      = ( comp_P8432976128825459156od_a_b @ F2 @ produc4276089182416139253od_a_b ) ) ).

% snd_comp_apsnd
thf(fact_937_snd__comp__apsnd,axiom,
    ! [F2: b > b] :
      ( ( comp_P2009515992434452078od_a_b @ product_snd_a_b @ ( product_apsnd_b_b_a @ F2 ) )
      = ( comp_b3886954628874447685od_a_b @ F2 @ product_snd_a_b ) ) ).

% snd_comp_apsnd
thf(fact_938_fst__comp__apfst,axiom,
    ! [F2: real > real] :
      ( ( comp_P630586971615063923od_a_b @ produc4505306568083885239od_a_b @ ( produc260968299626356370od_a_b @ F2 ) )
      = ( comp_r9159313671239757870od_a_b @ F2 @ produc4505306568083885239od_a_b ) ) ).

% fst_comp_apfst
thf(fact_939_fst__comp__apfst,axiom,
    ! [F2: a > a] :
      ( ( comp_P2648956292766268207od_a_b @ product_fst_a_b @ ( product_apfst_a_a_b @ F2 ) )
      = ( comp_a586446342581427589od_a_b @ F2 @ product_fst_a_b ) ) ).

% fst_comp_apfst
thf(fact_940_fst__comp__apfst,axiom,
    ! [F2: real > real] :
      ( ( comp_P3276979369905350645l_real @ produc5828954698716094813l_real @ ( produc8087084934854060354l_real @ F2 ) )
      = ( comp_r4460121664545661500l_real @ F2 @ produc5828954698716094813l_real ) ) ).

% fst_comp_apfst
thf(fact_941_fst__comp__apfst,axiom,
    ! [F2: nat > real] :
      ( ( comp_P5065359899111419289t_real @ produc5828954698716094813l_real @ ( produc8022920515623649382l_real @ F2 ) )
      = ( comp_n6680983964067316668t_real @ F2 @ product_fst_nat_real ) ) ).

% fst_comp_apfst
thf(fact_942_fst__comp__apfst,axiom,
    ! [F2: real > nat] :
      ( ( comp_P4469282871999149869l_real @ product_fst_nat_real @ ( produc3847397252069619942t_real @ F2 ) )
      = ( comp_r2044289011909133336l_real @ F2 @ produc5828954698716094813l_real ) ) ).

% fst_comp_apfst
thf(fact_943_fst__comp__apfst,axiom,
    ! [F2: nat > nat] :
      ( ( comp_P694186714645584081t_real @ product_fst_nat_real @ ( produc2755829627112137226t_real @ F2 ) )
      = ( comp_n7504733004837634456t_real @ F2 @ product_fst_nat_real ) ) ).

% fst_comp_apfst
thf(fact_944_fst__comp__apfst,axiom,
    ! [F2: real > real] :
      ( ( comp_P62423180901884703real_a @ product_fst_real_a @ ( produc8528259113123954408real_a @ F2 ) )
      = ( comp_r4041486331334303364real_a @ F2 @ product_fst_real_a ) ) ).

% fst_comp_apfst
thf(fact_945_real_Oqbs__morphism__dest,axiom,
    ! [K2: real > b > c,Y3: sigma_measure_b_c] :
      ( ( member_real_b_c @ K2 @ ( qbs_mo6398413456135019852al_b_c @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur1405370791648741458bs_b_c @ Y3 ) ) )
     => ( member_real_b_c @ K2 @ ( sigma_219859910464686500al_b_c @ borel_5078946678739801102l_real @ Y3 ) ) ) ).

% real.qbs_morphism_dest
thf(fact_946_real_Oqbs__morphism__dest,axiom,
    ! [K2: real > a > b > c,Y3: sigma_measure_a_b_c] :
      ( ( member_real_a_b_c @ K2 @ ( qbs_mo534596117765811055_a_b_c @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur1184878058648827625_a_b_c @ Y3 ) ) )
     => ( member_real_a_b_c @ K2 @ ( sigma_8538461840762587415_a_b_c @ borel_5078946678739801102l_real @ Y3 ) ) ) ).

% real.qbs_morphism_dest
thf(fact_947_real_Oqbs__morphism__dest,axiom,
    ! [K2: real > produc2422161461964618553l_real,Y3: sigma_2308072346491277622l_real] :
      ( ( member9086635009091248365l_real @ K2 @ ( qbs_mo6845038431372961811l_real @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur3029786804310284173l_real @ Y3 ) ) )
     => ( member9086635009091248365l_real @ K2 @ ( sigma_7998147297565726139l_real @ borel_5078946678739801102l_real @ Y3 ) ) ) ).

% real.qbs_morphism_dest
thf(fact_948_real_Oqbs__morphism__dest,axiom,
    ! [K2: real > produc7716430852924023517t_real,Y3: sigma_5310753476256395226t_real] :
      ( ( member969486235890772753t_real @ K2 @ ( qbs_mo3601394221918002359t_real @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur2011440102552004913t_real @ Y3 ) ) )
     => ( member969486235890772753t_real @ K2 @ ( sigma_2975298441655967327t_real @ borel_5078946678739801102l_real @ Y3 ) ) ) ).

% real.qbs_morphism_dest
thf(fact_949_real_Oqbs__morphism__dest,axiom,
    ! [K2: real > real,Y3: sigma_measure_real] :
      ( ( member_real_real @ K2 @ ( qbs_mo5229770564518008146l_real @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur6875533127466166616s_real @ Y3 ) ) )
     => ( member_real_real @ K2 @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ Y3 ) ) ) ).

% real.qbs_morphism_dest
thf(fact_950_real_Oqbs__morphism__dest,axiom,
    ! [K2: real > $o,Y3: sigma_measure_o] :
      ( ( member_real_o @ K2 @ ( qbs_morphism_real_o @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur2705496967258476524_qbs_o @ Y3 ) ) )
     => ( member_real_o @ K2 @ ( sigma_3939073009482781210real_o @ borel_5078946678739801102l_real @ Y3 ) ) ) ).

% real.qbs_morphism_dest
thf(fact_951_real_Oqbs__morphism__dest,axiom,
    ! [K2: real > nat,Y3: sigma_measure_nat] :
      ( ( member_real_nat @ K2 @ ( qbs_mo6567951568834356598al_nat @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur4416158800429964412bs_nat @ Y3 ) ) )
     => ( member_real_nat @ K2 @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ Y3 ) ) ) ).

% real.qbs_morphism_dest
thf(fact_952_real_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_b_c] :
      ( ( sigma_219859910464686500al_b_c @ borel_5078946678739801102l_real @ Y3 )
      = ( qbs_mo6398413456135019852al_b_c @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur1405370791648741458bs_b_c @ Y3 ) ) ) ).

% real.standard_borel_r_full_faithful
thf(fact_953_real_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_a_b_c] :
      ( ( sigma_8538461840762587415_a_b_c @ borel_5078946678739801102l_real @ Y3 )
      = ( qbs_mo534596117765811055_a_b_c @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur1184878058648827625_a_b_c @ Y3 ) ) ) ).

% real.standard_borel_r_full_faithful
thf(fact_954_real_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_2308072346491277622l_real] :
      ( ( sigma_7998147297565726139l_real @ borel_5078946678739801102l_real @ Y3 )
      = ( qbs_mo6845038431372961811l_real @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur3029786804310284173l_real @ Y3 ) ) ) ).

% real.standard_borel_r_full_faithful
thf(fact_955_real_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_5310753476256395226t_real] :
      ( ( sigma_2975298441655967327t_real @ borel_5078946678739801102l_real @ Y3 )
      = ( qbs_mo3601394221918002359t_real @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur2011440102552004913t_real @ Y3 ) ) ) ).

% real.standard_borel_r_full_faithful
thf(fact_956_real_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_real] :
      ( ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ Y3 )
      = ( qbs_mo5229770564518008146l_real @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur6875533127466166616s_real @ Y3 ) ) ) ).

% real.standard_borel_r_full_faithful
thf(fact_957_real_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_o] :
      ( ( sigma_3939073009482781210real_o @ borel_5078946678739801102l_real @ Y3 )
      = ( qbs_morphism_real_o @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur2705496967258476524_qbs_o @ Y3 ) ) ) ).

% real.standard_borel_r_full_faithful
thf(fact_958_real_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_nat] :
      ( ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ Y3 )
      = ( qbs_mo6567951568834356598al_nat @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur4416158800429964412bs_nat @ Y3 ) ) ) ).

% real.standard_borel_r_full_faithful
thf(fact_959_apfst__conv,axiom,
    ! [F2: real > real,X4: real,Y4: a] :
      ( ( produc8528259113123954408real_a @ F2 @ ( product_Pair_real_a @ X4 @ Y4 ) )
      = ( product_Pair_real_a @ ( F2 @ X4 ) @ Y4 ) ) ).

% apfst_conv
thf(fact_960_apfst__conv,axiom,
    ! [F2: real > b,X4: real,Y4: a] :
      ( ( produc4414189394973590951al_b_a @ F2 @ ( product_Pair_real_a @ X4 @ Y4 ) )
      = ( product_Pair_b_a @ ( F2 @ X4 ) @ Y4 ) ) ).

% apfst_conv
thf(fact_961_apfst__conv,axiom,
    ! [F2: real > real,X4: real,Y4: b] :
      ( ( produc8528259113123954409real_b @ F2 @ ( product_Pair_real_b @ X4 @ Y4 ) )
      = ( product_Pair_real_b @ ( F2 @ X4 ) @ Y4 ) ) ).

% apfst_conv
thf(fact_962_apfst__conv,axiom,
    ! [F2: b > real,X4: b,Y4: a] :
      ( ( produc4299820562685853389real_a @ F2 @ ( product_Pair_b_a @ X4 @ Y4 ) )
      = ( product_Pair_real_a @ ( F2 @ X4 ) @ Y4 ) ) ).

% apfst_conv
thf(fact_963_apfst__conv,axiom,
    ! [F2: b > b,X4: b,Y4: a] :
      ( ( product_apfst_b_b_a @ F2 @ ( product_Pair_b_a @ X4 @ Y4 ) )
      = ( product_Pair_b_a @ ( F2 @ X4 ) @ Y4 ) ) ).

% apfst_conv
thf(fact_964_apfst__conv,axiom,
    ! [F2: a > a,X4: a,Y4: real] :
      ( ( produc2181839757918105064a_real @ F2 @ ( product_Pair_a_real @ X4 @ Y4 ) )
      = ( product_Pair_a_real @ ( F2 @ X4 ) @ Y4 ) ) ).

% apfst_conv
thf(fact_965_apfst__conv,axiom,
    ! [F2: a > b,X4: a,Y4: real] :
      ( ( produc7778058373106235753b_real @ F2 @ ( product_Pair_a_real @ X4 @ Y4 ) )
      = ( product_Pair_b_real @ ( F2 @ X4 ) @ Y4 ) ) ).

% apfst_conv
thf(fact_966_apfst__conv,axiom,
    ! [F2: b > a,X4: b,Y4: real] :
      ( ( produc3669801795212903591a_real @ F2 @ ( product_Pair_b_real @ X4 @ Y4 ) )
      = ( product_Pair_a_real @ ( F2 @ X4 ) @ Y4 ) ) ).

% apfst_conv
thf(fact_967_apfst__conv,axiom,
    ! [F2: b > b,X4: b,Y4: real] :
      ( ( produc42648373546258472b_real @ F2 @ ( product_Pair_b_real @ X4 @ Y4 ) )
      = ( product_Pair_b_real @ ( F2 @ X4 ) @ Y4 ) ) ).

% apfst_conv
thf(fact_968_apfst__conv,axiom,
    ! [F2: a > product_prod_a_b,X4: a,Y4: real] :
      ( ( produc4353770629056038290b_real @ F2 @ ( product_Pair_a_real @ X4 @ Y4 ) )
      = ( produc9021675809588086653b_real @ ( F2 @ X4 ) @ Y4 ) ) ).

% apfst_conv
thf(fact_969_apsnd__conv,axiom,
    ! [F2: a > a,X4: real,Y4: a] :
      ( ( produc9061045181056197674a_real @ F2 @ ( product_Pair_real_a @ X4 @ Y4 ) )
      = ( product_Pair_real_a @ X4 @ ( F2 @ Y4 ) ) ) ).

% apsnd_conv
thf(fact_970_apsnd__conv,axiom,
    ! [F2: a > b,X4: real,Y4: a] :
      ( ( produc5433891759389552555b_real @ F2 @ ( product_Pair_real_a @ X4 @ Y4 ) )
      = ( product_Pair_real_b @ X4 @ ( F2 @ Y4 ) ) ) ).

% apsnd_conv
thf(fact_971_apsnd__conv,axiom,
    ! [F2: b > a,X4: real,Y4: b] :
      ( ( produc1325635181496220393a_real @ F2 @ ( product_Pair_real_b @ X4 @ Y4 ) )
      = ( product_Pair_real_a @ X4 @ ( F2 @ Y4 ) ) ) ).

% apsnd_conv
thf(fact_972_apsnd__conv,axiom,
    ! [F2: b > b,X4: real,Y4: b] :
      ( ( produc6921853796684351082b_real @ F2 @ ( product_Pair_real_b @ X4 @ Y4 ) )
      = ( product_Pair_real_b @ X4 @ ( F2 @ Y4 ) ) ) ).

% apsnd_conv
thf(fact_973_apsnd__conv,axiom,
    ! [F2: a > a,X4: b,Y4: a] :
      ( ( product_apsnd_a_a_b @ F2 @ ( product_Pair_b_a @ X4 @ Y4 ) )
      = ( product_Pair_b_a @ X4 @ ( F2 @ Y4 ) ) ) ).

% apsnd_conv
thf(fact_974_apsnd__conv,axiom,
    ! [F2: a > real,X4: b,Y4: a] :
      ( ( produc467691911674371665real_b @ F2 @ ( product_Pair_b_a @ X4 @ Y4 ) )
      = ( product_Pair_b_real @ X4 @ ( F2 @ Y4 ) ) ) ).

% apsnd_conv
thf(fact_975_apsnd__conv,axiom,
    ! [F2: real > real,X4: a,Y4: real] :
      ( ( produc4355207152332119334real_a @ F2 @ ( product_Pair_a_real @ X4 @ Y4 ) )
      = ( product_Pair_a_real @ X4 @ ( F2 @ Y4 ) ) ) ).

% apsnd_conv
thf(fact_976_apsnd__conv,axiom,
    ! [F2: real > a,X4: b,Y4: real] :
      ( ( produc4857478363229583787al_a_b @ F2 @ ( product_Pair_b_real @ X4 @ Y4 ) )
      = ( product_Pair_b_a @ X4 @ ( F2 @ Y4 ) ) ) ).

% apsnd_conv
thf(fact_977_apsnd__conv,axiom,
    ! [F2: real > real,X4: b,Y4: real] :
      ( ( produc4355207152332119335real_b @ F2 @ ( product_Pair_b_real @ X4 @ Y4 ) )
      = ( product_Pair_b_real @ X4 @ ( F2 @ Y4 ) ) ) ).

% apsnd_conv
thf(fact_978_apsnd__conv,axiom,
    ! [F2: real > real,X4: product_prod_a_b,Y4: real] :
      ( ( produc1799751413027327696od_a_b @ F2 @ ( produc9021675809588086653b_real @ X4 @ Y4 ) )
      = ( produc9021675809588086653b_real @ X4 @ ( F2 @ Y4 ) ) ) ).

% apsnd_conv
thf(fact_979_fst__apfst,axiom,
    ! [F2: real > real,X4: produc1405624045518934769od_a_b] :
      ( ( produc4505306568083885239od_a_b @ ( produc260968299626356370od_a_b @ F2 @ X4 ) )
      = ( F2 @ ( produc4505306568083885239od_a_b @ X4 ) ) ) ).

% fst_apfst
thf(fact_980_fst__apfst,axiom,
    ! [F2: a > a,X4: product_prod_a_b] :
      ( ( product_fst_a_b @ ( product_apfst_a_a_b @ F2 @ X4 ) )
      = ( F2 @ ( product_fst_a_b @ X4 ) ) ) ).

% fst_apfst
thf(fact_981_fst__apfst,axiom,
    ! [F2: real > real,X4: produc2422161461964618553l_real] :
      ( ( produc5828954698716094813l_real @ ( produc8087084934854060354l_real @ F2 @ X4 ) )
      = ( F2 @ ( produc5828954698716094813l_real @ X4 ) ) ) ).

% fst_apfst
thf(fact_982_fst__apfst,axiom,
    ! [F2: nat > real,X4: produc7716430852924023517t_real] :
      ( ( produc5828954698716094813l_real @ ( produc8022920515623649382l_real @ F2 @ X4 ) )
      = ( F2 @ ( product_fst_nat_real @ X4 ) ) ) ).

% fst_apfst
thf(fact_983_fst__apfst,axiom,
    ! [F2: real > nat,X4: produc2422161461964618553l_real] :
      ( ( product_fst_nat_real @ ( produc3847397252069619942t_real @ F2 @ X4 ) )
      = ( F2 @ ( produc5828954698716094813l_real @ X4 ) ) ) ).

% fst_apfst
thf(fact_984_fst__apfst,axiom,
    ! [F2: nat > nat,X4: produc7716430852924023517t_real] :
      ( ( product_fst_nat_real @ ( produc2755829627112137226t_real @ F2 @ X4 ) )
      = ( F2 @ ( product_fst_nat_real @ X4 ) ) ) ).

% fst_apfst
thf(fact_985_fst__apfst,axiom,
    ! [F2: real > real,X4: product_prod_real_a] :
      ( ( product_fst_real_a @ ( produc8528259113123954408real_a @ F2 @ X4 ) )
      = ( F2 @ ( product_fst_real_a @ X4 ) ) ) ).

% fst_apfst
thf(fact_986_snd__apfst,axiom,
    ! [F2: real > real,X4: produc1405624045518934769od_a_b] :
      ( ( produc4276089182416139253od_a_b @ ( produc260968299626356370od_a_b @ F2 @ X4 ) )
      = ( produc4276089182416139253od_a_b @ X4 ) ) ).

% snd_apfst
thf(fact_987_snd__apfst,axiom,
    ! [F2: a > a,X4: product_prod_a_b] :
      ( ( product_snd_a_b @ ( product_apfst_a_a_b @ F2 @ X4 ) )
      = ( product_snd_a_b @ X4 ) ) ).

% snd_apfst
thf(fact_988_fst__apsnd,axiom,
    ! [F2: b > b,X4: product_prod_a_b] :
      ( ( product_fst_a_b @ ( product_apsnd_b_b_a @ F2 @ X4 ) )
      = ( product_fst_a_b @ X4 ) ) ).

% fst_apsnd
thf(fact_989_fst__apsnd,axiom,
    ! [F2: real > real,X4: produc2422161461964618553l_real] :
      ( ( produc5828954698716094813l_real @ ( produc3783210147413284484l_real @ F2 @ X4 ) )
      = ( produc5828954698716094813l_real @ X4 ) ) ).

% fst_apsnd
thf(fact_990_fst__apsnd,axiom,
    ! [F2: a > real,X4: product_prod_real_a] :
      ( ( produc5828954698716094813l_real @ ( produc4907827405351646170l_real @ F2 @ X4 ) )
      = ( product_fst_real_a @ X4 ) ) ).

% fst_apsnd
thf(fact_991_fst__apsnd,axiom,
    ! [F2: real > real,X4: produc7716430852924023517t_real] :
      ( ( product_fst_nat_real @ ( produc434436795479515048al_nat @ F2 @ X4 ) )
      = ( product_fst_nat_real @ X4 ) ) ).

% fst_apsnd
thf(fact_992_fst__apsnd,axiom,
    ! [F2: real > a,X4: produc2422161461964618553l_real] :
      ( ( product_fst_real_a @ ( produc3725188384859169536a_real @ F2 @ X4 ) )
      = ( produc5828954698716094813l_real @ X4 ) ) ).

% fst_apsnd
thf(fact_993_fst__apsnd,axiom,
    ! [F2: a > a,X4: product_prod_real_a] :
      ( ( product_fst_real_a @ ( produc9061045181056197674a_real @ F2 @ X4 ) )
      = ( product_fst_real_a @ X4 ) ) ).

% fst_apsnd
thf(fact_994_fst__apsnd,axiom,
    ! [F2: real > product_prod_a_b,X4: produc2422161461964618553l_real] :
      ( ( produc4505306568083885239od_a_b @ ( produc4560813760262300330b_real @ F2 @ X4 ) )
      = ( produc5828954698716094813l_real @ X4 ) ) ).

% fst_apsnd
thf(fact_995_fst__apsnd,axiom,
    ! [F2: a > product_prod_a_b,X4: product_prod_real_a] :
      ( ( produc4505306568083885239od_a_b @ ( produc7441025843487746516b_real @ F2 @ X4 ) )
      = ( product_fst_real_a @ X4 ) ) ).

% fst_apsnd
thf(fact_996_fst__apsnd,axiom,
    ! [F2: product_prod_a_b > real,X4: produc1405624045518934769od_a_b] :
      ( ( produc5828954698716094813l_real @ ( produc423608079082504580l_real @ F2 @ X4 ) )
      = ( produc4505306568083885239od_a_b @ X4 ) ) ).

% fst_apsnd
thf(fact_997_fst__apsnd,axiom,
    ! [F2: product_prod_a_b > a,X4: produc1405624045518934769od_a_b] :
      ( ( product_fst_real_a @ ( produc3052887137737668608a_real @ F2 @ X4 ) )
      = ( produc4505306568083885239od_a_b @ X4 ) ) ).

% fst_apsnd
thf(fact_998_snd__apsnd,axiom,
    ! [F2: product_prod_a_b > product_prod_a_b,X4: produc1405624045518934769od_a_b] :
      ( ( produc4276089182416139253od_a_b @ ( produc2010715641590200234b_real @ F2 @ X4 ) )
      = ( F2 @ ( produc4276089182416139253od_a_b @ X4 ) ) ) ).

% snd_apsnd
thf(fact_999_snd__apsnd,axiom,
    ! [F2: b > b,X4: product_prod_a_b] :
      ( ( product_snd_a_b @ ( product_apsnd_b_b_a @ F2 @ X4 ) )
      = ( F2 @ ( product_snd_a_b @ X4 ) ) ) ).

% snd_apsnd
thf(fact_1000_snd__comp__apfst,axiom,
    ! [F2: real > real] :
      ( ( comp_P1649614271169106373od_a_b @ produc4276089182416139253od_a_b @ ( produc260968299626356370od_a_b @ F2 ) )
      = produc4276089182416139253od_a_b ) ).

% snd_comp_apfst
thf(fact_1001_snd__comp__apfst,axiom,
    ! [F2: a > a] :
      ( ( comp_P2009515992434452078od_a_b @ product_snd_a_b @ ( product_apfst_a_a_b @ F2 ) )
      = product_snd_a_b ) ).

% snd_comp_apfst
thf(fact_1002_fst__comp__apsnd,axiom,
    ! [F2: b > b] :
      ( ( comp_P2648956292766268207od_a_b @ product_fst_a_b @ ( product_apsnd_b_b_a @ F2 ) )
      = product_fst_a_b ) ).

% fst_comp_apsnd
thf(fact_1003_fst__comp__apsnd,axiom,
    ! [F2: real > real] :
      ( ( comp_P3276979369905350645l_real @ produc5828954698716094813l_real @ ( produc3783210147413284484l_real @ F2 ) )
      = produc5828954698716094813l_real ) ).

% fst_comp_apsnd
thf(fact_1004_fst__comp__apsnd,axiom,
    ! [F2: a > real] :
      ( ( comp_P1589298742348195979real_a @ produc5828954698716094813l_real @ ( produc4907827405351646170l_real @ F2 ) )
      = product_fst_real_a ) ).

% fst_comp_apsnd
thf(fact_1005_fst__comp__apsnd,axiom,
    ! [F2: real > real] :
      ( ( comp_P694186714645584081t_real @ product_fst_nat_real @ ( produc434436795479515048al_nat @ F2 ) )
      = product_fst_nat_real ) ).

% fst_comp_apsnd
thf(fact_1006_fst__comp__apsnd,axiom,
    ! [F2: real > a] :
      ( ( comp_P549788833721629281l_real @ product_fst_real_a @ ( produc3725188384859169536a_real @ F2 ) )
      = produc5828954698716094813l_real ) ).

% fst_comp_apsnd
thf(fact_1007_fst__comp__apsnd,axiom,
    ! [F2: a > a] :
      ( ( comp_P62423180901884703real_a @ product_fst_real_a @ ( produc9061045181056197674a_real @ F2 ) )
      = product_fst_real_a ) ).

% fst_comp_apsnd
thf(fact_1008_fst__comp__apsnd,axiom,
    ! [F2: real > product_prod_a_b] :
      ( ( comp_P5152745405570707767l_real @ produc4505306568083885239od_a_b @ ( produc4560813760262300330b_real @ F2 ) )
      = produc5828954698716094813l_real ) ).

% fst_comp_apsnd
thf(fact_1009_fst__comp__apsnd,axiom,
    ! [F2: a > product_prod_a_b] :
      ( ( comp_P6767852656780618441real_a @ produc4505306568083885239od_a_b @ ( produc7441025843487746516b_real @ F2 ) )
      = product_fst_real_a ) ).

% fst_comp_apsnd
thf(fact_1010_fst__comp__apsnd,axiom,
    ! [F2: product_prod_a_b > real] :
      ( ( comp_P544700997026044725od_a_b @ produc5828954698716094813l_real @ ( produc423608079082504580l_real @ F2 ) )
      = produc4505306568083885239od_a_b ) ).

% fst_comp_apsnd
thf(fact_1011_fst__comp__apsnd,axiom,
    ! [F2: product_prod_a_b > a] :
      ( ( comp_P7339791398657499593od_a_b @ product_fst_real_a @ ( produc3052887137737668608a_real @ F2 ) )
      = produc4505306568083885239od_a_b ) ).

% fst_comp_apsnd
thf(fact_1012_qbs__Mx__R,axiom,
    ! [X3: sigma_2308072346491277622l_real] :
      ( ( qbs_Mx2863504943393711152l_real @ ( measur3029786804310284173l_real @ X3 ) )
      = ( sigma_7998147297565726139l_real @ borel_5078946678739801102l_real @ X3 ) ) ).

% qbs_Mx_R
thf(fact_1013_qbs__Mx__R,axiom,
    ! [X3: sigma_5310753476256395226t_real] :
      ( ( qbs_Mx6884344600386557780t_real @ ( measur2011440102552004913t_real @ X3 ) )
      = ( sigma_2975298441655967327t_real @ borel_5078946678739801102l_real @ X3 ) ) ).

% qbs_Mx_R
thf(fact_1014_qbs__Mx__R,axiom,
    ! [X3: sigma_measure_real] :
      ( ( qbs_Mx_real @ ( measur6875533127466166616s_real @ X3 ) )
      = ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ X3 ) ) ).

% qbs_Mx_R
thf(fact_1015_qbs__Mx__R,axiom,
    ! [X3: sigma_measure_o] :
      ( ( qbs_Mx_o @ ( measur2705496967258476524_qbs_o @ X3 ) )
      = ( sigma_3939073009482781210real_o @ borel_5078946678739801102l_real @ X3 ) ) ).

% qbs_Mx_R
thf(fact_1016_qbs__Mx__R,axiom,
    ! [X3: sigma_measure_nat] :
      ( ( qbs_Mx_nat @ ( measur4416158800429964412bs_nat @ X3 ) )
      = ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ X3 ) ) ).

% qbs_Mx_R
thf(fact_1017_apfst__apsnd,axiom,
    ! [F2: real > real,G2: real > a,X4: produc2422161461964618553l_real] :
      ( ( produc8528259113123954408real_a @ F2 @ ( produc3725188384859169536a_real @ G2 @ X4 ) )
      = ( product_Pair_real_a @ ( F2 @ ( produc5828954698716094813l_real @ X4 ) ) @ ( G2 @ ( produc3484788084999411615l_real @ X4 ) ) ) ) ).

% apfst_apsnd
thf(fact_1018_apfst__apsnd,axiom,
    ! [F2: real > real,G2: real > b,X4: produc2422161461964618553l_real] :
      ( ( produc8528259113123954409real_b @ F2 @ ( produc98034963192524417b_real @ G2 @ X4 ) )
      = ( product_Pair_real_b @ ( F2 @ ( produc5828954698716094813l_real @ X4 ) ) @ ( G2 @ ( produc3484788084999411615l_real @ X4 ) ) ) ) ).

% apfst_apsnd
thf(fact_1019_apfst__apsnd,axiom,
    ! [F2: real > b,G2: real > a,X4: produc2422161461964618553l_real] :
      ( ( produc4414189394973590951al_b_a @ F2 @ ( produc3725188384859169536a_real @ G2 @ X4 ) )
      = ( product_Pair_b_a @ ( F2 @ ( produc5828954698716094813l_real @ X4 ) ) @ ( G2 @ ( produc3484788084999411615l_real @ X4 ) ) ) ) ).

% apfst_apsnd
thf(fact_1020_apfst__apsnd,axiom,
    ! [F2: real > a,G2: real > real,X4: produc2422161461964618553l_real] :
      ( ( produc7898240345651004610a_real @ F2 @ ( produc3783210147413284484l_real @ G2 @ X4 ) )
      = ( product_Pair_a_real @ ( F2 @ ( produc5828954698716094813l_real @ X4 ) ) @ ( G2 @ ( produc3484788084999411615l_real @ X4 ) ) ) ) ).

% apfst_apsnd
thf(fact_1021_apfst__apsnd,axiom,
    ! [F2: real > b,G2: real > real,X4: produc2422161461964618553l_real] :
      ( ( produc4271086923984359491b_real @ F2 @ ( produc3783210147413284484l_real @ G2 @ X4 ) )
      = ( product_Pair_b_real @ ( F2 @ ( produc5828954698716094813l_real @ X4 ) ) @ ( G2 @ ( produc3484788084999411615l_real @ X4 ) ) ) ) ).

% apfst_apsnd
thf(fact_1022_apfst__apsnd,axiom,
    ! [F2: nat > real,G2: real > a,X4: produc7716430852924023517t_real] :
      ( ( produc1726059739256919748real_a @ F2 @ ( produc113449075794782756_a_nat @ G2 @ X4 ) )
      = ( product_Pair_real_a @ ( F2 @ ( product_fst_nat_real @ X4 ) ) @ ( G2 @ ( product_snd_nat_real @ X4 ) ) ) ) ).

% apfst_apsnd
thf(fact_1023_apfst__apsnd,axiom,
    ! [F2: nat > real,G2: real > b,X4: produc7716430852924023517t_real] :
      ( ( produc1726059739256919749real_b @ F2 @ ( produc1348893404751177253_b_nat @ G2 @ X4 ) )
      = ( product_Pair_real_b @ ( F2 @ ( product_fst_nat_real @ X4 ) ) @ ( G2 @ ( product_snd_nat_real @ X4 ) ) ) ) ).

% apfst_apsnd
thf(fact_1024_apfst__apsnd,axiom,
    ! [F2: nat > b,G2: real > a,X4: produc7716430852924023517t_real] :
      ( ( produc198757087254200011at_b_a @ F2 @ ( produc113449075794782756_a_nat @ G2 @ X4 ) )
      = ( product_Pair_b_a @ ( F2 @ ( product_fst_nat_real @ X4 ) ) @ ( G2 @ ( product_snd_nat_real @ X4 ) ) ) ) ).

% apfst_apsnd
thf(fact_1025_apfst__apsnd,axiom,
    ! [F2: nat > a,G2: real > real,X4: produc7716430852924023517t_real] :
      ( ( produc1096040971783969950a_real @ F2 @ ( produc434436795479515048al_nat @ G2 @ X4 ) )
      = ( product_Pair_a_real @ ( F2 @ ( product_fst_nat_real @ X4 ) ) @ ( G2 @ ( product_snd_nat_real @ X4 ) ) ) ) ).

% apfst_apsnd
thf(fact_1026_apfst__apsnd,axiom,
    ! [F2: nat > b,G2: real > real,X4: produc7716430852924023517t_real] :
      ( ( produc6692259586972100639b_real @ F2 @ ( produc434436795479515048al_nat @ G2 @ X4 ) )
      = ( product_Pair_b_real @ ( F2 @ ( product_fst_nat_real @ X4 ) ) @ ( G2 @ ( product_snd_nat_real @ X4 ) ) ) ) ).

% apfst_apsnd
thf(fact_1027_apsnd__apfst,axiom,
    ! [F2: real > a,G2: real > real,X4: produc2422161461964618553l_real] :
      ( ( produc3725188384859169536a_real @ F2 @ ( produc8087084934854060354l_real @ G2 @ X4 ) )
      = ( product_Pair_real_a @ ( G2 @ ( produc5828954698716094813l_real @ X4 ) ) @ ( F2 @ ( produc3484788084999411615l_real @ X4 ) ) ) ) ).

% apsnd_apfst
thf(fact_1028_apsnd__apfst,axiom,
    ! [F2: real > b,G2: real > real,X4: produc2422161461964618553l_real] :
      ( ( produc98034963192524417b_real @ F2 @ ( produc8087084934854060354l_real @ G2 @ X4 ) )
      = ( product_Pair_real_b @ ( G2 @ ( produc5828954698716094813l_real @ X4 ) ) @ ( F2 @ ( produc3484788084999411615l_real @ X4 ) ) ) ) ).

% apsnd_apfst
thf(fact_1029_apsnd__apfst,axiom,
    ! [F2: real > a,G2: real > b,X4: produc2422161461964618553l_real] :
      ( ( produc4857478363229583787al_a_b @ F2 @ ( produc4271086923984359491b_real @ G2 @ X4 ) )
      = ( product_Pair_b_a @ ( G2 @ ( produc5828954698716094813l_real @ X4 ) ) @ ( F2 @ ( produc3484788084999411615l_real @ X4 ) ) ) ) ).

% apsnd_apfst
thf(fact_1030_apsnd__apfst,axiom,
    ! [F2: real > real,G2: real > a,X4: produc2422161461964618553l_real] :
      ( ( produc4355207152332119334real_a @ F2 @ ( produc7898240345651004610a_real @ G2 @ X4 ) )
      = ( product_Pair_a_real @ ( G2 @ ( produc5828954698716094813l_real @ X4 ) ) @ ( F2 @ ( produc3484788084999411615l_real @ X4 ) ) ) ) ).

% apsnd_apfst
thf(fact_1031_apsnd__apfst,axiom,
    ! [F2: real > real,G2: real > b,X4: produc2422161461964618553l_real] :
      ( ( produc4355207152332119335real_b @ F2 @ ( produc4271086923984359491b_real @ G2 @ X4 ) )
      = ( product_Pair_b_real @ ( G2 @ ( produc5828954698716094813l_real @ X4 ) ) @ ( F2 @ ( produc3484788084999411615l_real @ X4 ) ) ) ) ).

% apsnd_apfst
thf(fact_1032_apsnd__apfst,axiom,
    ! [F2: real > a,G2: nat > real,X4: produc7716430852924023517t_real] :
      ( ( produc3725188384859169536a_real @ F2 @ ( produc8022920515623649382l_real @ G2 @ X4 ) )
      = ( product_Pair_real_a @ ( G2 @ ( product_fst_nat_real @ X4 ) ) @ ( F2 @ ( product_snd_nat_real @ X4 ) ) ) ) ).

% apsnd_apfst
thf(fact_1033_apsnd__apfst,axiom,
    ! [F2: real > b,G2: nat > real,X4: produc7716430852924023517t_real] :
      ( ( produc98034963192524417b_real @ F2 @ ( produc8022920515623649382l_real @ G2 @ X4 ) )
      = ( product_Pair_real_b @ ( G2 @ ( product_fst_nat_real @ X4 ) ) @ ( F2 @ ( product_snd_nat_real @ X4 ) ) ) ) ).

% apsnd_apfst
thf(fact_1034_apsnd__apfst,axiom,
    ! [F2: real > a,G2: nat > b,X4: produc7716430852924023517t_real] :
      ( ( produc4857478363229583787al_a_b @ F2 @ ( produc6692259586972100639b_real @ G2 @ X4 ) )
      = ( product_Pair_b_a @ ( G2 @ ( product_fst_nat_real @ X4 ) ) @ ( F2 @ ( product_snd_nat_real @ X4 ) ) ) ) ).

% apsnd_apfst
thf(fact_1035_apsnd__apfst,axiom,
    ! [F2: real > real,G2: nat > a,X4: produc7716430852924023517t_real] :
      ( ( produc4355207152332119334real_a @ F2 @ ( produc1096040971783969950a_real @ G2 @ X4 ) )
      = ( product_Pair_a_real @ ( G2 @ ( product_fst_nat_real @ X4 ) ) @ ( F2 @ ( product_snd_nat_real @ X4 ) ) ) ) ).

% apsnd_apfst
thf(fact_1036_apsnd__apfst,axiom,
    ! [F2: real > real,G2: nat > b,X4: produc7716430852924023517t_real] :
      ( ( produc4355207152332119335real_b @ F2 @ ( produc6692259586972100639b_real @ G2 @ X4 ) )
      = ( product_Pair_b_real @ ( G2 @ ( product_fst_nat_real @ X4 ) ) @ ( F2 @ ( product_snd_nat_real @ X4 ) ) ) ) ).

% apsnd_apfst
thf(fact_1037_qbs__closed1__dest,axiom,
    ! [Alpha2: real > real,X3: quasi_borel_real,F2: real > real] :
      ( ( member_real_real @ Alpha2 @ ( qbs_Mx_real @ X3 ) )
     => ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) )
       => ( member_real_real @ ( comp_real_real_real @ Alpha2 @ F2 ) @ ( qbs_Mx_real @ X3 ) ) ) ) ).

% qbs_closed1_dest
thf(fact_1038_qbs__closed1__dest,axiom,
    ! [Alpha2: real > $o,X3: quasi_borel_o,F2: real > real] :
      ( ( member_real_o @ Alpha2 @ ( qbs_Mx_o @ X3 ) )
     => ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) )
       => ( member_real_o @ ( comp_real_o_real @ Alpha2 @ F2 ) @ ( qbs_Mx_o @ X3 ) ) ) ) ).

% qbs_closed1_dest
thf(fact_1039_qbs__closed1__dest,axiom,
    ! [Alpha2: real > nat,X3: quasi_borel_nat,F2: real > real] :
      ( ( member_real_nat @ Alpha2 @ ( qbs_Mx_nat @ X3 ) )
     => ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) )
       => ( member_real_nat @ ( comp_real_nat_real @ Alpha2 @ F2 ) @ ( qbs_Mx_nat @ X3 ) ) ) ) ).

% qbs_closed1_dest
thf(fact_1040_qbs__closed1__dest,axiom,
    ! [Alpha2: real > b > c,X3: quasi_borel_b_c,F2: real > real] :
      ( ( member_real_b_c @ Alpha2 @ ( qbs_Mx_b_c @ X3 ) )
     => ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) )
       => ( member_real_b_c @ ( comp_real_b_c_real @ Alpha2 @ F2 ) @ ( qbs_Mx_b_c @ X3 ) ) ) ) ).

% qbs_closed1_dest
thf(fact_1041_qbs__closed1__dest,axiom,
    ! [Alpha2: real > a > b > c,X3: quasi_borel_a_b_c,F2: real > real] :
      ( ( member_real_a_b_c @ Alpha2 @ ( qbs_Mx_a_b_c @ X3 ) )
     => ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) )
       => ( member_real_a_b_c @ ( comp_real_a_b_c_real @ Alpha2 @ F2 ) @ ( qbs_Mx_a_b_c @ X3 ) ) ) ) ).

% qbs_closed1_dest
thf(fact_1042_measurable__split__replace,axiom,
    ! [F2: real > real > real > real,G2: real > produc2422161461964618553l_real,M: sigma_measure_real,N: sigma_measure_real] :
      ( ( member_real_real
        @ ^ [X2: real] : ( F2 @ X2 @ ( produc5828954698716094813l_real @ ( G2 @ X2 ) ) @ ( produc3484788084999411615l_real @ ( G2 @ X2 ) ) )
        @ ( sigma_5267869275261027754l_real @ M @ N ) )
     => ( member_real_real
        @ ^ [X2: real] : ( produc313441363659479858l_real @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
        @ ( sigma_5267869275261027754l_real @ M @ N ) ) ) ).

% measurable_split_replace
thf(fact_1043_measurable__split__replace,axiom,
    ! [F2: real > nat > real > real,G2: real > produc7716430852924023517t_real,M: sigma_measure_real,N: sigma_measure_real] :
      ( ( member_real_real
        @ ^ [X2: real] : ( F2 @ X2 @ ( product_fst_nat_real @ ( G2 @ X2 ) ) @ ( product_snd_nat_real @ ( G2 @ X2 ) ) )
        @ ( sigma_5267869275261027754l_real @ M @ N ) )
     => ( member_real_real
        @ ^ [X2: real] : ( produc6486743989331012182l_real @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
        @ ( sigma_5267869275261027754l_real @ M @ N ) ) ) ).

% measurable_split_replace
thf(fact_1044_measurable__split__replace,axiom,
    ! [F2: real > real > a > real,G2: real > product_prod_real_a,M: sigma_measure_real,N: sigma_measure_real] :
      ( ( member_real_real
        @ ^ [X2: real] : ( F2 @ X2 @ ( product_fst_real_a @ ( G2 @ X2 ) ) @ ( product_snd_real_a @ ( G2 @ X2 ) ) )
        @ ( sigma_5267869275261027754l_real @ M @ N ) )
     => ( member_real_real
        @ ^ [X2: real] : ( produc1204397526812833490a_real @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
        @ ( sigma_5267869275261027754l_real @ M @ N ) ) ) ).

% measurable_split_replace
thf(fact_1045_measurable__split__replace,axiom,
    ! [F2: real > a > b > real,G2: real > product_prod_a_b,M: sigma_measure_real,N: sigma_measure_real] :
      ( ( member_real_real
        @ ^ [X2: real] : ( F2 @ X2 @ ( product_fst_a_b @ ( G2 @ X2 ) ) @ ( product_snd_a_b @ ( G2 @ X2 ) ) )
        @ ( sigma_5267869275261027754l_real @ M @ N ) )
     => ( member_real_real
        @ ^ [X2: real] : ( produc6199331350699860825b_real @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
        @ ( sigma_5267869275261027754l_real @ M @ N ) ) ) ).

% measurable_split_replace
thf(fact_1046_measurable__split__replace,axiom,
    ! [F2: real > real > real > $o,G2: real > produc2422161461964618553l_real,M: sigma_measure_real,N: sigma_measure_o] :
      ( ( member_real_o
        @ ^ [X2: real] : ( F2 @ X2 @ ( produc5828954698716094813l_real @ ( G2 @ X2 ) ) @ ( produc3484788084999411615l_real @ ( G2 @ X2 ) ) )
        @ ( sigma_3939073009482781210real_o @ M @ N ) )
     => ( member_real_o
        @ ^ [X2: real] : ( produc5414030515140494994real_o @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
        @ ( sigma_3939073009482781210real_o @ M @ N ) ) ) ).

% measurable_split_replace
thf(fact_1047_measurable__split__replace,axiom,
    ! [F2: real > nat > real > $o,G2: real > produc7716430852924023517t_real,M: sigma_measure_real,N: sigma_measure_o] :
      ( ( member_real_o
        @ ^ [X2: real] : ( F2 @ X2 @ ( product_fst_nat_real @ ( G2 @ X2 ) ) @ ( product_snd_nat_real @ ( G2 @ X2 ) ) )
        @ ( sigma_3939073009482781210real_o @ M @ N ) )
     => ( member_real_o
        @ ^ [X2: real] : ( produc3110475541085787246real_o @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
        @ ( sigma_3939073009482781210real_o @ M @ N ) ) ) ).

% measurable_split_replace
thf(fact_1048_measurable__split__replace,axiom,
    ! [F2: real > real > a > $o,G2: real > product_prod_real_a,M: sigma_measure_real,N: sigma_measure_o] :
      ( ( member_real_o
        @ ^ [X2: real] : ( F2 @ X2 @ ( product_fst_real_a @ ( G2 @ X2 ) ) @ ( product_snd_real_a @ ( G2 @ X2 ) ) )
        @ ( sigma_3939073009482781210real_o @ M @ N ) )
     => ( member_real_o
        @ ^ [X2: real] : ( produc8713834143731921650al_a_o @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
        @ ( sigma_3939073009482781210real_o @ M @ N ) ) ) ).

% measurable_split_replace
thf(fact_1049_measurable__split__replace,axiom,
    ! [F2: real > a > b > $o,G2: real > product_prod_a_b,M: sigma_measure_real,N: sigma_measure_o] :
      ( ( member_real_o
        @ ^ [X2: real] : ( F2 @ X2 @ ( product_fst_a_b @ ( G2 @ X2 ) ) @ ( product_snd_a_b @ ( G2 @ X2 ) ) )
        @ ( sigma_3939073009482781210real_o @ M @ N ) )
     => ( member_real_o
        @ ^ [X2: real] : ( produc3537405659489547051_a_b_o @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
        @ ( sigma_3939073009482781210real_o @ M @ N ) ) ) ).

% measurable_split_replace
thf(fact_1050_measurable__split__replace,axiom,
    ! [F2: real > real > real > nat,G2: real > produc2422161461964618553l_real,M: sigma_measure_real,N: sigma_measure_nat] :
      ( ( member_real_nat
        @ ^ [X2: real] : ( F2 @ X2 @ ( produc5828954698716094813l_real @ ( G2 @ X2 ) ) @ ( produc3484788084999411615l_real @ ( G2 @ X2 ) ) )
        @ ( sigma_6315060578831106510al_nat @ M @ N ) )
     => ( member_real_nat
        @ ^ [X2: real] : ( produc6878529298905881430al_nat @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
        @ ( sigma_6315060578831106510al_nat @ M @ N ) ) ) ).

% measurable_split_replace
thf(fact_1051_measurable__split__replace,axiom,
    ! [F2: real > nat > real > nat,G2: real > produc7716430852924023517t_real,M: sigma_measure_real,N: sigma_measure_nat] :
      ( ( member_real_nat
        @ ^ [X2: real] : ( F2 @ X2 @ ( product_fst_nat_real @ ( G2 @ X2 ) ) @ ( product_snd_nat_real @ ( G2 @ X2 ) ) )
        @ ( sigma_6315060578831106510al_nat @ M @ N ) )
     => ( member_real_nat
        @ ^ [X2: real] : ( produc6270885368079350906al_nat @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
        @ ( sigma_6315060578831106510al_nat @ M @ N ) ) ) ).

% measurable_split_replace
thf(fact_1052_borel__measurable__Pair,axiom,
    ! [F2: real > real,M: sigma_measure_real,G2: real > real] :
      ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ M @ borel_5078946678739801102l_real ) )
     => ( ( member_real_real @ G2 @ ( sigma_5267869275261027754l_real @ M @ borel_5078946678739801102l_real ) )
       => ( member9086635009091248365l_real
          @ ^ [X2: real] : ( produc4511245868158468465l_real @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
          @ ( sigma_7998147297565726139l_real @ M @ borel_9155112475215227991l_real ) ) ) ) ).

% borel_measurable_Pair
thf(fact_1053_borel__measurable__Pair,axiom,
    ! [F2: $o > real,M: sigma_measure_o,G2: $o > real] :
      ( ( member_o_real @ F2 @ ( sigma_2430008634441611636o_real @ M @ borel_5078946678739801102l_real ) )
     => ( ( member_o_real @ G2 @ ( sigma_2430008634441611636o_real @ M @ borel_5078946678739801102l_real ) )
       => ( member8602590400058854173l_real
          @ ^ [X2: $o] : ( produc4511245868158468465l_real @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
          @ ( sigma_2489502367751881329l_real @ M @ borel_9155112475215227991l_real ) ) ) ) ).

% borel_measurable_Pair
thf(fact_1054_borel__measurable__Pair,axiom,
    ! [F2: nat > real,M: sigma_measure_nat,G2: nat > real] :
      ( ( member_nat_real @ F2 @ ( sigma_1747752005702207822t_real @ M @ borel_5078946678739801102l_real ) )
     => ( ( member_nat_real @ G2 @ ( sigma_1747752005702207822t_real @ M @ borel_5078946678739801102l_real ) )
       => ( member4944736856719700937l_real
          @ ^ [X2: nat] : ( produc4511245868158468465l_real @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
          @ ( sigma_5893925349391517463l_real @ M @ borel_9155112475215227991l_real ) ) ) ) ).

% borel_measurable_Pair
thf(fact_1055_borel__measurable__Pair,axiom,
    ! [F2: real > real,M: sigma_measure_real,G2: real > nat] :
      ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ M @ borel_5078946678739801102l_real ) )
     => ( ( member_real_nat @ G2 @ ( sigma_6315060578831106510al_nat @ M @ borel_8449730974584783410el_nat ) )
       => ( member4159480375084375953al_nat
          @ ^ [X2: real] : ( produc3181502643871035669al_nat @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
          @ ( sigma_8223622787033862879al_nat @ M @ borel_8300761668267423611al_nat ) ) ) ) ).

% borel_measurable_Pair
thf(fact_1056_borel__measurable__Pair,axiom,
    ! [F2: $o > real,M: sigma_measure_o,G2: $o > nat] :
      ( ( member_o_real @ F2 @ ( sigma_2430008634441611636o_real @ M @ borel_5078946678739801102l_real ) )
     => ( ( member_o_nat @ G2 @ ( sigma_1999164137574644376_o_nat @ M @ borel_8449730974584783410el_nat ) )
       => ( member2706604780226699713al_nat
          @ ^ [X2: $o] : ( produc3181502643871035669al_nat @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
          @ ( sigma_5929096572201269909al_nat @ M @ borel_8300761668267423611al_nat ) ) ) ) ).

% borel_measurable_Pair
thf(fact_1057_borel__measurable__Pair,axiom,
    ! [F2: nat > real,M: sigma_measure_nat,G2: nat > nat] :
      ( ( member_nat_real @ F2 @ ( sigma_1747752005702207822t_real @ M @ borel_5078946678739801102l_real ) )
     => ( ( member_nat_nat @ G2 @ ( sigma_4350458207664084850at_nat @ M @ borel_8449730974584783410el_nat ) )
       => ( member7427358445142253677al_nat
          @ ^ [X2: nat] : ( produc3181502643871035669al_nat @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
          @ ( sigma_4775202647280382523al_nat @ M @ borel_8300761668267423611al_nat ) ) ) ) ).

% borel_measurable_Pair
thf(fact_1058_borel__measurable__Pair,axiom,
    ! [F2: real > real,M: sigma_measure_real,G2: real > extend8495563244428889912nnreal] :
      ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ M @ borel_5078946678739801102l_real ) )
     => ( ( member2919562650594848410nnreal @ G2 @ ( sigma_9017504469962657078nnreal @ M @ borel_6524799422816628122nnreal ) )
       => ( member4263462704469908217nnreal
          @ ^ [X2: real] : ( produc4778015194254607485nnreal @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
          @ ( sigma_1079880282724612679nnreal @ M @ borel_4974289084073311971nnreal ) ) ) ) ).

% borel_measurable_Pair
thf(fact_1059_borel__measurable__Pair,axiom,
    ! [F2: $o > real,M: sigma_measure_o,G2: $o > extend8495563244428889912nnreal] :
      ( ( member_o_real @ F2 @ ( sigma_2430008634441611636o_real @ M @ borel_5078946678739801102l_real ) )
     => ( ( member5265953103328284778nnreal @ G2 @ ( sigma_6459699357617223168nnreal @ M @ borel_6524799422816628122nnreal ) )
       => ( member8012821517253025065nnreal
          @ ^ [X2: $o] : ( produc4778015194254607485nnreal @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
          @ ( sigma_8212496664001311229nnreal @ M @ borel_4974289084073311971nnreal ) ) ) ) ).

% borel_measurable_Pair
thf(fact_1060_borel__measurable__Pair,axiom,
    ! [F2: nat > real,M: sigma_measure_nat,G2: nat > extend8495563244428889912nnreal] :
      ( ( member_nat_real @ F2 @ ( sigma_1747752005702207822t_real @ M @ borel_5078946678739801102l_real ) )
     => ( ( member8283130129095025342nnreal @ G2 @ ( sigma_6306161311797543642nnreal @ M @ borel_6524799422816628122nnreal ) )
       => ( member1617991602746293205nnreal
          @ ^ [X2: nat] : ( produc4778015194254607485nnreal @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
          @ ( sigma_4192619376674453923nnreal @ M @ borel_4974289084073311971nnreal ) ) ) ) ).

% borel_measurable_Pair
thf(fact_1061_borel__measurable__Pair,axiom,
    ! [F2: $o > nat,M: sigma_measure_o,G2: $o > real] :
      ( ( member_o_nat @ F2 @ ( sigma_1999164137574644376_o_nat @ M @ borel_8449730974584783410el_nat ) )
     => ( ( member_o_real @ G2 @ ( sigma_2430008634441611636o_real @ M @ borel_5078946678739801102l_real ) )
       => ( member8739982677887872321t_real
          @ ^ [X2: $o] : ( produc7837566107596912789t_real @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
          @ ( sigma_680772226823374357t_real @ M @ borel_3052437322889528059t_real ) ) ) ) ).

% borel_measurable_Pair
thf(fact_1062_fstOp__def,axiom,
    ( bNF_fs5479770303754431564a_real
    = ( ^ [P4: real > a > $o,Q3: a > real > $o,Ac: produc2422161461964618553l_real] : ( product_Pair_real_a @ ( produc5828954698716094813l_real @ Ac ) @ ( bNF_pi8131508402373045914a_real @ P4 @ Q3 @ ( produc5828954698716094813l_real @ Ac ) @ ( produc3484788084999411615l_real @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_1063_fstOp__def,axiom,
    ( bNF_fs1852616882087786445b_real
    = ( ^ [P4: real > b > $o,Q3: b > real > $o,Ac: produc2422161461964618553l_real] : ( product_Pair_real_b @ ( produc5828954698716094813l_real @ Ac ) @ ( bNF_pi4504354980706400795b_real @ P4 @ Q3 @ ( produc5828954698716094813l_real @ Ac ) @ ( produc3484788084999411615l_real @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_1064_fstOp__def,axiom,
    ( bNF_fstOp_real_a_a
    = ( ^ [P4: real > a > $o,Q3: a > a > $o,Ac: product_prod_real_a] : ( product_Pair_real_a @ ( product_fst_real_a @ Ac ) @ ( bNF_pi8219073671537963920al_a_a @ P4 @ Q3 @ ( product_fst_real_a @ Ac ) @ ( product_snd_real_a @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_1065_fstOp__def,axiom,
    ( bNF_fstOp_real_b_a
    = ( ^ [P4: real > b > $o,Q3: b > a > $o,Ac: product_prod_real_a] : ( product_Pair_real_b @ ( product_fst_real_a @ Ac ) @ ( bNF_pi5431618089565287887al_b_a @ P4 @ Q3 @ ( product_fst_real_a @ Ac ) @ ( product_snd_real_a @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_1066_fstOp__def,axiom,
    ( bNF_fs5697544725373665032od_a_b
    = ( ^ [P4: real > a > $o,Q3: a > product_prod_a_b > $o,Ac: produc1405624045518934769od_a_b] : ( product_Pair_real_a @ ( produc4505306568083885239od_a_b @ Ac ) @ ( bNF_pi215755999452490554od_a_b @ P4 @ Q3 @ ( produc4505306568083885239od_a_b @ Ac ) @ ( produc4276089182416139253od_a_b @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_1067_fstOp__def,axiom,
    ( bNF_fs5058104425041848903od_a_b
    = ( ^ [P4: real > b > $o,Q3: b > product_prod_a_b > $o,Ac: produc1405624045518934769od_a_b] : ( product_Pair_real_b @ ( produc4505306568083885239od_a_b @ Ac ) @ ( bNF_pi8799687735975450233od_a_b @ P4 @ Q3 @ ( produc4505306568083885239od_a_b @ Ac ) @ ( produc4276089182416139253od_a_b @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_1068_fstOp__def,axiom,
    ( bNF_fstOp_a_real_b
    = ( ^ [P4: a > real > $o,Q3: real > b > $o,Ac: product_prod_a_b] : ( product_Pair_a_real @ ( product_fst_a_b @ Ac ) @ ( bNF_pi3829287219982751799real_b @ P4 @ Q3 @ ( product_fst_a_b @ Ac ) @ ( product_snd_a_b @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_1069_sndOp__def,axiom,
    ( bNF_sn7094760764887436170a_real
    = ( ^ [P4: real > a > $o,Q3: a > real > $o,Ac: produc2422161461964618553l_real] : ( product_Pair_a_real @ ( bNF_pi8131508402373045914a_real @ P4 @ Q3 @ ( produc5828954698716094813l_real @ Ac ) @ ( produc3484788084999411615l_real @ Ac ) ) @ ( produc3484788084999411615l_real @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_1070_sndOp__def,axiom,
    ( bNF_sn3467607343220791051b_real
    = ( ^ [P4: real > b > $o,Q3: b > real > $o,Ac: produc2422161461964618553l_real] : ( product_Pair_b_real @ ( bNF_pi4504354980706400795b_real @ P4 @ Q3 @ ( produc5828954698716094813l_real @ Ac ) @ ( produc3484788084999411615l_real @ Ac ) ) @ ( produc3484788084999411615l_real @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_1071_sndOp__def,axiom,
    ( bNF_sn7256173965670363444b_real
    = ( ^ [P4: real > product_prod_a_b > $o,Q3: product_prod_a_b > real > $o,Ac: produc2422161461964618553l_real] : ( produc9021675809588086653b_real @ ( bNF_pi353393763585934404b_real @ P4 @ Q3 @ ( produc5828954698716094813l_real @ Ac ) @ ( produc3484788084999411615l_real @ Ac ) ) @ ( produc3484788084999411615l_real @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_1072_sndOp__def,axiom,
    ( bNF_sndOp_nat_a_real
    = ( ^ [P4: nat > a > $o,Q3: a > real > $o,Ac: produc7716430852924023517t_real] : ( product_Pair_a_real @ ( bNF_pi4581077271498945142a_real @ P4 @ Q3 @ ( product_fst_nat_real @ Ac ) @ ( product_snd_nat_real @ Ac ) ) @ ( product_snd_nat_real @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_1073_sndOp__def,axiom,
    ( bNF_sndOp_nat_b_real
    = ( ^ [P4: nat > b > $o,Q3: b > real > $o,Ac: produc7716430852924023517t_real] : ( product_Pair_b_real @ ( bNF_pi953923849832300023b_real @ P4 @ Q3 @ ( product_fst_nat_real @ Ac ) @ ( product_snd_nat_real @ Ac ) ) @ ( product_snd_nat_real @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_1074_sndOp__def,axiom,
    ( bNF_sn1909883276703707408b_real
    = ( ^ [P4: nat > product_prod_a_b > $o,Q3: product_prod_a_b > real > $o,Ac: produc7716430852924023517t_real] : ( produc9021675809588086653b_real @ ( bNF_pi3352055721067236384b_real @ P4 @ Q3 @ ( product_fst_nat_real @ Ac ) @ ( product_snd_nat_real @ Ac ) ) @ ( product_snd_nat_real @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_1075_sndOp__def,axiom,
    ( bNF_sn7724779532360385968real_a
    = ( ^ [P4: real > real > $o,Q3: real > a > $o,Ac: product_prod_real_a] : ( product_Pair_real_a @ ( bNF_pi8761527169845995712real_a @ P4 @ Q3 @ ( product_fst_real_a @ Ac ) @ ( product_snd_real_a @ Ac ) ) @ ( product_snd_real_a @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_1076_sndOp__def,axiom,
    ( bNF_sndOp_real_b_a
    = ( ^ [P4: real > b > $o,Q3: b > a > $o,Ac: product_prod_real_a] : ( product_Pair_b_a @ ( bNF_pi5431618089565287887al_b_a @ P4 @ Q3 @ ( product_fst_real_a @ Ac ) @ ( product_snd_real_a @ Ac ) ) @ ( product_snd_real_a @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_1077_sndOp__def,axiom,
    ( bNF_sndOp_a_real_b
    = ( ^ [P4: a > real > $o,Q3: real > b > $o,Ac: product_prod_a_b] : ( product_Pair_real_b @ ( bNF_pi3829287219982751799real_b @ P4 @ Q3 @ ( product_fst_a_b @ Ac ) @ ( product_snd_a_b @ Ac ) ) @ ( product_snd_a_b @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_1078_borel__measurable__const,axiom,
    ! [C: real,M: sigma_measure_real] :
      ( member_real_real
      @ ^ [X2: real] : C
      @ ( sigma_5267869275261027754l_real @ M @ borel_5078946678739801102l_real ) ) ).

% borel_measurable_const
thf(fact_1079_borel__measurable__const,axiom,
    ! [C: real,M: sigma_measure_o] :
      ( member_o_real
      @ ^ [X2: $o] : C
      @ ( sigma_2430008634441611636o_real @ M @ borel_5078946678739801102l_real ) ) ).

% borel_measurable_const
thf(fact_1080_borel__measurable__const,axiom,
    ! [C: real,M: sigma_measure_nat] :
      ( member_nat_real
      @ ^ [X2: nat] : C
      @ ( sigma_1747752005702207822t_real @ M @ borel_5078946678739801102l_real ) ) ).

% borel_measurable_const
thf(fact_1081_borel__measurable__const,axiom,
    ! [C: nat,M: sigma_measure_real] :
      ( member_real_nat
      @ ^ [X2: real] : C
      @ ( sigma_6315060578831106510al_nat @ M @ borel_8449730974584783410el_nat ) ) ).

% borel_measurable_const
thf(fact_1082_borel__measurable__const,axiom,
    ! [C: $o,M: sigma_measure_real] :
      ( member_real_o
      @ ^ [X2: real] : C
      @ ( sigma_3939073009482781210real_o @ M @ borel_5500255247093592246orel_o ) ) ).

% borel_measurable_const
thf(fact_1083_apfst__convE,axiom,
    ! [Q: product_prod_real_a,F2: real > real,P: product_prod_real_a] :
      ( ( Q
        = ( produc8528259113123954408real_a @ F2 @ P ) )
     => ~ ! [X5: real,Y5: a] :
            ( ( P
              = ( product_Pair_real_a @ X5 @ Y5 ) )
           => ( Q
             != ( product_Pair_real_a @ ( F2 @ X5 ) @ Y5 ) ) ) ) ).

% apfst_convE
thf(fact_1084_apfst__convE,axiom,
    ! [Q: product_prod_b_a,F2: real > b,P: product_prod_real_a] :
      ( ( Q
        = ( produc4414189394973590951al_b_a @ F2 @ P ) )
     => ~ ! [X5: real,Y5: a] :
            ( ( P
              = ( product_Pair_real_a @ X5 @ Y5 ) )
           => ( Q
             != ( product_Pair_b_a @ ( F2 @ X5 ) @ Y5 ) ) ) ) ).

% apfst_convE
thf(fact_1085_apfst__convE,axiom,
    ! [Q: product_prod_real_b,F2: real > real,P: product_prod_real_b] :
      ( ( Q
        = ( produc8528259113123954409real_b @ F2 @ P ) )
     => ~ ! [X5: real,Y5: b] :
            ( ( P
              = ( product_Pair_real_b @ X5 @ Y5 ) )
           => ( Q
             != ( product_Pair_real_b @ ( F2 @ X5 ) @ Y5 ) ) ) ) ).

% apfst_convE
thf(fact_1086_apfst__convE,axiom,
    ! [Q: product_prod_real_a,F2: b > real,P: product_prod_b_a] :
      ( ( Q
        = ( produc4299820562685853389real_a @ F2 @ P ) )
     => ~ ! [X5: b,Y5: a] :
            ( ( P
              = ( product_Pair_b_a @ X5 @ Y5 ) )
           => ( Q
             != ( product_Pair_real_a @ ( F2 @ X5 ) @ Y5 ) ) ) ) ).

% apfst_convE
thf(fact_1087_apfst__convE,axiom,
    ! [Q: product_prod_b_a,F2: b > b,P: product_prod_b_a] :
      ( ( Q
        = ( product_apfst_b_b_a @ F2 @ P ) )
     => ~ ! [X5: b,Y5: a] :
            ( ( P
              = ( product_Pair_b_a @ X5 @ Y5 ) )
           => ( Q
             != ( product_Pair_b_a @ ( F2 @ X5 ) @ Y5 ) ) ) ) ).

% apfst_convE
thf(fact_1088_apfst__convE,axiom,
    ! [Q: product_prod_a_real,F2: a > a,P: product_prod_a_real] :
      ( ( Q
        = ( produc2181839757918105064a_real @ F2 @ P ) )
     => ~ ! [X5: a,Y5: real] :
            ( ( P
              = ( product_Pair_a_real @ X5 @ Y5 ) )
           => ( Q
             != ( product_Pair_a_real @ ( F2 @ X5 ) @ Y5 ) ) ) ) ).

% apfst_convE
thf(fact_1089_apfst__convE,axiom,
    ! [Q: product_prod_b_real,F2: a > b,P: product_prod_a_real] :
      ( ( Q
        = ( produc7778058373106235753b_real @ F2 @ P ) )
     => ~ ! [X5: a,Y5: real] :
            ( ( P
              = ( product_Pair_a_real @ X5 @ Y5 ) )
           => ( Q
             != ( product_Pair_b_real @ ( F2 @ X5 ) @ Y5 ) ) ) ) ).

% apfst_convE
thf(fact_1090_apfst__convE,axiom,
    ! [Q: product_prod_a_real,F2: b > a,P: product_prod_b_real] :
      ( ( Q
        = ( produc3669801795212903591a_real @ F2 @ P ) )
     => ~ ! [X5: b,Y5: real] :
            ( ( P
              = ( product_Pair_b_real @ X5 @ Y5 ) )
           => ( Q
             != ( product_Pair_a_real @ ( F2 @ X5 ) @ Y5 ) ) ) ) ).

% apfst_convE
thf(fact_1091_apfst__convE,axiom,
    ! [Q: product_prod_b_real,F2: b > b,P: product_prod_b_real] :
      ( ( Q
        = ( produc42648373546258472b_real @ F2 @ P ) )
     => ~ ! [X5: b,Y5: real] :
            ( ( P
              = ( product_Pair_b_real @ X5 @ Y5 ) )
           => ( Q
             != ( product_Pair_b_real @ ( F2 @ X5 ) @ Y5 ) ) ) ) ).

% apfst_convE
thf(fact_1092_apfst__convE,axiom,
    ! [Q: produc7929879615859924995b_real,F2: a > product_prod_a_b,P: product_prod_a_real] :
      ( ( Q
        = ( produc4353770629056038290b_real @ F2 @ P ) )
     => ~ ! [X5: a,Y5: real] :
            ( ( P
              = ( product_Pair_a_real @ X5 @ Y5 ) )
           => ( Q
             != ( produc9021675809588086653b_real @ ( F2 @ X5 ) @ Y5 ) ) ) ) ).

% apfst_convE
thf(fact_1093_R__correct,axiom,
    ! [X3: sigma_2308072346491277622l_real] :
      ( ( quasi_2376713246294942192l_real @ ( measur3029786804310284173l_real @ X3 ) )
      = ( produc5420172574571962722l_real @ ( sigma_2519298556039103681l_real @ X3 ) @ ( sigma_7998147297565726139l_real @ borel_5078946678739801102l_real @ X3 ) ) ) ).

% R_correct
thf(fact_1094_R__correct,axiom,
    ! [X3: sigma_5310753476256395226t_real] :
      ( ( quasi_1341009766961362196t_real @ ( measur2011440102552004913t_real @ X3 ) )
      = ( produc2405820699097220962t_real @ ( sigma_2177939267068080229t_real @ X3 ) @ ( sigma_2975298441655967327t_real @ borel_5078946678739801102l_real @ X3 ) ) ) ).

% R_correct
thf(fact_1095_R__correct,axiom,
    ! [X3: sigma_measure_real] :
      ( ( quasi_4307383193256703285l_real @ ( measur6875533127466166616s_real @ X3 ) )
      = ( produc3470952364605845544l_real @ ( sigma_space_real @ X3 ) @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ X3 ) ) ) ).

% R_correct
thf(fact_1096_R__correct,axiom,
    ! [X3: sigma_measure_o] :
      ( ( quasi_3788804942992426063orel_o @ ( measur2705496967258476524_qbs_o @ X3 ) )
      = ( produc2133903995702845986real_o @ ( sigma_space_o @ X3 ) @ ( sigma_3939073009482781210real_o @ borel_5078946678739801102l_real @ X3 ) ) ) ).

% R_correct
thf(fact_1097_R__correct,axiom,
    ! [X3: sigma_measure_nat] :
      ( ( quasi_2638801612224710361el_nat @ ( measur4416158800429964412bs_nat @ X3 ) )
      = ( produc3843710909396041968al_nat @ ( sigma_space_nat @ X3 ) @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ X3 ) ) ) ).

% R_correct
thf(fact_1098_measurable__comp,axiom,
    ! [F2: $o > $o,M: sigma_measure_o,N: sigma_measure_o,G2: $o > real,L3: sigma_measure_real] :
      ( ( member_o_o @ F2 @ ( sigma_measurable_o_o @ M @ N ) )
     => ( ( member_o_real @ G2 @ ( sigma_2430008634441611636o_real @ N @ L3 ) )
       => ( member_o_real @ ( comp_o_real_o @ G2 @ F2 ) @ ( sigma_2430008634441611636o_real @ M @ L3 ) ) ) ) ).

% measurable_comp
thf(fact_1099_measurable__comp,axiom,
    ! [F2: nat > $o,M: sigma_measure_nat,N: sigma_measure_o,G2: $o > real,L3: sigma_measure_real] :
      ( ( member_nat_o @ F2 @ ( sigma_5101835498682829686_nat_o @ M @ N ) )
     => ( ( member_o_real @ G2 @ ( sigma_2430008634441611636o_real @ N @ L3 ) )
       => ( member_nat_real @ ( comp_o_real_nat @ G2 @ F2 ) @ ( sigma_1747752005702207822t_real @ M @ L3 ) ) ) ) ).

% measurable_comp
thf(fact_1100_measurable__comp,axiom,
    ! [F2: $o > nat,M: sigma_measure_o,N: sigma_measure_nat,G2: nat > real,L3: sigma_measure_real] :
      ( ( member_o_nat @ F2 @ ( sigma_1999164137574644376_o_nat @ M @ N ) )
     => ( ( member_nat_real @ G2 @ ( sigma_1747752005702207822t_real @ N @ L3 ) )
       => ( member_o_real @ ( comp_nat_real_o @ G2 @ F2 ) @ ( sigma_2430008634441611636o_real @ M @ L3 ) ) ) ) ).

% measurable_comp
thf(fact_1101_measurable__comp,axiom,
    ! [F2: nat > nat,M: sigma_measure_nat,N: sigma_measure_nat,G2: nat > real,L3: sigma_measure_real] :
      ( ( member_nat_nat @ F2 @ ( sigma_4350458207664084850at_nat @ M @ N ) )
     => ( ( member_nat_real @ G2 @ ( sigma_1747752005702207822t_real @ N @ L3 ) )
       => ( member_nat_real @ ( comp_nat_real_nat @ G2 @ F2 ) @ ( sigma_1747752005702207822t_real @ M @ L3 ) ) ) ) ).

% measurable_comp
thf(fact_1102_measurable__comp,axiom,
    ! [F2: real > real,M: sigma_measure_real,N: sigma_measure_real,G2: real > real,L3: sigma_measure_real] :
      ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ M @ N ) )
     => ( ( member_real_real @ G2 @ ( sigma_5267869275261027754l_real @ N @ L3 ) )
       => ( member_real_real @ ( comp_real_real_real @ G2 @ F2 ) @ ( sigma_5267869275261027754l_real @ M @ L3 ) ) ) ) ).

% measurable_comp
thf(fact_1103_measurable__comp,axiom,
    ! [F2: real > real,M: sigma_measure_real,N: sigma_measure_real,G2: real > $o,L3: sigma_measure_o] :
      ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ M @ N ) )
     => ( ( member_real_o @ G2 @ ( sigma_3939073009482781210real_o @ N @ L3 ) )
       => ( member_real_o @ ( comp_real_o_real @ G2 @ F2 ) @ ( sigma_3939073009482781210real_o @ M @ L3 ) ) ) ) ).

% measurable_comp
thf(fact_1104_measurable__comp,axiom,
    ! [F2: real > real,M: sigma_measure_real,N: sigma_measure_real,G2: real > nat,L3: sigma_measure_nat] :
      ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ M @ N ) )
     => ( ( member_real_nat @ G2 @ ( sigma_6315060578831106510al_nat @ N @ L3 ) )
       => ( member_real_nat @ ( comp_real_nat_real @ G2 @ F2 ) @ ( sigma_6315060578831106510al_nat @ M @ L3 ) ) ) ) ).

% measurable_comp
thf(fact_1105_measurable__comp,axiom,
    ! [F2: real > $o,M: sigma_measure_real,N: sigma_measure_o,G2: $o > $o,L3: sigma_measure_o] :
      ( ( member_real_o @ F2 @ ( sigma_3939073009482781210real_o @ M @ N ) )
     => ( ( member_o_o @ G2 @ ( sigma_measurable_o_o @ N @ L3 ) )
       => ( member_real_o @ ( comp_o_o_real @ G2 @ F2 ) @ ( sigma_3939073009482781210real_o @ M @ L3 ) ) ) ) ).

% measurable_comp
thf(fact_1106_measurable__comp,axiom,
    ! [F2: real > $o,M: sigma_measure_real,N: sigma_measure_o,G2: $o > nat,L3: sigma_measure_nat] :
      ( ( member_real_o @ F2 @ ( sigma_3939073009482781210real_o @ M @ N ) )
     => ( ( member_o_nat @ G2 @ ( sigma_1999164137574644376_o_nat @ N @ L3 ) )
       => ( member_real_nat @ ( comp_o_nat_real @ G2 @ F2 ) @ ( sigma_6315060578831106510al_nat @ M @ L3 ) ) ) ) ).

% measurable_comp
thf(fact_1107_measurable__comp,axiom,
    ! [F2: real > $o,M: sigma_measure_real,N: sigma_measure_o,G2: $o > real,L3: sigma_measure_real] :
      ( ( member_real_o @ F2 @ ( sigma_3939073009482781210real_o @ M @ N ) )
     => ( ( member_o_real @ G2 @ ( sigma_2430008634441611636o_real @ N @ L3 ) )
       => ( member_real_real @ ( comp_o_real_real @ G2 @ F2 ) @ ( sigma_5267869275261027754l_real @ M @ L3 ) ) ) ) ).

% measurable_comp
thf(fact_1108_nat_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: nat > produc2422161461964618553l_real,Y3: sigma_2308072346491277622l_real] :
      ( ( member4944736856719700937l_real @ K2 @ ( sigma_5893925349391517463l_real @ borel_8449730974584783410el_nat @ Y3 ) )
     => ( member4944736856719700937l_real @ K2 @ ( qbs_mo6520021129653552495l_real @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur3029786804310284173l_real @ Y3 ) ) ) ) ).

% nat.qbs_morphism_measurable_intro
thf(fact_1109_nat_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: nat > produc7716430852924023517t_real,Y3: sigma_5310753476256395226t_real] :
      ( ( member4237364305948650477t_real @ K2 @ ( sigma_8750250338757262779t_real @ borel_8449730974584783410el_nat @ Y3 ) )
     => ( member4237364305948650477t_real @ K2 @ ( qbs_mo2896996399151425555t_real @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur2011440102552004913t_real @ Y3 ) ) ) ) ).

% nat.qbs_morphism_measurable_intro
thf(fact_1110_nat_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: nat > real,Y3: sigma_measure_real] :
      ( ( member_nat_real @ K2 @ ( sigma_1747752005702207822t_real @ borel_8449730974584783410el_nat @ Y3 ) )
     => ( member_nat_real @ K2 @ ( qbs_mo2000642995705457910t_real @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur6875533127466166616s_real @ Y3 ) ) ) ) ).

% nat.qbs_morphism_measurable_intro
thf(fact_1111_nat_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: nat > $o,Y3: sigma_measure_o] :
      ( ( member_nat_o @ K2 @ ( sigma_5101835498682829686_nat_o @ borel_8449730974584783410el_nat @ Y3 ) )
     => ( member_nat_o @ K2 @ ( qbs_morphism_nat_o @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur2705496967258476524_qbs_o @ Y3 ) ) ) ) ).

% nat.qbs_morphism_measurable_intro
thf(fact_1112_nat_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: nat > nat,Y3: sigma_measure_nat] :
      ( ( member_nat_nat @ K2 @ ( sigma_4350458207664084850at_nat @ borel_8449730974584783410el_nat @ Y3 ) )
     => ( member_nat_nat @ K2 @ ( qbs_morphism_nat_nat @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur4416158800429964412bs_nat @ Y3 ) ) ) ) ).

% nat.qbs_morphism_measurable_intro
thf(fact_1113_bool_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: $o > produc2422161461964618553l_real,Y3: sigma_2308072346491277622l_real] :
      ( ( member8602590400058854173l_real @ K2 @ ( sigma_2489502367751881329l_real @ borel_5500255247093592246orel_o @ Y3 ) )
     => ( member8602590400058854173l_real @ K2 @ ( qbs_mo6076292073755557401l_real @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur3029786804310284173l_real @ Y3 ) ) ) ) ).

% bool.qbs_morphism_measurable_intro
thf(fact_1114_bool_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: $o > produc7716430852924023517t_real,Y3: sigma_5310753476256395226t_real] :
      ( ( member8739982677887872321t_real @ K2 @ ( sigma_680772226823374357t_real @ borel_5500255247093592246orel_o @ Y3 ) )
     => ( member8739982677887872321t_real @ K2 @ ( qbs_mo928686258813670845t_real @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur2011440102552004913t_real @ Y3 ) ) ) ) ).

% bool.qbs_morphism_measurable_intro
thf(fact_1115_bool_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: $o > real,Y3: sigma_measure_real] :
      ( ( member_o_real @ K2 @ ( sigma_2430008634441611636o_real @ borel_5500255247093592246orel_o @ Y3 ) )
     => ( member_o_real @ K2 @ ( qbs_morphism_o_real @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur6875533127466166616s_real @ Y3 ) ) ) ) ).

% bool.qbs_morphism_measurable_intro
thf(fact_1116_bool_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: $o > $o,Y3: sigma_measure_o] :
      ( ( member_o_o @ K2 @ ( sigma_measurable_o_o @ borel_5500255247093592246orel_o @ Y3 ) )
     => ( member_o_o @ K2 @ ( qbs_morphism_o_o @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur2705496967258476524_qbs_o @ Y3 ) ) ) ) ).

% bool.qbs_morphism_measurable_intro
thf(fact_1117_bool_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: $o > nat,Y3: sigma_measure_nat] :
      ( ( member_o_nat @ K2 @ ( sigma_1999164137574644376_o_nat @ borel_5500255247093592246orel_o @ Y3 ) )
     => ( member_o_nat @ K2 @ ( qbs_morphism_o_nat @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur4416158800429964412bs_nat @ Y3 ) ) ) ) ).

% bool.qbs_morphism_measurable_intro
thf(fact_1118_ennreal_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: extend8495563244428889912nnreal > produc2422161461964618553l_real,Y3: sigma_2308072346491277622l_real] :
      ( ( member7354208599470296673l_real @ K2 @ ( sigma_1014563338549229999l_real @ borel_6524799422816628122nnreal @ Y3 ) )
     => ( member7354208599470296673l_real @ K2 @ ( qbs_mo8045053474288007175l_real @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur3029786804310284173l_real @ Y3 ) ) ) ) ).

% ennreal.qbs_morphism_measurable_intro
thf(fact_1119_ennreal_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: extend8495563244428889912nnreal > produc7716430852924023517t_real,Y3: sigma_5310753476256395226t_real] :
      ( ( member2197300837325509253t_real @ K2 @ ( sigma_2672489485171276883t_real @ borel_6524799422816628122nnreal @ Y3 ) )
     => ( member2197300837325509253t_real @ K2 @ ( qbs_mo3970737951806219947t_real @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur2011440102552004913t_real @ Y3 ) ) ) ) ).

% ennreal.qbs_morphism_measurable_intro
thf(fact_1120_ennreal_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: extend8495563244428889912nnreal > real,Y3: sigma_measure_real] :
      ( ( member2874014351250825754l_real @ K2 @ ( sigma_7049758200512112822l_real @ borel_6524799422816628122nnreal @ Y3 ) )
     => ( member2874014351250825754l_real @ K2 @ ( qbs_mo8573344932208643166l_real @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur6875533127466166616s_real @ Y3 ) ) ) ) ).

% ennreal.qbs_morphism_measurable_intro
thf(fact_1121_ennreal_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: extend8495563244428889912nnreal > $o,Y3: sigma_measure_o] :
      ( ( member8095236870201115968real_o @ K2 @ ( sigma_6279906219187228174real_o @ borel_6524799422816628122nnreal @ Y3 ) )
     => ( member8095236870201115968real_o @ K2 @ ( qbs_mo7845494039804091494real_o @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur2705496967258476524_qbs_o @ Y3 ) ) ) ) ).

% ennreal.qbs_morphism_measurable_intro
thf(fact_1122_ennreal_Oqbs__morphism__measurable__intro,axiom,
    ! [K2: extend8495563244428889912nnreal > nat,Y3: sigma_measure_nat] :
      ( ( member6436672275262627518al_nat @ K2 @ ( sigma_1856489715609627354al_nat @ borel_6524799422816628122nnreal @ Y3 ) )
     => ( member6436672275262627518al_nat @ K2 @ ( qbs_mo182749989559755394al_nat @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur4416158800429964412bs_nat @ Y3 ) ) ) ) ).

% ennreal.qbs_morphism_measurable_intro
thf(fact_1123_qbs__space__R,axiom,
    ! [X3: sigma_2308072346491277622l_real] :
      ( ( qbs_sp935892911445737839l_real @ ( measur3029786804310284173l_real @ X3 ) )
      = ( sigma_2519298556039103681l_real @ X3 ) ) ).

% qbs_space_R
thf(fact_1124_qbs__space__R,axiom,
    ! [X3: sigma_5310753476256395226t_real] :
      ( ( qbs_sp7178206101462885395t_real @ ( measur2011440102552004913t_real @ X3 ) )
      = ( sigma_2177939267068080229t_real @ X3 ) ) ).

% qbs_space_R
thf(fact_1125_qbs__space__R,axiom,
    ! [X3: sigma_measure_real] :
      ( ( qbs_space_real @ ( measur6875533127466166616s_real @ X3 ) )
      = ( sigma_space_real @ X3 ) ) ).

% qbs_space_R
thf(fact_1126_qbs__space__R,axiom,
    ! [X3: sigma_measure_o] :
      ( ( qbs_space_o @ ( measur2705496967258476524_qbs_o @ X3 ) )
      = ( sigma_space_o @ X3 ) ) ).

% qbs_space_R
thf(fact_1127_qbs__space__R,axiom,
    ! [X3: sigma_measure_nat] :
      ( ( qbs_space_nat @ ( measur4416158800429964412bs_nat @ X3 ) )
      = ( sigma_space_nat @ X3 ) ) ).

% qbs_space_R
thf(fact_1128_nat_Oqbs__morphism__dest,axiom,
    ! [K2: nat > produc2422161461964618553l_real,Y3: sigma_2308072346491277622l_real] :
      ( ( member4944736856719700937l_real @ K2 @ ( qbs_mo6520021129653552495l_real @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur3029786804310284173l_real @ Y3 ) ) )
     => ( member4944736856719700937l_real @ K2 @ ( sigma_5893925349391517463l_real @ borel_8449730974584783410el_nat @ Y3 ) ) ) ).

% nat.qbs_morphism_dest
thf(fact_1129_nat_Oqbs__morphism__dest,axiom,
    ! [K2: nat > produc7716430852924023517t_real,Y3: sigma_5310753476256395226t_real] :
      ( ( member4237364305948650477t_real @ K2 @ ( qbs_mo2896996399151425555t_real @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur2011440102552004913t_real @ Y3 ) ) )
     => ( member4237364305948650477t_real @ K2 @ ( sigma_8750250338757262779t_real @ borel_8449730974584783410el_nat @ Y3 ) ) ) ).

% nat.qbs_morphism_dest
thf(fact_1130_nat_Oqbs__morphism__dest,axiom,
    ! [K2: nat > real,Y3: sigma_measure_real] :
      ( ( member_nat_real @ K2 @ ( qbs_mo2000642995705457910t_real @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur6875533127466166616s_real @ Y3 ) ) )
     => ( member_nat_real @ K2 @ ( sigma_1747752005702207822t_real @ borel_8449730974584783410el_nat @ Y3 ) ) ) ).

% nat.qbs_morphism_dest
thf(fact_1131_nat_Oqbs__morphism__dest,axiom,
    ! [K2: nat > $o,Y3: sigma_measure_o] :
      ( ( member_nat_o @ K2 @ ( qbs_morphism_nat_o @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur2705496967258476524_qbs_o @ Y3 ) ) )
     => ( member_nat_o @ K2 @ ( sigma_5101835498682829686_nat_o @ borel_8449730974584783410el_nat @ Y3 ) ) ) ).

% nat.qbs_morphism_dest
thf(fact_1132_nat_Oqbs__morphism__dest,axiom,
    ! [K2: nat > nat,Y3: sigma_measure_nat] :
      ( ( member_nat_nat @ K2 @ ( qbs_morphism_nat_nat @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur4416158800429964412bs_nat @ Y3 ) ) )
     => ( member_nat_nat @ K2 @ ( sigma_4350458207664084850at_nat @ borel_8449730974584783410el_nat @ Y3 ) ) ) ).

% nat.qbs_morphism_dest
thf(fact_1133_bool_Oqbs__morphism__dest,axiom,
    ! [K2: $o > produc2422161461964618553l_real,Y3: sigma_2308072346491277622l_real] :
      ( ( member8602590400058854173l_real @ K2 @ ( qbs_mo6076292073755557401l_real @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur3029786804310284173l_real @ Y3 ) ) )
     => ( member8602590400058854173l_real @ K2 @ ( sigma_2489502367751881329l_real @ borel_5500255247093592246orel_o @ Y3 ) ) ) ).

% bool.qbs_morphism_dest
thf(fact_1134_bool_Oqbs__morphism__dest,axiom,
    ! [K2: $o > produc7716430852924023517t_real,Y3: sigma_5310753476256395226t_real] :
      ( ( member8739982677887872321t_real @ K2 @ ( qbs_mo928686258813670845t_real @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur2011440102552004913t_real @ Y3 ) ) )
     => ( member8739982677887872321t_real @ K2 @ ( sigma_680772226823374357t_real @ borel_5500255247093592246orel_o @ Y3 ) ) ) ).

% bool.qbs_morphism_dest
thf(fact_1135_bool_Oqbs__morphism__dest,axiom,
    ! [K2: $o > real,Y3: sigma_measure_real] :
      ( ( member_o_real @ K2 @ ( qbs_morphism_o_real @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur6875533127466166616s_real @ Y3 ) ) )
     => ( member_o_real @ K2 @ ( sigma_2430008634441611636o_real @ borel_5500255247093592246orel_o @ Y3 ) ) ) ).

% bool.qbs_morphism_dest
thf(fact_1136_bool_Oqbs__morphism__dest,axiom,
    ! [K2: $o > $o,Y3: sigma_measure_o] :
      ( ( member_o_o @ K2 @ ( qbs_morphism_o_o @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur2705496967258476524_qbs_o @ Y3 ) ) )
     => ( member_o_o @ K2 @ ( sigma_measurable_o_o @ borel_5500255247093592246orel_o @ Y3 ) ) ) ).

% bool.qbs_morphism_dest
thf(fact_1137_bool_Oqbs__morphism__dest,axiom,
    ! [K2: $o > nat,Y3: sigma_measure_nat] :
      ( ( member_o_nat @ K2 @ ( qbs_morphism_o_nat @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur4416158800429964412bs_nat @ Y3 ) ) )
     => ( member_o_nat @ K2 @ ( sigma_1999164137574644376_o_nat @ borel_5500255247093592246orel_o @ Y3 ) ) ) ).

% bool.qbs_morphism_dest
thf(fact_1138_ennreal_Oqbs__morphism__dest,axiom,
    ! [K2: extend8495563244428889912nnreal > produc2422161461964618553l_real,Y3: sigma_2308072346491277622l_real] :
      ( ( member7354208599470296673l_real @ K2 @ ( qbs_mo8045053474288007175l_real @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur3029786804310284173l_real @ Y3 ) ) )
     => ( member7354208599470296673l_real @ K2 @ ( sigma_1014563338549229999l_real @ borel_6524799422816628122nnreal @ Y3 ) ) ) ).

% ennreal.qbs_morphism_dest
thf(fact_1139_ennreal_Oqbs__morphism__dest,axiom,
    ! [K2: extend8495563244428889912nnreal > produc7716430852924023517t_real,Y3: sigma_5310753476256395226t_real] :
      ( ( member2197300837325509253t_real @ K2 @ ( qbs_mo3970737951806219947t_real @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur2011440102552004913t_real @ Y3 ) ) )
     => ( member2197300837325509253t_real @ K2 @ ( sigma_2672489485171276883t_real @ borel_6524799422816628122nnreal @ Y3 ) ) ) ).

% ennreal.qbs_morphism_dest
thf(fact_1140_ennreal_Oqbs__morphism__dest,axiom,
    ! [K2: extend8495563244428889912nnreal > real,Y3: sigma_measure_real] :
      ( ( member2874014351250825754l_real @ K2 @ ( qbs_mo8573344932208643166l_real @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur6875533127466166616s_real @ Y3 ) ) )
     => ( member2874014351250825754l_real @ K2 @ ( sigma_7049758200512112822l_real @ borel_6524799422816628122nnreal @ Y3 ) ) ) ).

% ennreal.qbs_morphism_dest
thf(fact_1141_ennreal_Oqbs__morphism__dest,axiom,
    ! [K2: extend8495563244428889912nnreal > $o,Y3: sigma_measure_o] :
      ( ( member8095236870201115968real_o @ K2 @ ( qbs_mo7845494039804091494real_o @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur2705496967258476524_qbs_o @ Y3 ) ) )
     => ( member8095236870201115968real_o @ K2 @ ( sigma_6279906219187228174real_o @ borel_6524799422816628122nnreal @ Y3 ) ) ) ).

% ennreal.qbs_morphism_dest
thf(fact_1142_ennreal_Oqbs__morphism__dest,axiom,
    ! [K2: extend8495563244428889912nnreal > nat,Y3: sigma_measure_nat] :
      ( ( member6436672275262627518al_nat @ K2 @ ( qbs_mo182749989559755394al_nat @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur4416158800429964412bs_nat @ Y3 ) ) )
     => ( member6436672275262627518al_nat @ K2 @ ( sigma_1856489715609627354al_nat @ borel_6524799422816628122nnreal @ Y3 ) ) ) ).

% ennreal.qbs_morphism_dest
thf(fact_1143_nat_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_2308072346491277622l_real] :
      ( ( sigma_5893925349391517463l_real @ borel_8449730974584783410el_nat @ Y3 )
      = ( qbs_mo6520021129653552495l_real @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur3029786804310284173l_real @ Y3 ) ) ) ).

% nat.standard_borel_r_full_faithful
thf(fact_1144_nat_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_5310753476256395226t_real] :
      ( ( sigma_8750250338757262779t_real @ borel_8449730974584783410el_nat @ Y3 )
      = ( qbs_mo2896996399151425555t_real @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur2011440102552004913t_real @ Y3 ) ) ) ).

% nat.standard_borel_r_full_faithful
thf(fact_1145_nat_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_real] :
      ( ( sigma_1747752005702207822t_real @ borel_8449730974584783410el_nat @ Y3 )
      = ( qbs_mo2000642995705457910t_real @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur6875533127466166616s_real @ Y3 ) ) ) ).

% nat.standard_borel_r_full_faithful
thf(fact_1146_nat_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_o] :
      ( ( sigma_5101835498682829686_nat_o @ borel_8449730974584783410el_nat @ Y3 )
      = ( qbs_morphism_nat_o @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur2705496967258476524_qbs_o @ Y3 ) ) ) ).

% nat.standard_borel_r_full_faithful
thf(fact_1147_nat_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_nat] :
      ( ( sigma_4350458207664084850at_nat @ borel_8449730974584783410el_nat @ Y3 )
      = ( qbs_morphism_nat_nat @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur4416158800429964412bs_nat @ Y3 ) ) ) ).

% nat.standard_borel_r_full_faithful
thf(fact_1148_bool_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_2308072346491277622l_real] :
      ( ( sigma_2489502367751881329l_real @ borel_5500255247093592246orel_o @ Y3 )
      = ( qbs_mo6076292073755557401l_real @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur3029786804310284173l_real @ Y3 ) ) ) ).

% bool.standard_borel_r_full_faithful
thf(fact_1149_bool_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_5310753476256395226t_real] :
      ( ( sigma_680772226823374357t_real @ borel_5500255247093592246orel_o @ Y3 )
      = ( qbs_mo928686258813670845t_real @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur2011440102552004913t_real @ Y3 ) ) ) ).

% bool.standard_borel_r_full_faithful
thf(fact_1150_bool_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_real] :
      ( ( sigma_2430008634441611636o_real @ borel_5500255247093592246orel_o @ Y3 )
      = ( qbs_morphism_o_real @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur6875533127466166616s_real @ Y3 ) ) ) ).

% bool.standard_borel_r_full_faithful
thf(fact_1151_bool_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_o] :
      ( ( sigma_measurable_o_o @ borel_5500255247093592246orel_o @ Y3 )
      = ( qbs_morphism_o_o @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur2705496967258476524_qbs_o @ Y3 ) ) ) ).

% bool.standard_borel_r_full_faithful
thf(fact_1152_bool_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_nat] :
      ( ( sigma_1999164137574644376_o_nat @ borel_5500255247093592246orel_o @ Y3 )
      = ( qbs_morphism_o_nat @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) @ ( measur4416158800429964412bs_nat @ Y3 ) ) ) ).

% bool.standard_borel_r_full_faithful
thf(fact_1153_ennreal_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_2308072346491277622l_real] :
      ( ( sigma_1014563338549229999l_real @ borel_6524799422816628122nnreal @ Y3 )
      = ( qbs_mo8045053474288007175l_real @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur3029786804310284173l_real @ Y3 ) ) ) ).

% ennreal.standard_borel_r_full_faithful
thf(fact_1154_ennreal_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_5310753476256395226t_real] :
      ( ( sigma_2672489485171276883t_real @ borel_6524799422816628122nnreal @ Y3 )
      = ( qbs_mo3970737951806219947t_real @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur2011440102552004913t_real @ Y3 ) ) ) ).

% ennreal.standard_borel_r_full_faithful
thf(fact_1155_ennreal_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_real] :
      ( ( sigma_7049758200512112822l_real @ borel_6524799422816628122nnreal @ Y3 )
      = ( qbs_mo8573344932208643166l_real @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur6875533127466166616s_real @ Y3 ) ) ) ).

% ennreal.standard_borel_r_full_faithful
thf(fact_1156_ennreal_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_o] :
      ( ( sigma_6279906219187228174real_o @ borel_6524799422816628122nnreal @ Y3 )
      = ( qbs_mo7845494039804091494real_o @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur2705496967258476524_qbs_o @ Y3 ) ) ) ).

% ennreal.standard_borel_r_full_faithful
thf(fact_1157_ennreal_Ostandard__borel__r__full__faithful,axiom,
    ! [Y3: sigma_measure_nat] :
      ( ( sigma_1856489715609627354al_nat @ borel_6524799422816628122nnreal @ Y3 )
      = ( qbs_mo182749989559755394al_nat @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) @ ( measur4416158800429964412bs_nat @ Y3 ) ) ) ).

% ennreal.standard_borel_r_full_faithful
thf(fact_1158_measurable__cong,axiom,
    ! [M: sigma_2262136186458356274a_real,F2: product_prod_a_real > b > c,G2: product_prod_a_real > b > c,M2: sigma_measure_b_c] :
      ( ! [W: product_prod_a_real] :
          ( ( member7037815648067680368a_real @ W @ ( sigma_5571412987386726097a_real @ M ) )
         => ( ( F2 @ W )
            = ( G2 @ W ) ) )
     => ( ( member2979925738865732021al_b_c @ F2 @ ( sigma_3321470038308056657al_b_c @ M @ M2 ) )
        = ( member2979925738865732021al_b_c @ G2 @ ( sigma_3321470038308056657al_b_c @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_1159_measurable__cong,axiom,
    ! [M: sigma_5782782616773303333od_a_b,F2: product_prod_a_b > c,G2: product_prod_a_b > c,M2: sigma_measure_c] :
      ( ! [W: product_prod_a_b] :
          ( ( member1426531481828664017od_a_b @ W @ ( sigma_1564438922714704432od_a_b @ M ) )
         => ( ( F2 @ W )
            = ( G2 @ W ) ) )
     => ( ( member1080921174361771732_a_b_c @ F2 @ ( sigma_7225552367035416488_a_b_c @ M @ M2 ) )
        = ( member1080921174361771732_a_b_c @ G2 @ ( sigma_7225552367035416488_a_b_c @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_1160_measurable__cong,axiom,
    ! [M: sigma_measure_a,F2: a > b > c,G2: a > b > c,M2: sigma_measure_b_c] :
      ( ! [W: a] :
          ( ( member_a @ W @ ( sigma_space_a @ M ) )
         => ( ( F2 @ W )
            = ( G2 @ W ) ) )
     => ( ( member_a_b_c @ F2 @ ( sigma_1183679740185033300_a_b_c @ M @ M2 ) )
        = ( member_a_b_c @ G2 @ ( sigma_1183679740185033300_a_b_c @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_1161_measurable__cong,axiom,
    ! [M: sigma_measure_real,F2: real > b > c,G2: real > b > c,M2: sigma_measure_b_c] :
      ( ! [W: real] :
          ( ( member_real @ W @ ( sigma_space_real @ M ) )
         => ( ( F2 @ W )
            = ( G2 @ W ) ) )
     => ( ( member_real_b_c @ F2 @ ( sigma_219859910464686500al_b_c @ M @ M2 ) )
        = ( member_real_b_c @ G2 @ ( sigma_219859910464686500al_b_c @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_1162_measurable__cong,axiom,
    ! [M: sigma_measure_real,F2: real > a > b > c,G2: real > a > b > c,M2: sigma_measure_a_b_c] :
      ( ! [W: real] :
          ( ( member_real @ W @ ( sigma_space_real @ M ) )
         => ( ( F2 @ W )
            = ( G2 @ W ) ) )
     => ( ( member_real_a_b_c @ F2 @ ( sigma_8538461840762587415_a_b_c @ M @ M2 ) )
        = ( member_real_a_b_c @ G2 @ ( sigma_8538461840762587415_a_b_c @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_1163_measurable__cong,axiom,
    ! [M: sigma_measure_real,F2: real > real,G2: real > real,M2: sigma_measure_real] :
      ( ! [W: real] :
          ( ( member_real @ W @ ( sigma_space_real @ M ) )
         => ( ( F2 @ W )
            = ( G2 @ W ) ) )
     => ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ M @ M2 ) )
        = ( member_real_real @ G2 @ ( sigma_5267869275261027754l_real @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_1164_measurable__cong,axiom,
    ! [M: sigma_measure_real,F2: real > $o,G2: real > $o,M2: sigma_measure_o] :
      ( ! [W: real] :
          ( ( member_real @ W @ ( sigma_space_real @ M ) )
         => ( ( F2 @ W )
            = ( G2 @ W ) ) )
     => ( ( member_real_o @ F2 @ ( sigma_3939073009482781210real_o @ M @ M2 ) )
        = ( member_real_o @ G2 @ ( sigma_3939073009482781210real_o @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_1165_measurable__cong,axiom,
    ! [M: sigma_measure_real,F2: real > nat,G2: real > nat,M2: sigma_measure_nat] :
      ( ! [W: real] :
          ( ( member_real @ W @ ( sigma_space_real @ M ) )
         => ( ( F2 @ W )
            = ( G2 @ W ) ) )
     => ( ( member_real_nat @ F2 @ ( sigma_6315060578831106510al_nat @ M @ M2 ) )
        = ( member_real_nat @ G2 @ ( sigma_6315060578831106510al_nat @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_1166_measurable__cong,axiom,
    ! [M: sigma_measure_o,F2: $o > real,G2: $o > real,M2: sigma_measure_real] :
      ( ! [W: $o] :
          ( ( member_o @ W @ ( sigma_space_o @ M ) )
         => ( ( F2 @ W )
            = ( G2 @ W ) ) )
     => ( ( member_o_real @ F2 @ ( sigma_2430008634441611636o_real @ M @ M2 ) )
        = ( member_o_real @ G2 @ ( sigma_2430008634441611636o_real @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_1167_measurable__cong,axiom,
    ! [M: sigma_measure_nat,F2: nat > real,G2: nat > real,M2: sigma_measure_real] :
      ( ! [W: nat] :
          ( ( member_nat @ W @ ( sigma_space_nat @ M ) )
         => ( ( F2 @ W )
            = ( G2 @ W ) ) )
     => ( ( member_nat_real @ F2 @ ( sigma_1747752005702207822t_real @ M @ M2 ) )
        = ( member_nat_real @ G2 @ ( sigma_1747752005702207822t_real @ M @ M2 ) ) ) ) ).

% measurable_cong
thf(fact_1168_measurable__space,axiom,
    ! [F2: $o > $o,M: sigma_measure_o,A5: sigma_measure_o,X4: $o] :
      ( ( member_o_o @ F2 @ ( sigma_measurable_o_o @ M @ A5 ) )
     => ( ( member_o @ X4 @ ( sigma_space_o @ M ) )
       => ( member_o @ ( F2 @ X4 ) @ ( sigma_space_o @ A5 ) ) ) ) ).

% measurable_space
thf(fact_1169_measurable__space,axiom,
    ! [F2: $o > nat,M: sigma_measure_o,A5: sigma_measure_nat,X4: $o] :
      ( ( member_o_nat @ F2 @ ( sigma_1999164137574644376_o_nat @ M @ A5 ) )
     => ( ( member_o @ X4 @ ( sigma_space_o @ M ) )
       => ( member_nat @ ( F2 @ X4 ) @ ( sigma_space_nat @ A5 ) ) ) ) ).

% measurable_space
thf(fact_1170_measurable__space,axiom,
    ! [F2: nat > $o,M: sigma_measure_nat,A5: sigma_measure_o,X4: nat] :
      ( ( member_nat_o @ F2 @ ( sigma_5101835498682829686_nat_o @ M @ A5 ) )
     => ( ( member_nat @ X4 @ ( sigma_space_nat @ M ) )
       => ( member_o @ ( F2 @ X4 ) @ ( sigma_space_o @ A5 ) ) ) ) ).

% measurable_space
thf(fact_1171_measurable__space,axiom,
    ! [F2: nat > nat,M: sigma_measure_nat,A5: sigma_measure_nat,X4: nat] :
      ( ( member_nat_nat @ F2 @ ( sigma_4350458207664084850at_nat @ M @ A5 ) )
     => ( ( member_nat @ X4 @ ( sigma_space_nat @ M ) )
       => ( member_nat @ ( F2 @ X4 ) @ ( sigma_space_nat @ A5 ) ) ) ) ).

% measurable_space
thf(fact_1172_measurable__space,axiom,
    ! [F2: real > real,M: sigma_measure_real,A5: sigma_measure_real,X4: real] :
      ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ M @ A5 ) )
     => ( ( member_real @ X4 @ ( sigma_space_real @ M ) )
       => ( member_real @ ( F2 @ X4 ) @ ( sigma_space_real @ A5 ) ) ) ) ).

% measurable_space
thf(fact_1173_measurable__space,axiom,
    ! [F2: real > $o,M: sigma_measure_real,A5: sigma_measure_o,X4: real] :
      ( ( member_real_o @ F2 @ ( sigma_3939073009482781210real_o @ M @ A5 ) )
     => ( ( member_real @ X4 @ ( sigma_space_real @ M ) )
       => ( member_o @ ( F2 @ X4 ) @ ( sigma_space_o @ A5 ) ) ) ) ).

% measurable_space
thf(fact_1174_measurable__space,axiom,
    ! [F2: real > nat,M: sigma_measure_real,A5: sigma_measure_nat,X4: real] :
      ( ( member_real_nat @ F2 @ ( sigma_6315060578831106510al_nat @ M @ A5 ) )
     => ( ( member_real @ X4 @ ( sigma_space_real @ M ) )
       => ( member_nat @ ( F2 @ X4 ) @ ( sigma_space_nat @ A5 ) ) ) ) ).

% measurable_space
thf(fact_1175_measurable__space,axiom,
    ! [F2: $o > real,M: sigma_measure_o,A5: sigma_measure_real,X4: $o] :
      ( ( member_o_real @ F2 @ ( sigma_2430008634441611636o_real @ M @ A5 ) )
     => ( ( member_o @ X4 @ ( sigma_space_o @ M ) )
       => ( member_real @ ( F2 @ X4 ) @ ( sigma_space_real @ A5 ) ) ) ) ).

% measurable_space
thf(fact_1176_measurable__space,axiom,
    ! [F2: nat > real,M: sigma_measure_nat,A5: sigma_measure_real,X4: nat] :
      ( ( member_nat_real @ F2 @ ( sigma_1747752005702207822t_real @ M @ A5 ) )
     => ( ( member_nat @ X4 @ ( sigma_space_nat @ M ) )
       => ( member_real @ ( F2 @ X4 ) @ ( sigma_space_real @ A5 ) ) ) ) ).

% measurable_space
thf(fact_1177_measurable__space,axiom,
    ! [F2: product_prod_a_b > c,M: sigma_5782782616773303333od_a_b,A5: sigma_measure_c,X4: product_prod_a_b] :
      ( ( member1080921174361771732_a_b_c @ F2 @ ( sigma_7225552367035416488_a_b_c @ M @ A5 ) )
     => ( ( member1426531481828664017od_a_b @ X4 @ ( sigma_1564438922714704432od_a_b @ M ) )
       => ( member_c @ ( F2 @ X4 ) @ ( sigma_space_c @ A5 ) ) ) ) ).

% measurable_space
thf(fact_1178_measurable__cong__simp,axiom,
    ! [M: sigma_5782782616773303333od_a_b,N: sigma_5782782616773303333od_a_b,M2: sigma_measure_c,N2: sigma_measure_c,F2: product_prod_a_b > c,G2: product_prod_a_b > c] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: product_prod_a_b] :
              ( ( member1426531481828664017od_a_b @ W @ ( sigma_1564438922714704432od_a_b @ M ) )
             => ( ( F2 @ W )
                = ( G2 @ W ) ) )
         => ( ( member1080921174361771732_a_b_c @ F2 @ ( sigma_7225552367035416488_a_b_c @ M @ M2 ) )
            = ( member1080921174361771732_a_b_c @ G2 @ ( sigma_7225552367035416488_a_b_c @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_1179_measurable__cong__simp,axiom,
    ! [M: sigma_measure_a,N: sigma_measure_a,M2: sigma_measure_b_c,N2: sigma_measure_b_c,F2: a > b > c,G2: a > b > c] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: a] :
              ( ( member_a @ W @ ( sigma_space_a @ M ) )
             => ( ( F2 @ W )
                = ( G2 @ W ) ) )
         => ( ( member_a_b_c @ F2 @ ( sigma_1183679740185033300_a_b_c @ M @ M2 ) )
            = ( member_a_b_c @ G2 @ ( sigma_1183679740185033300_a_b_c @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_1180_measurable__cong__simp,axiom,
    ! [M: sigma_measure_real,N: sigma_measure_real,M2: sigma_measure_b_c,N2: sigma_measure_b_c,F2: real > b > c,G2: real > b > c] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: real] :
              ( ( member_real @ W @ ( sigma_space_real @ M ) )
             => ( ( F2 @ W )
                = ( G2 @ W ) ) )
         => ( ( member_real_b_c @ F2 @ ( sigma_219859910464686500al_b_c @ M @ M2 ) )
            = ( member_real_b_c @ G2 @ ( sigma_219859910464686500al_b_c @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_1181_measurable__cong__simp,axiom,
    ! [M: sigma_measure_real,N: sigma_measure_real,M2: sigma_measure_a_b_c,N2: sigma_measure_a_b_c,F2: real > a > b > c,G2: real > a > b > c] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: real] :
              ( ( member_real @ W @ ( sigma_space_real @ M ) )
             => ( ( F2 @ W )
                = ( G2 @ W ) ) )
         => ( ( member_real_a_b_c @ F2 @ ( sigma_8538461840762587415_a_b_c @ M @ M2 ) )
            = ( member_real_a_b_c @ G2 @ ( sigma_8538461840762587415_a_b_c @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_1182_measurable__cong__simp,axiom,
    ! [M: sigma_measure_real,N: sigma_measure_real,M2: sigma_measure_real,N2: sigma_measure_real,F2: real > real,G2: real > real] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: real] :
              ( ( member_real @ W @ ( sigma_space_real @ M ) )
             => ( ( F2 @ W )
                = ( G2 @ W ) ) )
         => ( ( member_real_real @ F2 @ ( sigma_5267869275261027754l_real @ M @ M2 ) )
            = ( member_real_real @ G2 @ ( sigma_5267869275261027754l_real @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_1183_measurable__cong__simp,axiom,
    ! [M: sigma_measure_real,N: sigma_measure_real,M2: sigma_measure_o,N2: sigma_measure_o,F2: real > $o,G2: real > $o] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: real] :
              ( ( member_real @ W @ ( sigma_space_real @ M ) )
             => ( ( F2 @ W )
                = ( G2 @ W ) ) )
         => ( ( member_real_o @ F2 @ ( sigma_3939073009482781210real_o @ M @ M2 ) )
            = ( member_real_o @ G2 @ ( sigma_3939073009482781210real_o @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_1184_measurable__cong__simp,axiom,
    ! [M: sigma_measure_real,N: sigma_measure_real,M2: sigma_measure_nat,N2: sigma_measure_nat,F2: real > nat,G2: real > nat] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: real] :
              ( ( member_real @ W @ ( sigma_space_real @ M ) )
             => ( ( F2 @ W )
                = ( G2 @ W ) ) )
         => ( ( member_real_nat @ F2 @ ( sigma_6315060578831106510al_nat @ M @ M2 ) )
            = ( member_real_nat @ G2 @ ( sigma_6315060578831106510al_nat @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_1185_measurable__cong__simp,axiom,
    ! [M: sigma_measure_o,N: sigma_measure_o,M2: sigma_measure_real,N2: sigma_measure_real,F2: $o > real,G2: $o > real] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: $o] :
              ( ( member_o @ W @ ( sigma_space_o @ M ) )
             => ( ( F2 @ W )
                = ( G2 @ W ) ) )
         => ( ( member_o_real @ F2 @ ( sigma_2430008634441611636o_real @ M @ M2 ) )
            = ( member_o_real @ G2 @ ( sigma_2430008634441611636o_real @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_1186_measurable__cong__simp,axiom,
    ! [M: sigma_measure_nat,N: sigma_measure_nat,M2: sigma_measure_real,N2: sigma_measure_real,F2: nat > real,G2: nat > real] :
      ( ( M = N )
     => ( ( M2 = N2 )
       => ( ! [W: nat] :
              ( ( member_nat @ W @ ( sigma_space_nat @ M ) )
             => ( ( F2 @ W )
                = ( G2 @ W ) ) )
         => ( ( member_nat_real @ F2 @ ( sigma_1747752005702207822t_real @ M @ M2 ) )
            = ( member_nat_real @ G2 @ ( sigma_1747752005702207822t_real @ N @ N2 ) ) ) ) ) ) ).

% measurable_cong_simp
thf(fact_1187_real_Oexist__fg,axiom,
    ? [X5: real > real] :
      ( ( member_real_real @ X5 @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) )
      & ? [Xa: real > real] :
          ( ( member_real_real @ Xa @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) )
          & ! [Xb: real] :
              ( ( member_real @ Xb @ ( sigma_space_real @ borel_5078946678739801102l_real ) )
             => ( ( comp_real_real_real @ Xa @ X5 @ Xb )
                = Xb ) ) ) ) ).

% real.exist_fg
thf(fact_1188_real__real_Oexist__fg,axiom,
    ? [X5: produc2422161461964618553l_real > real] :
      ( ( member6699615393305559423l_real @ X5 @ ( sigma_8002782794886939285l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) @ borel_5078946678739801102l_real ) )
      & ? [Xa: real > produc2422161461964618553l_real] :
          ( ( member9086635009091248365l_real @ Xa @ ( sigma_7998147297565726139l_real @ borel_5078946678739801102l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) )
          & ! [Xb: produc2422161461964618553l_real] :
              ( ( member7849222048561428706l_real @ Xb @ ( sigma_2519298556039103681l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) )
             => ( ( comp_r97482993418849103l_real @ Xa @ X5 @ Xb )
                = Xb ) ) ) ) ).

% real_real.exist_fg
thf(fact_1189_nat__real_Oexist__fg,axiom,
    ? [X5: produc7716430852924023517t_real > real] :
      ( ( member4539693599630147619l_real @ X5 @ ( sigma_7880537205408866233l_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) @ borel_5078946678739801102l_real ) )
      & ? [Xa: real > produc7716430852924023517t_real] :
          ( ( member969486235890772753t_real @ Xa @ ( sigma_2975298441655967327t_real @ borel_5078946678739801102l_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) )
          & ! [Xb: produc7716430852924023517t_real] :
              ( ( member557208447399453958t_real @ Xb @ ( sigma_2177939267068080229t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) )
             => ( ( comp_r4825950202331181903t_real @ Xa @ X5 @ Xb )
                = Xb ) ) ) ) ).

% nat_real.exist_fg
thf(fact_1190_nat_Oexist__fg,axiom,
    ? [X5: nat > real] :
      ( ( member_nat_real @ X5 @ ( sigma_1747752005702207822t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) )
      & ? [Xa: real > nat] :
          ( ( member_real_nat @ Xa @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ borel_8449730974584783410el_nat ) )
          & ! [Xb: nat] :
              ( ( member_nat @ Xb @ ( sigma_space_nat @ borel_8449730974584783410el_nat ) )
             => ( ( comp_real_nat_nat @ Xa @ X5 @ Xb )
                = Xb ) ) ) ) ).

% nat.exist_fg
thf(fact_1191_bool_Oexist__fg,axiom,
    ? [X5: $o > real] :
      ( ( member_o_real @ X5 @ ( sigma_2430008634441611636o_real @ borel_5500255247093592246orel_o @ borel_5078946678739801102l_real ) )
      & ? [Xa: real > $o] :
          ( ( member_real_o @ Xa @ ( sigma_3939073009482781210real_o @ borel_5078946678739801102l_real @ borel_5500255247093592246orel_o ) )
          & ! [Xb: $o] :
              ( ( member_o @ Xb @ ( sigma_space_o @ borel_5500255247093592246orel_o ) )
             => ( ( comp_real_o_o @ Xa @ X5 @ Xb )
                = Xb ) ) ) ) ).

% bool.exist_fg
thf(fact_1192_ennreal_Oexist__fg,axiom,
    ? [X5: extend8495563244428889912nnreal > real] :
      ( ( member2874014351250825754l_real @ X5 @ ( sigma_7049758200512112822l_real @ borel_6524799422816628122nnreal @ borel_5078946678739801102l_real ) )
      & ? [Xa: real > extend8495563244428889912nnreal] :
          ( ( member2919562650594848410nnreal @ Xa @ ( sigma_9017504469962657078nnreal @ borel_5078946678739801102l_real @ borel_6524799422816628122nnreal ) )
          & ! [Xb: extend8495563244428889912nnreal] :
              ( ( member7908768830364227535nnreal @ Xb @ ( sigma_3147302497200244656nnreal @ borel_6524799422816628122nnreal ) )
             => ( ( comp_r6281409797179841921nnreal @ Xa @ X5 @ Xb )
                = Xb ) ) ) ) ).

% ennreal.exist_fg
thf(fact_1193_r01__to__r01__r01__measurable,axiom,
    member9086635009091248365l_real @ r01_to_r01_r01 @ ( sigma_7998147297565726139l_real @ borel_5078946678739801102l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) ).

% r01_to_r01_r01_measurable
thf(fact_1194_nat__real_Ol__r__r__sets,axiom,
    ( ( sigma_2363344875859395388t_real @ ( measur6583539744506187129t_real @ ( binary2938201662863479403t_real @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) ) ) )
    = ( sigma_2363344875859395388t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) ) ).

% nat_real.l_r_r_sets
thf(fact_1195_r01__r01__to__r01__measurable,axiom,
    member6699615393305559423l_real @ r01_r01_to_r01 @ ( sigma_8002782794886939285l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) @ borel_5078946678739801102l_real ) ).

% r01_r01_to_r01_measurable
thf(fact_1196_nat__real_Og__meas,axiom,
    member969486235890772753t_real @ ( standa3432675769617534289t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) @ ( sigma_2975298441655967327t_real @ borel_5078946678739801102l_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) ).

% nat_real.g_meas
thf(fact_1197_nat__real_Of__meas,axiom,
    member4539693599630147619l_real @ ( standa2191550596119666194t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) @ ( sigma_7880537205408866233l_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) @ borel_5078946678739801102l_real ) ).

% nat_real.f_meas
thf(fact_1198_nat__real_Ostandard__borel__lr__sets__ident,axiom,
    ( ( sigma_2363344875859395388t_real @ ( measur6583539744506187129t_real @ ( measur2011440102552004913t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) ) )
    = ( sigma_2363344875859395388t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) ) ).

% nat_real.standard_borel_lr_sets_ident
thf(fact_1199_nat__real_Ogf__comp__id_H_I2_J,axiom,
    ! [X4: produc7716430852924023517t_real] :
      ( ( standa3432675769617534289t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) @ ( standa2191550596119666194t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) @ X4 ) )
      = X4 ) ).

% nat_real.gf_comp_id'(2)
thf(fact_1200_nat__real_Ogf__comp__id_I2_J,axiom,
    ! [X4: produc7716430852924023517t_real] :
      ( ( member557208447399453958t_real @ X4 @ ( sigma_2177939267068080229t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) )
     => ( ( standa3432675769617534289t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) @ ( standa2191550596119666194t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) @ X4 ) )
        = X4 ) ) ).

% nat_real.gf_comp_id(2)
thf(fact_1201_nat__real_Ogf__comp__id_I1_J,axiom,
    ! [X4: produc7716430852924023517t_real] :
      ( ( member557208447399453958t_real @ X4 @ ( sigma_2177939267068080229t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) )
     => ( ( comp_r4825950202331181903t_real @ ( standa3432675769617534289t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) @ ( standa2191550596119666194t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) @ X4 )
        = X4 ) ) ).

% nat_real.gf_comp_id(1)
thf(fact_1202_nat__real_Ogf__comp__id_H_I1_J,axiom,
    ( ( comp_r4825950202331181903t_real @ ( standa3432675769617534289t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) @ ( standa2191550596119666194t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) )
    = id_Pro272570185591972174t_real ) ).

% nat_real.gf_comp_id'(1)
thf(fact_1203_r01__to__r01__r01__fst__measurable,axiom,
    member_real_real @ r01_to_r01_r01_fst @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ).

% r01_to_r01_r01_fst_measurable
thf(fact_1204_r01__to__r01__r01__snd__measurable,axiom,
    member_real_real @ r01_to_r01_r01_snd @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ).

% r01_to_r01_r01_snd_measurable
thf(fact_1205_real_Ostandard__borel__lr__sets__ident,axiom,
    ( ( sigma_sets_real @ ( measur1733462625046462224e_real @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) ) )
    = ( sigma_sets_real @ borel_5078946678739801102l_real ) ) ).

% real.standard_borel_lr_sets_ident
thf(fact_1206_nat_Ostandard__borel__lr__sets__ident,axiom,
    ( ( sigma_sets_nat @ ( measur7418878410283781684re_nat @ ( measur4416158800429964412bs_nat @ borel_8449730974584783410el_nat ) ) )
    = ( sigma_sets_nat @ borel_8449730974584783410el_nat ) ) ).

% nat.standard_borel_lr_sets_ident
thf(fact_1207_ennreal_Ostandard__borel__lr__sets__ident,axiom,
    ( ( sigma_5465916536984168985nnreal @ ( measur7384687747506661788nnreal @ ( measur2642298986910087140nnreal @ borel_6524799422816628122nnreal ) ) )
    = ( sigma_5465916536984168985nnreal @ borel_6524799422816628122nnreal ) ) ).

% ennreal.standard_borel_lr_sets_ident
thf(fact_1208_bool_Ostandard__borel__lr__sets__ident,axiom,
    ( ( sigma_sets_o @ ( measur2926627334652526644sure_o @ ( measur2705496967258476524_qbs_o @ borel_5500255247093592246orel_o ) ) )
    = ( sigma_sets_o @ borel_5500255247093592246orel_o ) ) ).

% bool.standard_borel_lr_sets_ident
thf(fact_1209_real__real_Ol__r__r__sets,axiom,
    ( ( sigma_1543982426361076760l_real @ ( measur6658399249024522197l_real @ ( binary210465342804807751l_real @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) ) ) )
    = ( sigma_1543982426361076760l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) ) ).

% real_real.l_r_r_sets
thf(fact_1210_real__real_Ostandard__borel__lr__sets__ident,axiom,
    ( ( sigma_1543982426361076760l_real @ ( measur6658399249024522197l_real @ ( measur3029786804310284173l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) ) )
    = ( sigma_1543982426361076760l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) ) ).

% real_real.standard_borel_lr_sets_ident
thf(fact_1211_real_Ostandard__borel__sets,axiom,
    ! [Y3: sigma_measure_real] :
      ( ( ( sigma_sets_real @ borel_5078946678739801102l_real )
        = ( sigma_sets_real @ Y3 ) )
     => ( standard_borel_real @ Y3 ) ) ).

% real.standard_borel_sets
thf(fact_1212_real__real_Ostandard__borel__sets,axiom,
    ! [Y3: sigma_2308072346491277622l_real] :
      ( ( ( sigma_1543982426361076760l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) )
        = ( sigma_1543982426361076760l_real @ Y3 ) )
     => ( standa8333227632594042252l_real @ Y3 ) ) ).

% real_real.standard_borel_sets
thf(fact_1213_real_Ostandard__borel__axioms,axiom,
    standard_borel_real @ borel_5078946678739801102l_real ).

% real.standard_borel_axioms
thf(fact_1214_real__real_Ostandard__borel__axioms,axiom,
    standa8333227632594042252l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ).

% real_real.standard_borel_axioms
thf(fact_1215_real__real_Opair__standard__borel__axioms,axiom,
    pair_s454119610699386988l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ).

% real_real.pair_standard_borel_axioms
thf(fact_1216_nat__real_Ostandard__borel__axioms,axiom,
    standa1520499236374798000t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ).

% nat_real.standard_borel_axioms
thf(fact_1217_nat__real_Opair__standard__borel__axioms,axiom,
    pair_s8264832550775477520t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ).

% nat_real.pair_standard_borel_axioms
thf(fact_1218_nat__real_Ostandard__borel__sets,axiom,
    ! [Y3: sigma_5310753476256395226t_real] :
      ( ( ( sigma_2363344875859395388t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) )
        = ( sigma_2363344875859395388t_real @ Y3 ) )
     => ( standa1520499236374798000t_real @ Y3 ) ) ).

% nat_real.standard_borel_sets
thf(fact_1219_real_Ogf__comp__id_H_I2_J,axiom,
    ! [X4: real] :
      ( ( standard_g_real @ borel_5078946678739801102l_real @ ( standard_f_real @ borel_5078946678739801102l_real @ X4 ) )
      = X4 ) ).

% real.gf_comp_id'(2)
thf(fact_1220_real__real_Ogf__comp__id_H_I2_J,axiom,
    ! [X4: produc2422161461964618553l_real] :
      ( ( standa5011908621721856941l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) @ ( standa1305434478922034158l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) @ X4 ) )
      = X4 ) ).

% real_real.gf_comp_id'(2)
thf(fact_1221_real_Ogf__comp__id_I2_J,axiom,
    ! [X4: real] :
      ( ( member_real @ X4 @ ( sigma_space_real @ borel_5078946678739801102l_real ) )
     => ( ( standard_g_real @ borel_5078946678739801102l_real @ ( standard_f_real @ borel_5078946678739801102l_real @ X4 ) )
        = X4 ) ) ).

% real.gf_comp_id(2)
thf(fact_1222_real_Ogf__comp__id_H_I1_J,axiom,
    ( ( comp_real_real_real @ ( standard_g_real @ borel_5078946678739801102l_real ) @ ( standard_f_real @ borel_5078946678739801102l_real ) )
    = id_real ) ).

% real.gf_comp_id'(1)
thf(fact_1223_ennreal_Ogf__comp__id_H_I1_J,axiom,
    ( ( comp_r6281409797179841921nnreal @ ( standa1398259892199664580nnreal @ borel_6524799422816628122nnreal ) @ ( standa4501783974915749827nnreal @ borel_6524799422816628122nnreal ) )
    = id_Ext8331313139072774535nnreal ) ).

% ennreal.gf_comp_id'(1)
thf(fact_1224_nat_Ogf__comp__id_H_I1_J,axiom,
    ( ( comp_real_nat_nat @ ( standard_g_nat @ borel_8449730974584783410el_nat ) @ ( standard_f_nat @ borel_8449730974584783410el_nat ) )
    = id_nat ) ).

% nat.gf_comp_id'(1)
thf(fact_1225_bool_Ogf__comp__id_H_I1_J,axiom,
    ( ( comp_real_o_o @ ( standard_g_o @ borel_5500255247093592246orel_o ) @ ( standard_f_o @ borel_5500255247093592246orel_o ) )
    = id_o ) ).

% bool.gf_comp_id'(1)
thf(fact_1226_real_Ogf__comp__id_I1_J,axiom,
    ! [X4: real] :
      ( ( member_real @ X4 @ ( sigma_space_real @ borel_5078946678739801102l_real ) )
     => ( ( comp_real_real_real @ ( standard_g_real @ borel_5078946678739801102l_real ) @ ( standard_f_real @ borel_5078946678739801102l_real ) @ X4 )
        = X4 ) ) ).

% real.gf_comp_id(1)
thf(fact_1227_real__real_Ogf__comp__id_I2_J,axiom,
    ! [X4: produc2422161461964618553l_real] :
      ( ( member7849222048561428706l_real @ X4 @ ( sigma_2519298556039103681l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) )
     => ( ( standa5011908621721856941l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) @ ( standa1305434478922034158l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) @ X4 ) )
        = X4 ) ) ).

% real_real.gf_comp_id(2)
thf(fact_1228_real__real_Ogf__comp__id_H_I1_J,axiom,
    ( ( comp_r97482993418849103l_real @ ( standa5011908621721856941l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) @ ( standa1305434478922034158l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) )
    = id_Pro8459329387447996714l_real ) ).

% real_real.gf_comp_id'(1)
thf(fact_1229_ennreal_Ogf__comp__id_I1_J,axiom,
    ! [X4: extend8495563244428889912nnreal] :
      ( ( member7908768830364227535nnreal @ X4 @ ( sigma_3147302497200244656nnreal @ borel_6524799422816628122nnreal ) )
     => ( ( comp_r6281409797179841921nnreal @ ( standa1398259892199664580nnreal @ borel_6524799422816628122nnreal ) @ ( standa4501783974915749827nnreal @ borel_6524799422816628122nnreal ) @ X4 )
        = X4 ) ) ).

% ennreal.gf_comp_id(1)
thf(fact_1230_nat_Ogf__comp__id_I1_J,axiom,
    ! [X4: nat] :
      ( ( member_nat @ X4 @ ( sigma_space_nat @ borel_8449730974584783410el_nat ) )
     => ( ( comp_real_nat_nat @ ( standard_g_nat @ borel_8449730974584783410el_nat ) @ ( standard_f_nat @ borel_8449730974584783410el_nat ) @ X4 )
        = X4 ) ) ).

% nat.gf_comp_id(1)
thf(fact_1231_bool_Ogf__comp__id_I1_J,axiom,
    ! [X4: $o] :
      ( ( member_o @ X4 @ ( sigma_space_o @ borel_5500255247093592246orel_o ) )
     => ( ( comp_real_o_o @ ( standard_g_o @ borel_5500255247093592246orel_o ) @ ( standard_f_o @ borel_5500255247093592246orel_o ) @ X4 )
        = X4 ) ) ).

% bool.gf_comp_id(1)
thf(fact_1232_real__real_Ogf__comp__id_I1_J,axiom,
    ! [X4: produc2422161461964618553l_real] :
      ( ( member7849222048561428706l_real @ X4 @ ( sigma_2519298556039103681l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) )
     => ( ( comp_r97482993418849103l_real @ ( standa5011908621721856941l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) @ ( standa1305434478922034158l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) @ X4 )
        = X4 ) ) ).

% real_real.gf_comp_id(1)
thf(fact_1233_real_Of__meas,axiom,
    member_real_real @ ( standard_f_real @ borel_5078946678739801102l_real ) @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ).

% real.f_meas
thf(fact_1234_real_Og__meas,axiom,
    member_real_real @ ( standard_g_real @ borel_5078946678739801102l_real ) @ ( sigma_5267869275261027754l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ).

% real.g_meas
thf(fact_1235_ennreal_Og__meas,axiom,
    member2919562650594848410nnreal @ ( standa1398259892199664580nnreal @ borel_6524799422816628122nnreal ) @ ( sigma_9017504469962657078nnreal @ borel_5078946678739801102l_real @ borel_6524799422816628122nnreal ) ).

% ennreal.g_meas
thf(fact_1236_nat_Og__meas,axiom,
    member_real_nat @ ( standard_g_nat @ borel_8449730974584783410el_nat ) @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ borel_8449730974584783410el_nat ) ).

% nat.g_meas
thf(fact_1237_ennreal_Of__meas,axiom,
    member2874014351250825754l_real @ ( standa4501783974915749827nnreal @ borel_6524799422816628122nnreal ) @ ( sigma_7049758200512112822l_real @ borel_6524799422816628122nnreal @ borel_5078946678739801102l_real ) ).

% ennreal.f_meas
thf(fact_1238_real__real_Of__meas,axiom,
    member6699615393305559423l_real @ ( standa1305434478922034158l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) @ ( sigma_8002782794886939285l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) @ borel_5078946678739801102l_real ) ).

% real_real.f_meas
thf(fact_1239_nat_Of__meas,axiom,
    member_nat_real @ ( standard_f_nat @ borel_8449730974584783410el_nat ) @ ( sigma_1747752005702207822t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ).

% nat.f_meas
thf(fact_1240_bool_Of__meas,axiom,
    member_o_real @ ( standard_f_o @ borel_5500255247093592246orel_o ) @ ( sigma_2430008634441611636o_real @ borel_5500255247093592246orel_o @ borel_5078946678739801102l_real ) ).

% bool.f_meas
thf(fact_1241_real__real_Og__meas,axiom,
    member9086635009091248365l_real @ ( standa5011908621721856941l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) @ ( sigma_7998147297565726139l_real @ borel_5078946678739801102l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) ).

% real_real.g_meas
thf(fact_1242_bool_Og__meas,axiom,
    member_real_o @ ( standard_g_o @ borel_5500255247093592246orel_o ) @ ( sigma_3939073009482781210real_o @ borel_5078946678739801102l_real @ borel_5500255247093592246orel_o ) ).

% bool.g_meas
thf(fact_1243_nat__real_Of__inj,axiom,
    inj_on7684460064353438680l_real @ ( standa2191550596119666194t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) @ ( sigma_2177939267068080229t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) ).

% nat_real.f_inj
thf(fact_1244_real_Ostandard__borel__space__UNIV__axioms,axiom,
    standa1306199911732814765V_real @ borel_5078946678739801102l_real ).

% real.standard_borel_space_UNIV_axioms
thf(fact_1245_real__real_Ostandard__borel__space__UNIV__axioms,axiom,
    standa8482556277449587064l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ).

% real_real.standard_borel_space_UNIV_axioms
thf(fact_1246_nat__real_Ostandard__borel__space__UNIV__axioms,axiom,
    standa1649057328583495836t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ).

% nat_real.standard_borel_space_UNIV_axioms
thf(fact_1247_nat__real_Of__inj_H,axiom,
    inj_on7684460064353438680l_real @ ( standa2191550596119666194t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) @ top_to4855536200657754381t_real ).

% nat_real.f_inj'
thf(fact_1248_nat__real_Opair__standard__borel__space__UNIV__axioms,axiom,
    pair_s5107880421860391064t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ).

% nat_real.pair_standard_borel_space_UNIV_axioms
thf(fact_1249_real_Of__inj_H,axiom,
    inj_on_real_real @ ( standard_f_real @ borel_5078946678739801102l_real ) @ top_top_set_real ).

% real.f_inj'
thf(fact_1250_real__real_Of__inj_H,axiom,
    inj_on8108481164468490036l_real @ ( standa1305434478922034158l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) @ top_to1175844992842649833l_real ).

% real_real.f_inj'
thf(fact_1251_real_Ospace__UNIV,axiom,
    ( ( sigma_space_real @ borel_5078946678739801102l_real )
    = top_top_set_real ) ).

% real.space_UNIV
thf(fact_1252_real_Of__inj,axiom,
    inj_on_real_real @ ( standard_f_real @ borel_5078946678739801102l_real ) @ ( sigma_space_real @ borel_5078946678739801102l_real ) ).

% real.f_inj
thf(fact_1253_real__real_Ospace__UNIV,axiom,
    ( ( sigma_2519298556039103681l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) )
    = top_to1175844992842649833l_real ) ).

% real_real.space_UNIV
thf(fact_1254_real__real_Of__inj,axiom,
    inj_on8108481164468490036l_real @ ( standa1305434478922034158l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) @ ( sigma_2519298556039103681l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) ).

% real_real.f_inj
thf(fact_1255_nat__real_Ospace__UNIV,axiom,
    ( ( sigma_2177939267068080229t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) )
    = top_to4855536200657754381t_real ) ).

% nat_real.space_UNIV
thf(fact_1256_nat__real_Og__surj_H,axiom,
    ( ( image_917144268913371882t_real @ ( standa3432675769617534289t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) @ top_top_set_real )
    = top_to4855536200657754381t_real ) ).

% nat_real.g_surj'
thf(fact_1257_real_Og__surj_H,axiom,
    ( ( image_real_real @ ( standard_g_real @ borel_5078946678739801102l_real ) @ top_top_set_real )
    = top_top_set_real ) ).

% real.g_surj'
thf(fact_1258_real__real_Og__surj_H,axiom,
    ( ( image_4241449277970500806l_real @ ( standa5011908621721856941l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) @ top_top_set_real )
    = top_to1175844992842649833l_real ) ).

% real_real.g_surj'
thf(fact_1259_nat__real_Osingleton__sets,axiom,
    ! [X4: produc7716430852924023517t_real] :
      ( ( member557208447399453958t_real @ X4 @ ( sigma_2177939267068080229t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) )
     => ( member6599792433088240102t_real @ ( insert8878517086468120749t_real @ X4 @ bot_bo4585460402199822889t_real ) @ ( sigma_2363344875859395388t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) ) ) ).

% nat_real.singleton_sets
thf(fact_1260_nat__real_Ostandard__borel__subset,axiom,
    ! [U: set_Pr320017278500174781t_real] :
      ( ( member6599792433088240102t_real @ U @ ( sigma_2363344875859395388t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) )
     => ( ( U != bot_bo4585460402199822889t_real )
       => ( standa1520499236374798000t_real @ ( sigma_1175968196457143329t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) @ U ) ) ) ) ).

% nat_real.standard_borel_subset
thf(fact_1261_real_Osingleton__sets,axiom,
    ! [X4: real] :
      ( ( member_real @ X4 @ ( sigma_space_real @ borel_5078946678739801102l_real ) )
     => ( member_set_real @ ( insert_real @ X4 @ bot_bot_set_real ) @ ( sigma_sets_real @ borel_5078946678739801102l_real ) ) ) ).

% real.singleton_sets
thf(fact_1262_real__real_Osingleton__sets,axiom,
    ! [X4: produc2422161461964618553l_real] :
      ( ( member7849222048561428706l_real @ X4 @ ( sigma_2519298556039103681l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) )
     => ( member6767226683953100098l_real @ ( insert7746734233410687241l_real @ X4 @ bot_bo3948376660626123781l_real ) @ ( sigma_1543982426361076760l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) ) ) ).

% real_real.singleton_sets
thf(fact_1263_real__standard__borel__subset,axiom,
    ! [U: set_real] :
      ( ( member_set_real @ U @ ( sigma_sets_real @ borel_5078946678739801102l_real ) )
     => ( ( U != bot_bot_set_real )
       => ( standard_borel_real @ ( sigma_5414646170262037096e_real @ borel_5078946678739801102l_real @ U ) ) ) ) ).

% real_standard_borel_subset
thf(fact_1264_real__real_Ostandard__borel__subset,axiom,
    ! [U: set_Pr6218003697084177305l_real] :
      ( ( member6767226683953100098l_real @ U @ ( sigma_1543982426361076760l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) )
     => ( ( U != bot_bo3948376660626123781l_real )
       => ( standa8333227632594042252l_real @ ( sigma_42152174237504125l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) @ U ) ) ) ) ).

% real_real.standard_borel_subset
thf(fact_1265_real_Ocountable__space__discrete,axiom,
    ( ( counta7319604579010473777e_real @ ( sigma_space_real @ borel_5078946678739801102l_real ) )
   => ( ( sigma_sets_real @ borel_5078946678739801102l_real )
      = ( sigma_sets_real @ ( sigma_8508918144308765139e_real @ ( sigma_space_real @ borel_5078946678739801102l_real ) ) ) ) ) ).

% real.countable_space_discrete
thf(fact_1266_real__real_Ocountable__space__discrete,axiom,
    ( ( counta6472190628005395188l_real @ ( sigma_2519298556039103681l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) )
   => ( ( sigma_1543982426361076760l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) )
      = ( sigma_1543982426361076760l_real @ ( sigma_7544814672420218578l_real @ ( sigma_2519298556039103681l_real @ ( binary6478037234023840930l_real @ borel_5078946678739801102l_real @ borel_5078946678739801102l_real ) ) ) ) ) ) ).

% real_real.countable_space_discrete
thf(fact_1267_nat__real_Ocountable__space__discrete,axiom,
    ( ( counta6100287699616567320t_real @ ( sigma_2177939267068080229t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) )
   => ( ( sigma_2363344875859395388t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) )
      = ( sigma_2363344875859395388t_real @ ( sigma_8348511806855285494t_real @ ( sigma_2177939267068080229t_real @ ( binary2880700947547503686t_real @ borel_8449730974584783410el_nat @ borel_5078946678739801102l_real ) ) ) ) ) ) ).

% nat_real.countable_space_discrete
thf(fact_1268_measurable__separate,axiom,
    ! [P2: real > nat,I2: nat] :
      ( ( member_real_nat @ P2 @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ borel_8449730974584783410el_nat ) )
     => ( member_set_real @ ( vimage_real_nat @ P2 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) @ ( sigma_sets_real @ borel_5078946678739801102l_real ) ) ) ).

% measurable_separate
thf(fact_1269_separate__measurable,axiom,
    ! [P2: real > nat] :
      ( ! [I3: nat] : ( member_set_real @ ( vimage_real_nat @ P2 @ ( insert_nat @ I3 @ bot_bot_set_nat ) ) @ ( sigma_sets_real @ borel_5078946678739801102l_real ) )
     => ( member_real_nat @ P2 @ ( sigma_6315060578831106510al_nat @ borel_5078946678739801102l_real @ borel_8449730974584783410el_nat ) ) ) ).

% separate_measurable
thf(fact_1270_finite__Collect__le__nat,axiom,
    ! [K2: nat] :
      ( finite_finite_nat
      @ ( collect_nat
        @ ^ [N3: nat] : ( ord_less_eq_nat @ N3 @ K2 ) ) ) ).

% finite_Collect_le_nat
thf(fact_1271_finite__less__ub,axiom,
    ! [F2: nat > nat,U2: nat] :
      ( ! [N4: nat] : ( ord_less_eq_nat @ N4 @ ( F2 @ N4 ) )
     => ( finite_finite_nat
        @ ( collect_nat
          @ ^ [N3: nat] : ( ord_less_eq_nat @ ( F2 @ N3 ) @ U2 ) ) ) ) ).

% finite_less_ub

% Conjectures (1)
thf(conj_0,conjecture,
    member6939723154228711331_a_b_c @ ( produc8409101302566321868_a_b_c @ k ) @ ( qbs_mo8653977514671865831_a_b_c @ ( binary5762279046363823267real_a @ ( measur6875533127466166616s_real @ borel_5078946678739801102l_real ) @ x ) @ ( exponent_exp_qbs_b_c @ y @ z ) ) ).

%------------------------------------------------------------------------------