%------------------------------------------------------------------------------
% File     : ITP146_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : measure.ax [Gau19]
%          : HL4146_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  633 ( 210 unt; 207 typ;   0 def)
%            Number of atoms       : 1342 ( 401 equ)
%            Maximal formula atoms :   37 (   2 avg)
%            Number of connectives :  952 (  36   ~;   3   |; 452   &)
%                                         (  84 <=>; 377  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   47 (   7 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  154 (  98   >;  56   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  202 ( 202 usr;  42 con; 0-6 aty)
%            Number of variables   : 2106 (1942   !;  11   ?;2106   :)
%                                         ( 153  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Eextreal_2Eextreal,type,
    tyop_2Eextreal_2Eextreal: $tType ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: $tType ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: $tType ).

tff(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).

tff(tyop_2Erealax_2Ereal,type,
    tyop_2Erealax_2Ereal: $tType ).

tff(app_2E2,type,
    app_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(p,type,
    p: tyop_2Emin_2Ebool > $o ).

tff(combin_i_2E0,type,
    combin_i_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).

tff(combin_k_2E0,type,
    combin_k_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).

tff(combin_s_2E0,type,
    combin_s_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).

tff(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).

tff(c_2Eseq_2E_2D_2D_3E_2E0,type,
    c_2Eseq_2E_2D_2D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).

tff(c_2Eseq_2E_2D_2D_3E_2E2,type,
    c_2Eseq_2E_2D_2D_3E_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal) * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Epred__set_2EBIGINTER_2E0,type,
    c_2Epred__set_2EBIGINTER_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2EBIGINTER_2E1,type,
    c_2Epred__set_2EBIGINTER_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EBIGUNION_2E0,type,
    c_2Epred__set_2EBIGUNION_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2EBIGUNION_2E1,type,
    c_2Epred__set_2EBIGUNION_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Emeasure_2EBorel_2E0,type,
    c_2Emeasure_2EBorel_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).

tff(c_2Epred__set_2ECROSS_2E0,type,
    c_2Epred__set_2ECROSS_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2ECROSS_2E2,type,
    c_2Epred__set_2ECROSS_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EDIFF_2E0,type,
    c_2Epred__set_2EDIFF_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EDIFF_2E2,type,
    c_2Epred__set_2EDIFF_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EDISJOINT_2E0,type,
    c_2Epred__set_2EDISJOINT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2EDISJOINT_2E2,type,
    c_2Epred__set_2EDISJOINT_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).

tff(c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E0,type,
    c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal)) ).

tff(c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2,type,
    c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Eextreal_2Eextreal ) ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2Epred__set_2EFINITE_2E0,type,
    c_2Epred__set_2EFINITE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Epred__set_2EFINITE_2E1,type,
    c_2Epred__set_2EFINITE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a) ).

tff(c_2Epred__set_2EFUNSET_2E0,type,
    c_2Epred__set_2EFUNSET_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EFUNSET_2E2,type,
    c_2Epred__set_2EFUNSET_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EGSPEC_2E0,type,
    c_2Epred__set_2EGSPEC_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2EGSPEC_2E1,type,
    c_2Epred__set_2EGSPEC_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Ecombin_2EI_2E0,type,
    c_2Ecombin_2EI_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).

tff(c_2Epred__set_2EIMAGE_2E0,type,
    c_2Epred__set_2EIMAGE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EIMAGE_2E2,type,
    c_2Epred__set_2EIMAGE_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).

tff(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epred__set_2EINSERT_2E0,type,
    c_2Epred__set_2EINSERT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EINSERT_2E2,type,
    c_2Epred__set_2EINSERT_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EINTER_2E0,type,
    c_2Epred__set_2EINTER_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EINTER_2E2,type,
    c_2Epred__set_2EINTER_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Eextreal_2ENegInf_2E0,type,
    c_2Eextreal_2ENegInf_2E0: tyop_2Eextreal_2Eextreal ).

tff(c_2Eextreal_2ENormal_2E0,type,
    c_2Eextreal_2ENormal_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eextreal_2Eextreal) ).

tff(c_2Eextreal_2ENormal_2E1,type,
    c_2Eextreal_2ENormal_2E1: tyop_2Erealax_2Ereal > tyop_2Eextreal_2Eextreal ).

tff(c_2Epred__set_2EPOW_2E0,type,
    c_2Epred__set_2EPOW_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2EPOW_2E1,type,
    c_2Epred__set_2EPOW_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EPREIMAGE_2E0,type,
    c_2Epred__set_2EPREIMAGE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EPREIMAGE_2E1,type,
    c_2Epred__set_2EPREIMAGE_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,A_27b) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).

tff(c_2Epred__set_2EPREIMAGE_2E2,type,
    c_2Epred__set_2EPREIMAGE_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Eextreal_2EPosInf_2E0,type,
    c_2Eextreal_2EPosInf_2E0: tyop_2Eextreal_2Eextreal ).

tff(c_2Eextreal_2EQ__set_2E0,type,
    c_2Eextreal_2EQ__set_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool) ).

tff(c_2Ereal__sigma_2EREAL__SUM__IMAGE_2E0,type,
    c_2Ereal__sigma_2EREAL__SUM__IMAGE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)) ).

tff(c_2Ereal__sigma_2EREAL__SUM__IMAGE_2E2,type,
    c_2Ereal__sigma_2EREAL__SUM__IMAGE_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Erealax_2Ereal ) ).

tff(c_2Epair_2ESND_2E0,type,
    c_2Epair_2ESND_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b) ).

tff(c_2Epred__set_2ESUBSET_2E0,type,
    c_2Epred__set_2ESUBSET_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2ESUBSET_2E2,type,
    c_2Epred__set_2ESUBSET_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Enum_2ESUC_2E1,type,
    c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(c_2Epred__set_2EUNION_2E0,type,
    c_2Epred__set_2EUNION_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EUNION_2E2,type,
    c_2Epred__set_2EUNION_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EUNIV_2E0,type,
    c_2Epred__set_2EUNIV_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Emeasure_2Eadditive_2E0,type,
    c_2Emeasure_2Eadditive_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool) ).

tff(c_2Emeasure_2Eadditive_2E1,type,
    c_2Emeasure_2Eadditive_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) > tyop_2Emin_2Ebool ) ).

tff(c_2Emeasure_2Ealgebra_2E0,type,
    c_2Emeasure_2Ealgebra_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Emeasure_2Ealgebra_2E1,type,
    c_2Emeasure_2Ealgebra_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Emeasure_2Eclosed__cdi_2E0,type,
    c_2Emeasure_2Eclosed__cdi_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Emeasure_2Eclosed__cdi_2E1,type,
    c_2Emeasure_2Eclosed__cdi_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Epred__set_2Ecount_2E0,type,
    c_2Epred__set_2Ecount_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2Ecount_2E1,type,
    c_2Epred__set_2Ecount_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2Epred__set_2Ecountable_2E0,type,
    c_2Epred__set_2Ecountable_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Epred__set_2Ecountable_2E1,type,
    c_2Epred__set_2Ecountable_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Emeasure_2Ecountably__additive_2E0,type,
    c_2Emeasure_2Ecountably__additive_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool) ).

tff(c_2Emeasure_2Ecountably__additive_2E1,type,
    c_2Emeasure_2Ecountably__additive_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) > tyop_2Emin_2Ebool ) ).

tff(c_2Emeasure_2Ecountably__subadditive_2E0,type,
    c_2Emeasure_2Ecountably__subadditive_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool) ).

tff(c_2Emeasure_2Ecountably__subadditive_2E1,type,
    c_2Emeasure_2Ecountably__subadditive_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) > tyop_2Emin_2Ebool ) ).

tff(c_2Eextreal_2Eext__suminf_2E0,type,
    c_2Eextreal_2Eext__suminf_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),tyop_2Eextreal_2Eextreal) ).

tff(c_2Eextreal_2Eext__suminf_2E1,type,
    c_2Eextreal_2Eext__suminf_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal) > tyop_2Eextreal_2Eextreal ).

tff(c_2Eextreal_2Eextreal__abs_2E0,type,
    c_2Eextreal_2Eextreal__abs_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal) ).

tff(c_2Eextreal_2Eextreal__abs_2E1,type,
    c_2Eextreal_2Eextreal__abs_2E1: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal ).

tff(c_2Eextreal_2Eextreal__add_2E0,type,
    c_2Eextreal_2Eextreal__add_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal)) ).

tff(c_2Eextreal_2Eextreal__add_2E2,type,
    c_2Eextreal_2Eextreal__add_2E2: ( tyop_2Eextreal_2Eextreal * tyop_2Eextreal_2Eextreal ) > tyop_2Eextreal_2Eextreal ).

tff(c_2Eextreal_2Eextreal__ainv_2E0,type,
    c_2Eextreal_2Eextreal__ainv_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal) ).

tff(c_2Eextreal_2Eextreal__ainv_2E1,type,
    c_2Eextreal_2Eextreal__ainv_2E1: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal ).

tff(c_2Eextreal_2Eextreal__le_2E0,type,
    c_2Eextreal_2Eextreal__le_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)) ).

tff(c_2Eextreal_2Eextreal__le_2E2,type,
    c_2Eextreal_2Eextreal__le_2E2: ( tyop_2Eextreal_2Eextreal * tyop_2Eextreal_2Eextreal ) > tyop_2Emin_2Ebool ).

tff(c_2Eextreal_2Eextreal__lt_2E0,type,
    c_2Eextreal_2Eextreal__lt_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)) ).

tff(c_2Eextreal_2Eextreal__lt_2E2,type,
    c_2Eextreal_2Eextreal__lt_2E2: ( tyop_2Eextreal_2Eextreal * tyop_2Eextreal_2Eextreal ) > tyop_2Emin_2Ebool ).

tff(c_2Eextreal_2Eextreal__max_2E0,type,
    c_2Eextreal_2Eextreal__max_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal)) ).

tff(c_2Eextreal_2Eextreal__max_2E2,type,
    c_2Eextreal_2Eextreal__max_2E2: ( tyop_2Eextreal_2Eextreal * tyop_2Eextreal_2Eextreal ) > tyop_2Eextreal_2Eextreal ).

tff(c_2Eextreal_2Eextreal__mul_2E0,type,
    c_2Eextreal_2Eextreal__mul_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal)) ).

tff(c_2Eextreal_2Eextreal__mul_2E2,type,
    c_2Eextreal_2Eextreal__mul_2E2: ( tyop_2Eextreal_2Eextreal * tyop_2Eextreal_2Eextreal ) > tyop_2Eextreal_2Eextreal ).

tff(c_2Eextreal_2Eextreal__of__num_2E0,type,
    c_2Eextreal_2Eextreal__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal) ).

tff(c_2Eextreal_2Eextreal__of__num_2E1,type,
    c_2Eextreal_2Eextreal__of__num_2E1: tyop_2Enum_2Enum > tyop_2Eextreal_2Eextreal ).

tff(c_2Eextreal_2Eextreal__pow_2E0,type,
    c_2Eextreal_2Eextreal__pow_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)) ).

tff(c_2Eextreal_2Eextreal__pow_2E2,type,
    c_2Eextreal_2Eextreal__pow_2E2: ( tyop_2Eextreal_2Eextreal * tyop_2Enum_2Enum ) > tyop_2Eextreal_2Eextreal ).

tff(c_2Eextreal_2Eextreal__sub_2E0,type,
    c_2Eextreal_2Eextreal__sub_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal)) ).

tff(c_2Eextreal_2Eextreal__sub_2E2,type,
    c_2Eextreal_2Eextreal__sub_2E2: ( tyop_2Eextreal_2Eextreal * tyop_2Eextreal_2Eextreal ) > tyop_2Eextreal_2Eextreal ).

tff(c_2Eextreal_2Eextreal__sup_2E0,type,
    c_2Eextreal_2Eextreal__sup_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal) ).

tff(c_2Eextreal_2Eextreal__sup_2E1,type,
    c_2Eextreal_2Eextreal__sup_2E1: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool) > tyop_2Eextreal_2Eextreal ).

tff(c_2Emeasure_2Efn__abs_2E0,type,
    c_2Emeasure_2Efn__abs_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)) ).

tff(c_2Emeasure_2Efn__abs_2E2,type,
    c_2Emeasure_2Efn__abs_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal) * A_27a ) > tyop_2Eextreal_2Eextreal ) ).

tff(c_2Emeasure_2Efn__minus_2E0,type,
    c_2Emeasure_2Efn__minus_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)) ).

tff(c_2Emeasure_2Efn__minus_2E1,type,
    c_2Emeasure_2Efn__minus_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal) > tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal) ) ).

tff(c_2Emeasure_2Efn__minus_2E2,type,
    c_2Emeasure_2Efn__minus_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal) * A_27a ) > tyop_2Eextreal_2Eextreal ) ).

tff(c_2Emeasure_2Efn__plus_2E0,type,
    c_2Emeasure_2Efn__plus_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)) ).

tff(c_2Emeasure_2Efn__plus_2E1,type,
    c_2Emeasure_2Efn__plus_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal) > tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal) ) ).

tff(c_2Emeasure_2Efn__plus_2E2,type,
    c_2Emeasure_2Efn__plus_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal) * A_27a ) > tyop_2Eextreal_2Eextreal ) ).

tff(c_2Emeasure_2Eincreasing_2E0,type,
    c_2Emeasure_2Eincreasing_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool) ).

tff(c_2Emeasure_2Eincreasing_2E1,type,
    c_2Emeasure_2Eincreasing_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) > tyop_2Emin_2Ebool ) ).

tff(c_2Emeasure_2Eindicator__fn_2E0,type,
    c_2Emeasure_2Eindicator__fn_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)) ).

tff(c_2Emeasure_2Eindicator__fn_2E2,type,
    c_2Emeasure_2Eindicator__fn_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Eextreal_2Eextreal ) ).

tff(c_2Ereal_2Einf_2E0,type,
    c_2Ereal_2Einf_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal) ).

tff(c_2Ereal_2Einf_2E1,type,
    c_2Ereal_2Einf_2E1: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool) > tyop_2Erealax_2Ereal ).

tff(c_2Emeasure_2Einf__measure_2E0,type,
    c_2Emeasure_2Einf__measure_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)) ).

tff(c_2Emeasure_2Einf__measure_2E1,type,
    c_2Emeasure_2Einf__measure_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal) ) ).

tff(c_2Emeasure_2Einf__measure_2E2,type,
    c_2Emeasure_2Einf__measure_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Erealax_2Ereal ) ).

tff(c_2Emeasure_2Elambda__system_2E0,type,
    c_2Emeasure_2Elambda__system_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).

tff(c_2Emeasure_2Elambda__system_2E2,type,
    c_2Emeasure_2Elambda__system_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal) ) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) ).

tff(c_2Emeasure_2Em__space_2E0,type,
    c_2Emeasure_2Em__space_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Emeasure_2Em__space_2E1,type,
    c_2Emeasure_2Em__space_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Emeasure_2Emeasurable_2E0,type,
    c_2Emeasure_2Emeasurable_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))) ).

tff(c_2Emeasure_2Emeasurable_2E2,type,
    c_2Emeasure_2Emeasurable_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) * tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).

tff(c_2Emeasure_2Emeasurable__sets_2E0,type,
    c_2Emeasure_2Emeasurable__sets_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Emeasure_2Emeasurable__sets_2E1,type,
    c_2Emeasure_2Emeasurable__sets_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) ).

tff(c_2Emeasure_2Emeasure_2E0,type,
    c_2Emeasure_2Emeasure_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)) ).

tff(c_2Emeasure_2Emeasure_2E1,type,
    c_2Emeasure_2Emeasure_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal) ) ).

tff(c_2Emeasure_2Emeasure_2E2,type,
    c_2Emeasure_2Emeasure_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Erealax_2Ereal ) ).

tff(c_2Emeasure_2Emeasure__preserving_2E0,type,
    c_2Emeasure_2Emeasure__preserving_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))) ).

tff(c_2Emeasure_2Emeasure__preserving_2E2,type,
    c_2Emeasure_2Emeasure__preserving_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) * tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) ) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).

tff(c_2Emeasure_2Emeasure__space_2E0,type,
    c_2Emeasure_2Emeasure__space_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool) ).

tff(c_2Emeasure_2Emeasure__space_2E1,type,
    c_2Emeasure_2Emeasure__space_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) > tyop_2Emin_2Ebool ) ).

tff(c_2Emeasure_2Enull__set_2E0,type,
    c_2Emeasure_2Enull__set_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Emeasure_2Enull__set_2E2,type,
    c_2Emeasure_2Enull__set_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).

tff(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).

tff(c_2Emeasure_2Eouter__measure__space_2E0,type,
    c_2Emeasure_2Eouter__measure__space_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool) ).

tff(c_2Emeasure_2Eouter__measure__space_2E1,type,
    c_2Emeasure_2Eouter__measure__space_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) > tyop_2Emin_2Ebool ) ).

tff(c_2Emeasure_2Epos__simple__fn_2E0,type,
    c_2Emeasure_2Epos__simple__fn_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool))))) ).

tff(c_2Emeasure_2Epos__simple__fn_2E5,type,
    c_2Emeasure_2Epos__simple__fn_2E5: 
      !>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) * tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Emeasure_2Epositive_2E0,type,
    c_2Emeasure_2Epositive_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool) ).

tff(c_2Emeasure_2Epositive_2E1,type,
    c_2Emeasure_2Epositive_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) > tyop_2Emin_2Ebool ) ).

tff(c_2Eutil__prob_2Eprod__sets_2E0,type,
    c_2Eutil__prob_2Eprod__sets_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).

tff(c_2Eutil__prob_2Eprod__sets_2E2,type,
    c_2Eutil__prob_2Eprod__sets_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) ).

tff(c_2Erealax_2Ereal__add_2E0,type,
    c_2Erealax_2Ereal__add_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).

tff(c_2Erealax_2Ereal__add_2E2,type,
    c_2Erealax_2Ereal__add_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).

tff(c_2Erealax_2Ereal__lt_2E0,type,
    c_2Erealax_2Ereal__lt_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).

tff(c_2Erealax_2Ereal__lt_2E2,type,
    c_2Erealax_2Ereal__lt_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).

tff(c_2Ereal_2Ereal__lte_2E0,type,
    c_2Ereal_2Ereal__lte_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).

tff(c_2Ereal_2Ereal__lte_2E2,type,
    c_2Ereal_2Ereal__lte_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).

tff(c_2Erealax_2Ereal__mul_2E0,type,
    c_2Erealax_2Ereal__mul_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).

tff(c_2Erealax_2Ereal__mul_2E2,type,
    c_2Erealax_2Ereal__mul_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).

tff(c_2Ereal_2Ereal__of__num_2E0,type,
    c_2Ereal_2Ereal__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal) ).

tff(c_2Ereal_2Ereal__of__num_2E1,type,
    c_2Ereal_2Ereal__of__num_2E1: tyop_2Enum_2Enum > tyop_2Erealax_2Ereal ).

tff(c_2Ereal_2Ereal__sub_2E0,type,
    c_2Ereal_2Ereal__sub_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).

tff(c_2Ereal_2Ereal__sub_2E2,type,
    c_2Ereal_2Ereal__sub_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).

tff(c_2Emeasure_2Esigma_2E0,type,
    c_2Emeasure_2Esigma_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))) ).

tff(c_2Emeasure_2Esigma_2E2,type,
    c_2Emeasure_2Esigma_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) > tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ) ).

tff(c_2Emeasure_2Esigma__algebra_2E0,type,
    c_2Emeasure_2Esigma__algebra_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Emeasure_2Esigma__algebra_2E1,type,
    c_2Emeasure_2Esigma__algebra_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Emeasure_2Esmallest__closed__cdi_2E0,type,
    c_2Emeasure_2Esmallest__closed__cdi_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).

tff(c_2Emeasure_2Esmallest__closed__cdi_2E1,type,
    c_2Emeasure_2Esmallest__closed__cdi_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) > tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ) ).

tff(c_2Emeasure_2Espace_2E0,type,
    c_2Emeasure_2Espace_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Emeasure_2Espace_2E1,type,
    c_2Emeasure_2Espace_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Emeasure_2Esubadditive_2E0,type,
    c_2Emeasure_2Esubadditive_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool) ).

tff(c_2Emeasure_2Esubadditive_2E1,type,
    c_2Emeasure_2Esubadditive_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))) > tyop_2Emin_2Ebool ) ).

tff(c_2Emeasure_2Esubset__class_2E0,type,
    c_2Emeasure_2Esubset__class_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Emeasure_2Esubset__class_2E2,type,
    c_2Emeasure_2Esubset__class_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Emeasure_2Esubsets_2E0,type,
    c_2Emeasure_2Esubsets_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Emeasure_2Esubsets_2E1,type,
    c_2Emeasure_2Esubsets_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) ).

tff(c_2Ereal_2Esum_2E0,type,
    c_2Ereal_2Esum_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal)) ).

tff(c_2Ereal_2Esum_2E2,type,
    c_2Ereal_2Esum_2E2: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal) ) > tyop_2Erealax_2Ereal ).

tff(c_2Eseq_2Esuminf_2E0,type,
    c_2Eseq_2Esuminf_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal) ).

tff(c_2Eseq_2Esuminf_2E1,type,
    c_2Eseq_2Esuminf_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal) > tyop_2Erealax_2Ereal ).

tff(c_2Eseq_2Esummable_2E0,type,
    c_2Eseq_2Esummable_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool) ).

tff(c_2Eseq_2Esummable_2E1,type,
    c_2Eseq_2Esummable_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal) > tyop_2Emin_2Ebool ).

tff(c_2Eseq_2Esums_2E0,type,
    c_2Eseq_2Esums_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).

tff(c_2Eseq_2Esums_2E2,type,
    c_2Eseq_2Esums_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal) * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).

tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
     => ( V0f_2E0 = V1g_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Eboolext,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V0_2E0)
      <=> p(V1_2E0) )
     => ( V0_2E0 = V1_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Etruth,axiom,
    p(c_2Ebool_2ET_2E0) ).

tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
    ~ p(c_2Ebool_2EF_2E0) ).

tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0: tyop_2Emin_2Ebool] :
      ( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
      | ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).

tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).

tff(thm_2Eextra_2Dho_2Es__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).

tff(logicdef_2E_2F_5C,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        & p(V1_2E0) ) ) ).

tff(logicdef_2E_5C_2F,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        | p(V1_2E0) ) ) ).

tff(logicdef_2E_7E,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_7E_2E1(V0_2E0))
    <=> ~ p(V0_2E0) ) ).

tff(logicdef_2E_3D_3D_3E,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
       => p(V1_2E0) ) ) ).

tff(logicdef_2E_3D,axiom,
    ! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
      ( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
    <=> ( V0_2E0 = V1_2E0 ) ) ).

tff(quantdef_2E_21,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
    <=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).

tff(quantdef_2E_3F,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
    <=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Eextreal_2Eextreal,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eseq_2E_2D_2D_3E_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Eseq_2E_2D_2D_3E_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Eseq_2E_2D_2D_3E_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
      ( ( X0_2E0 = X1_2E0 )
    <=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGINTER_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGINTER_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGINTER_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGINTER_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eextreal_2Eextreal,X2_2E0: tyop_2Eextreal_2Eextreal] : ( c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal)),c_2Ebool_2ECOND_2E0(tyop_2Eextreal_2Eextreal),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EDIFF_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EDIFF_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDISJOINT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EDISJOINT_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal),c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal),c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EFUNSET_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EFUNSET_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EFUNSET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFUNSET_2E2(A_27a,tyop_2Eextreal_2Eextreal,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool)),c_2Epred__set_2EFUNSET_2E0(A_27a,tyop_2Eextreal_2Eextreal),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EFUNSET_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFUNSET_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),c_2Epred__set_2EFUNSET_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EFUNSET_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFUNSET_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Epred__set_2EFUNSET_2E0(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EFUNSET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Epred__set_2EFUNSET_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eextreal_2Eextreal_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Erealax_2Ereal,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Erealax_2Ereal),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
    ! [X0_2E0: tyop_2Eextreal_2Eextreal,X1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Eextreal_2Eextreal,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Eextreal_2Eextreal),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINTER_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EINTER_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINTER_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Eextreal_2ENormal_2E1,axiom,
    ! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Eextreal_2ENormal_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Eextreal_2Eextreal,c_2Eextreal_2ENormal_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EPOW_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPOW_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EPOW_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPOW_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EPREIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Epred__set_2EPREIMAGE_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,tyop_2Eextreal_2Eextreal,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E0(A_27a,tyop_2Eextreal_2Eextreal),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ereal__sigma_2EREAL__SUM__IMAGE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ereal__sigma_2EREAL__SUM__IMAGE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Ereal__sigma_2EREAL__SUM__IMAGE_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ereal__sigma_2EREAL__SUM__IMAGE_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ereal__sigma_2EREAL__SUM__IMAGE_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Ereal__sigma_2EREAL__SUM__IMAGE_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        | p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Emeasure_2Eadditive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Eadditive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool,c_2Emeasure_2Eadditive_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Ealgebra_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Ealgebra_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Emeasure_2Ealgebra_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Eclosed__cdi_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Eclosed__cdi_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Emeasure_2Eclosed__cdi_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2Ecount_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Ecount_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Ecountably__additive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Ecountably__additive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool,c_2Emeasure_2Ecountably__additive_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Ecountably__subadditive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Ecountably__subadditive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool,c_2Emeasure_2Ecountably__subadditive_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eextreal_2Eext__suminf_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)] : ( c_2Eextreal_2Eext__suminf_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eext__suminf_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Eextreal_2Eextreal__abs_2E1,axiom,
    ! [X0_2E0: tyop_2Eextreal_2Eextreal] : ( c_2Eextreal_2Eextreal__abs_2E1(X0_2E0) = app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__abs_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Eextreal_2Eextreal__add_2E2,axiom,
    ! [X0_2E0: tyop_2Eextreal_2Eextreal,X1_2E0: tyop_2Eextreal_2Eextreal] : ( c_2Eextreal_2Eextreal__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),c_2Eextreal_2Eextreal__add_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eextreal_2Eextreal__ainv_2E1,axiom,
    ! [X0_2E0: tyop_2Eextreal_2Eextreal] : ( c_2Eextreal_2Eextreal__ainv_2E1(X0_2E0) = app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__ainv_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Eextreal_2Eextreal__le_2E2,axiom,
    ! [X0_2E0: tyop_2Eextreal_2Eextreal,X1_2E0: tyop_2Eextreal_2Eextreal] : ( c_2Eextreal_2Eextreal__le_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Eextreal_2Eextreal__le_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eextreal_2Eextreal__lt_2E2,axiom,
    ! [X0_2E0: tyop_2Eextreal_2Eextreal,X1_2E0: tyop_2Eextreal_2Eextreal] : ( c_2Eextreal_2Eextreal__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Eextreal_2Eextreal__lt_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eextreal_2Eextreal__max_2E2,axiom,
    ! [X0_2E0: tyop_2Eextreal_2Eextreal,X1_2E0: tyop_2Eextreal_2Eextreal] : ( c_2Eextreal_2Eextreal__max_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),c_2Eextreal_2Eextreal__max_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eextreal_2Eextreal__mul_2E2,axiom,
    ! [X0_2E0: tyop_2Eextreal_2Eextreal,X1_2E0: tyop_2Eextreal_2Eextreal] : ( c_2Eextreal_2Eextreal__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),c_2Eextreal_2Eextreal__mul_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eextreal_2Eextreal__of__num_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eextreal_2Eextreal__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__of__num_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Eextreal_2Eextreal__pow_2E2,axiom,
    ! [X0_2E0: tyop_2Eextreal_2Eextreal,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eextreal_2Eextreal__pow_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),c_2Eextreal_2Eextreal__pow_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eextreal_2Eextreal__sub_2E2,axiom,
    ! [X0_2E0: tyop_2Eextreal_2Eextreal,X1_2E0: tyop_2Eextreal_2Eextreal] : ( c_2Eextreal_2Eextreal__sub_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),c_2Eextreal_2Eextreal__sub_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eextreal_2Eextreal__sup_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)] : ( c_2Eextreal_2Eextreal__sup_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__sup_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Efn__abs_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0: A_27a] : ( c_2Emeasure_2Efn__abs_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Emeasure_2Efn__abs_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Efn__minus_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] : ( c_2Emeasure_2Efn__minus_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Emeasure_2Efn__minus_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Efn__minus_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0: A_27a] : ( c_2Emeasure_2Efn__minus_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Emeasure_2Efn__minus_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Efn__plus_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] : ( c_2Emeasure_2Efn__plus_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Emeasure_2Efn__plus_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Efn__plus_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0: A_27a] : ( c_2Emeasure_2Efn__plus_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Emeasure_2Efn__plus_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Eincreasing_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Eincreasing_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool,c_2Emeasure_2Eincreasing_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Eindicator__fn_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Emeasure_2Eindicator__fn_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Emeasure_2Eindicator__fn_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ereal_2Einf_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] : ( c_2Ereal_2Einf_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,c_2Ereal_2Einf_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Einf__measure_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Einf__measure_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Einf__measure_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Einf__measure_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Einf__measure_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Einf__measure_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Elambda__system_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] : ( c_2Emeasure_2Elambda__system_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Emeasure_2Elambda__system_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Em__space_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Em__space_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Em__space_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Em__space_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Emeasurable_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Emeasurable_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Emeasure_2Emeasurable_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Emeasurable_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Emeasure_2Emeasurable_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Emeasurable_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Emeasurable_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool)),c_2Emeasure_2Emeasurable_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Emeasurable_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool)),c_2Emeasure_2Emeasurable_2E0(A_27a,tyop_2Eextreal_2Eextreal),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Emeasurable_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool)),c_2Emeasure_2Emeasurable_2E0(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Emeasurable_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Emeasurable_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),c_2Emeasure_2Emeasurable_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Emeasurable__sets_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Emeasurable__sets_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Emeasurable__sets_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Emeasurable__sets_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Emeasurable__sets_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Emeasurable__sets_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Emeasure_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Emeasure_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Emeasure_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Emeasure_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Emeasure_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Emeasure_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Emeasure_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Emeasure_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Emeasure_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Emeasure_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Emeasure_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Emeasure_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Emeasure__preserving_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Emeasure_2Emeasure__preserving_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Emeasure__space_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Emeasure__space_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool,c_2Emeasure_2Emeasure__space_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Emeasure__space_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Emeasure__space_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool,c_2Emeasure_2Emeasure__space_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Enull__set_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Enull__set_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Enull__set_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ecombin_2Eo_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27b,tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27c,tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ecombin_2Eo_2E0(A_27a,A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Eouter__measure__space_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Eouter__measure__space_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool,c_2Emeasure_2Eouter__measure__space_2E0(A_27a),X0_2E0) ) ).

tff(arityeq5_2Ec_2Emeasure_2Epos__simple__fn_2E5_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X4_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)] : ( c_2Emeasure_2Epos__simple__fn_2E5(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool))),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)))),c_2Emeasure_2Epos__simple__fn_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Epositive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Epositive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool,c_2Emeasure_2Epositive_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eutil__prob_2Eprod__sets_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Eutil__prob_2Eprod__sets_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eutil__prob_2Eprod__sets_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Erealax_2Ereal__add_2E2,axiom,
    ! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__add_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Erealax_2Ereal__lt_2E2,axiom,
    ! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Erealax_2Ereal__lt_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ereal_2Ereal__lte_2E2,axiom,
    ! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__lte_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Erealax_2Ereal__mul_2E2,axiom,
    ! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__mul_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ereal_2Ereal__of__num_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ereal_2Ereal__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Ereal_2Ereal__sub_2E2,axiom,
    ! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2Ereal__sub_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Esigma_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Esigma_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Emeasure_2Esigma_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Esigma_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Esigma_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Emeasure_2Esigma_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Esigma_2E2_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Esigma_2E2(tyop_2Eextreal_2Eextreal,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Emeasure_2Esigma_2E0(tyop_2Eextreal_2Eextreal),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Esigma_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Esigma_2E2(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Emeasure_2Esigma_2E0(tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Esigma__algebra_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Esigma__algebra_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Emeasure_2Esigma__algebra_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Esigma__algebra_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Esigma__algebra_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Emeasure_2Esigma__algebra_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Esigma__algebra_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Esigma__algebra_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Emeasure_2Esigma__algebra_2E0(A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Esigma__algebra_2E1_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Esigma__algebra_2E1(tyop_2Eextreal_2Eextreal,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Emeasure_2Esigma__algebra_2E0(tyop_2Eextreal_2Eextreal),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Esmallest__closed__cdi_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Esmallest__closed__cdi_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Emeasure_2Esmallest__closed__cdi_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Espace_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Espace_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Espace_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Espace_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Espace_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Emeasure_2Espace_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Espace_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Espace_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Emeasure_2Espace_2E0(A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Espace_2E1_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Espace_2E1(tyop_2Eextreal_2Eextreal,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Emeasure_2Espace_2E0(tyop_2Eextreal_2Eextreal),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Esubadditive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Esubadditive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool,c_2Emeasure_2Esubadditive_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Esubset__class_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Esubset__class_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Esubset__class_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emeasure_2Esubset__class_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Esubset__class_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Esubset__class_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Esubsets_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Esubsets_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Esubsets_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Esubsets_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Esubsets_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Esubsets_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E0(A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emeasure_2Esubsets_2E1_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E0(tyop_2Eextreal_2Eextreal),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ereal_2Esum_2E2,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)] : ( c_2Ereal_2Esum_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal),c_2Ereal_2Esum_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eseq_2Esuminf_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)] : ( c_2Eseq_2Esuminf_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal,c_2Eseq_2Esuminf_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Eseq_2Esummable_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)] : ( c_2Eseq_2Esummable_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,c_2Eseq_2Esummable_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Eseq_2Esums_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Eseq_2Esums_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Eseq_2Esums_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool] :
      ( ~ p(X0_2E0)
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).

tff(thm_2Emeasure_2Espace__def,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Espace_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0x_2E0,V1y_2E0)) = V0x_2E0 ) ).

tff(thm_2Emeasure_2Esubsets__def,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Esubsets_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0x_2E0,V1y_2E0)) = V1y_2E0 ) ).

tff(thm_2Emeasure_2Esubset__class__def,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1sts_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( p(c_2Emeasure_2Esubset__class_2E2(A_27a,V0sp_2E0,V1sts_2E0))
    <=> ! [V2x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0,V1sts_2E0))
         => p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2x_2E0,V0sp_2E0)) ) ) ).

tff(thm_2Emeasure_2Ealgebra__def,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
    <=> ( p(c_2Emeasure_2Esubset__class_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),V1s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
        & ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
              & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(A_27a,V2s_2E0,V3t_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2Esigma__algebra__def,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
    <=> ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
        & ! [V1c_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
            ( ( p(c_2Epred__set_2Ecountable_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0))
              & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,V1c_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2Esigma__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))] :
      ( ! [V1st_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V1st_2E0),V2s_2E0),V0sp_2E0))
        <=> ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1st_2E0,V2s_2E0))
            & p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,V2s_2E0))) ) )
     => ( ! [V1st_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V1st_2E0),V0sp_2E0),V2s_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2s_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V1st_2E0),V2s_2E0),V0sp_2E0)) )
       => ! [V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1st_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V1st_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,c_2Epred__set_2EBIGINTER_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V1st_2E0),V0sp_2E0)))) ) ) ) ).

tff(thm_2Emeasure_2Em__space__def,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1sts_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2mu_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] : ( c_2Emeasure_2Em__space_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),V0sp_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V1sts_2E0,V2mu_2E0))) = V0sp_2E0 ) ).

tff(thm_2Emeasure_2Emeasurable__sets__def,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1sts_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2mu_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] : ( c_2Emeasure_2Emeasurable__sets_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),V0sp_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V1sts_2E0,V2mu_2E0))) = V1sts_2E0 ) ).

tff(thm_2Emeasure_2Emeasure__def,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1sts_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2mu_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] : ( c_2Emeasure_2Emeasure_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),V0sp_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V1sts_2E0,V2mu_2E0))) = V2mu_2E0 ) ).

tff(thm_2Emeasure_2Epositive__def,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
    <=> ( ( c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
        & ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
           => p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0))) ) ) ) ).

tff(thm_2Emeasure_2Eadditive__def,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Eadditive_2E1(A_27a,V0m_2E0))
    <=> ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
            & p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V1s_2E0,V2t_2E0)) )
         => ( c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0)) = c_2Erealax_2Ereal__add_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V2t_2E0)) ) ) ) ).

tff(thm_2Emeasure_2Ecountably__additive__def,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Ecountably__additive_2E1(A_27a,V0m_2E0))
    <=> ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
            & ! [V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
                ( ( V2m_2E0 != V3n_2E0 )
               => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V2m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V3n_2E0))) )
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
         => p(c_2Eseq_2Esums_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V1f_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))))) ) ) ).

tff(thm_2Emeasure_2Esubadditive__def,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Esubadditive_2E1(A_27a,V0m_2E0))
    <=> ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
         => p(c_2Ereal_2Ereal__lte_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0)),c_2Erealax_2Ereal__add_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V2t_2E0)))) ) ) ).

tff(thm_2Emeasure_2Ecountably__subadditive__def,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Ecountably__subadditive_2E1(A_27a,V0m_2E0))
    <=> ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
            & p(c_2Eseq_2Esummable_2E1(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V1f_2E0))) )
         => p(c_2Ereal_2Ereal__lte_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),c_2Eseq_2Esuminf_2E1(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V1f_2E0)))) ) ) ).

tff(thm_2Emeasure_2Eincreasing__def,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Eincreasing_2E1(A_27a,V0m_2E0))
    <=> ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
            & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2t_2E0)) )
         => p(c_2Ereal_2Ereal__lte_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V2t_2E0))) ) ) ).

tff(thm_2Emeasure_2Emeasure__space__def,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
    <=> ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Ecountably__additive_2E1(A_27a,V0m_2E0)) ) ) ).

tff(thm_2Emeasure_2Elambda__system__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))] :
      ( ! [V2l_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0gen_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)),F1_2E0,V2l_2E0),V0gen_2E0),V1lam_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0gen_2E0)))
            & ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0gen_2E0)))
               => ( c_2Erealax_2Ereal__add_2E2(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,V1lam_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V2l_2E0,V3s_2E0)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,V1lam_2E0,c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0gen_2E0),V2l_2E0),V3s_2E0))) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,V1lam_2E0,V3s_2E0) ) ) ) )
     => ( ! [V0gen_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V2l_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V0gen_2E0),V1lam_2E0),V2l_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2l_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)),F1_2E0,V2l_2E0),V0gen_2E0),V1lam_2E0)) )
       => ! [V0gen_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] : ( c_2Emeasure_2Elambda__system_2E2(A_27a,V0gen_2E0,V1lam_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V0gen_2E0),V1lam_2E0)) ) ) ) ).

tff(thm_2Emeasure_2Eouter__measure__space__def,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Eouter__measure__space_2E1(A_27a,V0m_2E0))
    <=> ( p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Eincreasing_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Ecountably__subadditive_2E1(A_27a,V0m_2E0)) ) ) ).

tff(thm_2Emeasure_2Einf__measure__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))))] :
      ( ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2r_2E0: tyop_2Erealax_2Ereal] :
          ( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0,V0m_2E0),V1s_2E0),V2r_2E0))
        <=> ? [V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
              & ! [V4m_2E0: tyop_2Enum_2Enum,V5n_2E0: tyop_2Enum_2Enum] :
                  ( ( V4m_2E0 != V5n_2E0 )
                 => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0,V4m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0,V5n_2E0))) )
              & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))))
              & p(c_2Eseq_2Esums_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V3f_2E0),V2r_2E0)) ) )
     => ( ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2r_2E0: tyop_2Erealax_2Ereal] : ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0,V0m_2E0),V1s_2E0),V2r_2E0) = c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V2r_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0,V0m_2E0),V1s_2E0),V2r_2E0)) )
       => ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Einf__measure_2E2(A_27a,V0m_2E0,V1s_2E0) = c_2Ereal_2Einf_2E1(c_2Epred__set_2EGSPEC_2E1(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0,V0m_2E0),V1s_2E0))) ) ) ) ).

tff(thm_2Emeasure_2Eclosed__cdi__def,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Eclosed__cdi_2E1(A_27a,V0p_2E0))
    <=> ( p(c_2Emeasure_2Esubset__class_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0p_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0)))
        & ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0p_2E0),V1s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))) )
        & ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))))
              & ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Enum_2E0_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
              & ! [V3n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,V3n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Enum_2ESUC_2E1(V3n_2E0)))) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))) )
        & ! [V4f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))))
              & ! [V5m_2E0: tyop_2Enum_2Enum,V6n_2E0: tyop_2Enum_2Enum] :
                  ( ( V5m_2E0 != V6n_2E0 )
                 => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,V5m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,V6n_2E0))) ) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))) ) ) ) ).

tff(thm_2Emeasure_2Esmallest__closed__cdi__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
      ( ! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V0a_2E0),V1b_2E0))
        <=> ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0),V1b_2E0))
            & p(c_2Emeasure_2Eclosed__cdi_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),V1b_2E0))) ) )
     => ( ! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0a_2E0),V1b_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1b_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V0a_2E0),V1b_2E0)) )
       => ! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Esmallest__closed__cdi_2E1(A_27a,V0a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Epred__set_2EBIGINTER_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0a_2E0)))) ) ) ) ).

tff(thm_2Emeasure_2Emeasurable__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))))] :
      ( ! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),F1_2E0,V0a_2E0),V1b_2E0),V2f_2E0))
        <=> ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
            & p(c_2Emeasure_2Esigma__algebra_2E1(A_27b,V1b_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Espace_2E1(A_27b,V1b_2E0))))
            & ! [V3s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_2E0,c_2Emeasure_2Esubsets_2E1(A_27b,V1b_2E0)))
               => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V2f_2E0,V3s_2E0),c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ) )
     => ( ! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0a_2E0),V1b_2E0),V2f_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,V2f_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),F1_2E0,V0a_2E0),V1b_2E0),V2f_2E0)) )
       => ! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,V0a_2E0,V1b_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0a_2E0),V1b_2E0)) ) ) ) ).

tff(thm_2Emeasure_2Emeasure__preserving__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))))] :
      ( ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V0m1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1m2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
          ( p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool)),F1_2E0,V2f_2E0),V0m1_2E0),V1m2_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m1_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m1_2E0)),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27b,V1m2_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27b,V1m2_2E0)))))
            & p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m1_2E0))
            & p(c_2Emeasure_2Emeasure__space_2E1(A_27b,V1m2_2E0))
            & ! [V3s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27b,V1m2_2E0)))
               => ( c_2Emeasure_2Emeasure_2E2(A_27a,V0m1_2E0,c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V2f_2E0,V3s_2E0),c_2Emeasure_2Em__space_2E1(A_27a,V0m1_2E0))) = c_2Emeasure_2Emeasure_2E2(A_27b,V1m2_2E0,V3s_2E0) ) ) ) )
     => ( ! [V0m1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1m2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0m1_2E0),V1m2_2E0),V2f_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,V2f_2E0,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool)),F1_2E0,V2f_2E0),V0m1_2E0),V1m2_2E0)) )
       => ! [V0m1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1m2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,V0m1_2E0,V1m2_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0m1_2E0),V1m2_2E0)) ) ) ) ).

tff(thm_2Emeasure_2Eindicator__fn__def,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( c_2Emeasure_2Eindicator__fn_2E2(A_27a,V0s_2E0,V1x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0),c_2Eextreal_2Eextreal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Eextreal_2Eextreal__of__num_2E1(c_2Enum_2E0_2E0)) ) ).

tff(thm_2Emeasure_2Epos__simple__fn__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal))))] :
      ( ! [V4x_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V3a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V6t_2E0: A_27a,V7i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal))),F0_2E0,V4x_2E0),V3a_2E0),V6t_2E0),V7i_2E0) = c_2Eextreal_2Eextreal__mul_2E2(c_2Eextreal_2ENormal_2E1(app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V4x_2E0,V7i_2E0)),c_2Emeasure_2Eindicator__fn_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0,V7i_2E0),V6t_2E0)) )
     => ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4x_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)] :
          ( p(c_2Emeasure_2Epos__simple__fn_2E5(A_27a,V0m_2E0,V1f_2E0,V2s_2E0,V3a_2E0,V4x_2E0))
        <=> ( ! [V5t_2E0: A_27a] : p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__of__num_2E1(c_2Enum_2E0_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V5t_2E0)))
            & ! [V6t_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V6t_2E0,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0)))
               => ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V6t_2E0) = c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2(tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal))),F0_2E0,V4x_2E0),V3a_2E0),V6t_2E0),V2s_2E0) ) )
            & ! [V8i_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V8i_2E0,V2s_2E0))
               => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0,V8i_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
            & p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V2s_2E0))
            & ! [V9i_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V9i_2E0,V2s_2E0))
               => p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V4x_2E0,V9i_2E0))) )
            & ! [V10i_2E0: tyop_2Enum_2Enum,V11j_2E0: tyop_2Enum_2Enum] :
                ( ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V10i_2E0,V2s_2E0))
                  & p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V11j_2E0,V2s_2E0))
                  & ( V10i_2E0 != V11j_2E0 ) )
               => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0,V10i_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0,V11j_2E0))) )
            & ( c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0,V2s_2E0)) = c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0) ) ) ) ) ).

tff(thm_2Emeasure_2Enull__set__def,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Emeasure_2Enull__set_2E2(A_27a,V0m_2E0,V1s_2E0))
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
        & ( c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ) ).

tff(thm_2Emeasure_2EBorel__def,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))] :
      ( ! [V0a_2E0: tyop_2Eextreal_2Eextreal,V1x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0a_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V1x_2E0,c_2Eextreal_2Eextreal__lt_2E2(V1x_2E0,V0a_2E0)) )
     => ( ! [V0a_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),F0_2E0,V0a_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0a_2E0)) )
       => ( c_2Emeasure_2EBorel_2E0 = c_2Emeasure_2Esigma_2E2(tyop_2Eextreal_2Eextreal,c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal),c_2Epred__set_2EIMAGE_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),F0_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal))) ) ) ) ).

tff(thm_2Emeasure_2Efn__plus__def,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1x_2E0: A_27a] : ( c_2Emeasure_2Efn__plus_2E2(A_27a,V0f_2E0,V1x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__lt_2E2(c_2Eextreal_2Eextreal__of__num_2E1(c_2Enum_2E0_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V1x_2E0)),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V1x_2E0),c_2Eextreal_2Eextreal__of__num_2E1(c_2Enum_2E0_2E0)) ) ).

tff(thm_2Emeasure_2Efn__minus__def,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1x_2E0: A_27a] : ( c_2Emeasure_2Efn__minus_2E2(A_27a,V0f_2E0,V1x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__lt_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V1x_2E0),c_2Eextreal_2Eextreal__of__num_2E1(c_2Enum_2E0_2E0)),c_2Eextreal_2Eextreal__ainv_2E1(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V1x_2E0)),c_2Eextreal_2Eextreal__of__num_2E1(c_2Enum_2E0_2E0)) ) ).

tff(thm_2Emeasure_2Efn__abs__def,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1x_2E0: A_27a] : ( c_2Emeasure_2Efn__abs_2E2(A_27a,V0f_2E0,V1x_2E0) = c_2Eextreal_2Eextreal__abs_2E1(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V1x_2E0)) ) ).

tff(thm_2Emeasure_2ESIGMA__PROPERTY__DISJOINT__LEMMA,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,V1a_2E0)))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0,V2p_2E0))
        & p(c_2Emeasure_2Eclosed__cdi_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,V2p_2E0))) )
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V1a_2E0)),V2p_2E0)) ) ).

tff(thm_2Emeasure_2ESIGMA__PROPERTY__DISJOINT__LEMMA2,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
     => ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esmallest__closed__cdi_2E1(A_27a,V0a_2E0))))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esmallest__closed__cdi_2E1(A_27a,V0a_2E0)))) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esmallest__closed__cdi_2E1(A_27a,V0a_2E0)))) ) ) ).

tff(thm_2Emeasure_2ESIGMA__PROPERTY__DISJOINT__LEMMA1,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
     => ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esmallest__closed__cdi_2E1(A_27a,V0a_2E0)))) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esmallest__closed__cdi_2E1(A_27a,V0a_2E0)))) ) ) ).

tff(thm_2Emeasure_2ECLOSED__CDI__INCREASING,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Eclosed__cdi_2E1(A_27a,V0p_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))))
        & ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Enum_2E0_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
        & ! [V2n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V2n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Enum_2ESUC_2E1(V2n_2E0)))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))) ) ).

tff(thm_2Emeasure_2ECLOSED__CDI__DISJOINT,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Eclosed__cdi_2E1(A_27a,V0p_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))))
        & ! [V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
            ( ( V2m_2E0 != V3n_2E0 )
           => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V2m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V3n_2E0))) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))) ) ).

tff(thm_2Emeasure_2ECLOSED__CDI__COMPL,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Eclosed__cdi_2E1(A_27a,V0p_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0p_2E0),V1s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))) ) ).

tff(thm_2Emeasure_2ECLOSED__CDI__DUNION,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0)))
        & p(c_2Emeasure_2Eclosed__cdi_2E1(A_27a,V0p_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0)))
        & p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V1s_2E0,V2t_2E0)) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))) ) ).

tff(thm_2Emeasure_2ESMALLEST__CLOSED__CDI,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
     => ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esmallest__closed__cdi_2E1(A_27a,V0a_2E0))))
        & p(c_2Emeasure_2Eclosed__cdi_2E1(A_27a,c_2Emeasure_2Esmallest__closed__cdi_2E1(A_27a,V0a_2E0)))
        & p(c_2Emeasure_2Esubset__class_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esmallest__closed__cdi_2E1(A_27a,V0a_2E0)))) ) ) ).

tff(thm_2Emeasure_2ESPACE__SMALLEST__CLOSED__CDI,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Emeasure_2Espace_2E1(A_27a,c_2Emeasure_2Esmallest__closed__cdi_2E1(A_27a,V0a_2E0)) = c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0) ) ).

tff(thm_2Emeasure_2ESPACE,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)) = V0a_2E0 ) ).

tff(thm_2Emeasure_2EALGEBRA__ALT__INTER,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
    <=> ( p(c_2Emeasure_2Esubset__class_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),V1s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
        & ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
              & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,V2s_2E0,V3t_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2EALGEBRA__EMPTY,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ).

tff(thm_2Emeasure_2EALGEBRA__SPACE,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ).

tff(thm_2Emeasure_2EALGEBRA__COMPL,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),V1s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ).

tff(thm_2Emeasure_2EALGEBRA__UNION,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ).

tff(thm_2Emeasure_2EALGEBRA__INTER,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ).

tff(thm_2Emeasure_2EALGEBRA__DIFF,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,V1s_2E0,V2t_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ).

tff(thm_2Emeasure_2EALGEBRA__FINITE__UNION,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1c_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,V1c_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ).

tff(thm_2Emeasure_2EALGEBRA__INTER__SPACE,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
     => ( ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),V1s_2E0) = V1s_2E0 )
        & ( c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)) = V1s_2E0 ) ) ) ).

tff(thm_2Emeasure_2ELAMBDA__SYSTEM__EMPTY,axiom,
    ! [A_27a: $tType,V0g0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0g0_2E0))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0g0_2E0),V1lam_2E0)))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0))) ) ).

tff(thm_2Emeasure_2ELAMBDA__SYSTEM__COMPL,axiom,
    ! [A_27a: $tType,V0g0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V2l_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0g0_2E0))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0g0_2E0),V1lam_2E0))))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0,c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),V2l_2E0),c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0))) ) ).

tff(thm_2Emeasure_2ELAMBDA__SYSTEM__INTER,axiom,
    ! [A_27a: $tType,V0g0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V2l1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3l2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0g0_2E0))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0g0_2E0),V1lam_2E0))))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l1_2E0,c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3l2_2E0,c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,V2l1_2E0,V3l2_2E0),c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0))) ) ).

tff(thm_2Emeasure_2ELAMBDA__SYSTEM__ALGEBRA,axiom,
    ! [A_27a: $tType,V0g0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0g0_2E0))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0g0_2E0),V1lam_2E0)))) )
     => p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0)))) ) ).

tff(thm_2Emeasure_2ELAMBDA__SYSTEM__STRONG__ADDITIVE,axiom,
    ! [A_27a: $tType,V0g0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3l1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4l2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0g0_2E0))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0g0_2E0),V1lam_2E0))))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0g0_2E0)))
        & p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V3l1_2E0,V4l2_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3l1_2E0,c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4l2_2E0,c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0))) )
     => ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,V1lam_2E0,c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V3l1_2E0,V4l2_2E0),V2g_2E0)) = c_2Erealax_2Ereal__add_2E2(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,V1lam_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V3l1_2E0,V2g_2E0)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,V1lam_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V4l2_2E0,V2g_2E0))) ) ) ).

tff(thm_2Emeasure_2ELAMBDA__SYSTEM__ADDITIVE,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0g0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V2l1_2E0: A_27b,V3l2_2E0: A_27c] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0g0_2E0))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0g0_2E0),V1lam_2E0)))) )
     => p(c_2Emeasure_2Eadditive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0),V1lam_2E0)))) ) ).

tff(thm_2Emeasure_2ECOUNTABLY__SUBADDITIVE__SUBADDITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Ecountably__subadditive_2E1(A_27a,V0m_2E0)) )
     => p(c_2Emeasure_2Esubadditive_2E1(A_27a,V0m_2E0)) ) ).

tff(thm_2Emeasure_2ESIGMA__ALGEBRA__ALT,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
    <=> ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
        & ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2ESIGMA__ALGEBRA__ALT__MONO,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
    <=> ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
        & ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))))
              & ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Enum_2E0_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
              & ! [V2n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V2n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Enum_2ESUC_2E1(V2n_2E0)))) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2ESIGMA__ALGEBRA__ALT__DISJOINT,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
    <=> ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0))
        & ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))))
              & ! [V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
                  ( ( V2m_2E0 != V3n_2E0 )
                 => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V2m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V3n_2E0))) ) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2ESUBADDITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Esubadditive_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
        & ( V3u_2E0 = c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0) ) )
     => p(c_2Ereal_2Ereal__lte_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V3u_2E0),c_2Erealax_2Ereal__add_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V2t_2E0)))) ) ).

tff(thm_2Emeasure_2EADDITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Eadditive_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
        & p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V1s_2E0,V2t_2E0))
        & ( V3u_2E0 = c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0) ) )
     => ( c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V3u_2E0) = c_2Erealax_2Ereal__add_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V2t_2E0)) ) ) ).

tff(thm_2Emeasure_2ECOUNTABLY__SUBADDITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ecountably__subadditive_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Eseq_2Esummable_2E1(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V1f_2E0)))
        & ( V2s_2E0 = c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) )
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
     => p(c_2Ereal_2Ereal__lte_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V2s_2E0),c_2Eseq_2Esuminf_2E1(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V1f_2E0)))) ) ).

tff(thm_2Emeasure_2EADDITIVE__SUM,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2n_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Eadditive_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & ! [V3m_2E0: tyop_2Enum_2Enum,V4n_2E0: tyop_2Enum_2Enum] :
            ( ( V3m_2E0 != V4n_2E0 )
           => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V3m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V4n_2E0))) ) )
     => ( c_2Ereal_2Esum_2E2(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2E0_2E0,V2n_2E0),c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V1f_2E0)) = c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2Ecount_2E1(V2n_2E0)))) ) ) ).

tff(thm_2Emeasure_2EINCREASING__ADDITIVE__SUMMABLE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Eincreasing_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Eadditive_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & ! [V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
            ( ( V2m_2E0 != V3n_2E0 )
           => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V2m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V3n_2E0))) ) )
     => p(c_2Eseq_2Esummable_2E1(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V1f_2E0))) ) ).

tff(thm_2Emeasure_2ELAMBDA__SYSTEM__POSITIVE,axiom,
    ! [A_27a: $tType,V0g0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] :
      ( p(c_2Emeasure_2Epositive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0g0_2E0),V1lam_2E0))))
     => p(c_2Emeasure_2Epositive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0),V1lam_2E0)))) ) ).

tff(thm_2Emeasure_2ELAMBDA__SYSTEM__INCREASING,axiom,
    ! [A_27a: $tType,V0g0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] :
      ( p(c_2Emeasure_2Eincreasing_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0g0_2E0),V1lam_2E0))))
     => p(c_2Emeasure_2Eincreasing_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0),V1lam_2E0)))) ) ).

tff(thm_2Emeasure_2ELAMBDA__SYSTEM__STRONG__SUM,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V7s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2g_2E0),V7s_2E0) = c_2Epred__set_2EINTER_2E2(A_27a,V7s_2E0,V2g_2E0) )
     => ! [V0g0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4n_2E0: tyop_2Enum_2Enum] :
          ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0g0_2E0))
            & p(c_2Emeasure_2Epositive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0g0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0g0_2E0),V1lam_2E0))))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0g0_2E0)))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Elambda__system_2E2(A_27a,V0g0_2E0,V1lam_2E0))))
            & ! [V5m_2E0: tyop_2Enum_2Enum,V6n_2E0: tyop_2Enum_2Enum] :
                ( ( V5m_2E0 != V6n_2E0 )
               => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0,V5m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0,V6n_2E0))) ) )
         => ( c_2Ereal_2Esum_2E2(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2E0_2E0,V4n_2E0),c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1lam_2E0,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2g_2E0),V3f_2E0))) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,V1lam_2E0,c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0,c_2Epred__set_2Ecount_2E1(V4n_2E0))),V2g_2E0)) ) ) ) ).

tff(thm_2Emeasure_2ESIGMA__ALGEBRA__ALGEBRA,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
     => p(c_2Emeasure_2Ealgebra_2E1(A_27a,V0a_2E0)) ) ).

tff(thm_2Emeasure_2EOUTER__MEASURE__SPACE__POSITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Eouter__measure__space_2E1(A_27a,V0m_2E0))
     => p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0)) ) ).

tff(thm_2Emeasure_2ELAMBDA__SYSTEM__CARATHEODORY,axiom,
    ! [A_27a: $tType,V0gsig_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0gsig_2E0))
        & p(c_2Emeasure_2Eouter__measure__space_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0gsig_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0gsig_2E0),V1lam_2E0)))) )
     => ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Elambda__system_2E2(A_27a,V0gsig_2E0,V1lam_2E0))))
            & ! [V3m_2E0: tyop_2Enum_2Enum,V4n_2E0: tyop_2Enum_2Enum] :
                ( ( V3m_2E0 != V4n_2E0 )
               => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,V3m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,V4n_2E0))) ) )
         => ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Elambda__system_2E2(A_27a,V0gsig_2E0,V1lam_2E0)))
            & p(c_2Eseq_2Esums_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1lam_2E0,V2f_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,V1lam_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))))) ) ) ) ).

tff(thm_2Emeasure_2ECARATHEODORY__LEMMA,axiom,
    ! [A_27a: $tType,V0gsig_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1lam_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0gsig_2E0))
        & p(c_2Emeasure_2Eouter__measure__space_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0gsig_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0gsig_2E0),V1lam_2E0)))) )
     => p(c_2Emeasure_2Emeasure__space_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0gsig_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Elambda__system_2E2(A_27a,V0gsig_2E0,V1lam_2E0),V1lam_2E0)))) ) ).

tff(thm_2Emeasure_2EINF__MEASURE__NONEMPTY,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))))] :
      ( ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3r_2E0: tyop_2Erealax_2Ereal] :
          ( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0,V0m_2E0),V1g_2E0),V3r_2E0))
        <=> ? [V4f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
              & ! [V5m_2E0: tyop_2Enum_2Enum,V6n_2E0: tyop_2Enum_2Enum] :
                  ( ( V5m_2E0 != V6n_2E0 )
                 => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,V5m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,V6n_2E0))) )
              & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1g_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))))
              & p(c_2Eseq_2Esums_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V4f_2E0),V3r_2E0)) ) )
     => ( ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3r_2E0: tyop_2Erealax_2Ereal] : ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0,V0m_2E0),V1g_2E0),V3r_2E0) = c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V3r_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0,V0m_2E0),V1g_2E0),V3r_2E0)) )
       => ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
              & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
              & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1g_2E0,V2s_2E0)) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Erealax_2Ereal,c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V2s_2E0),c_2Epred__set_2EGSPEC_2E1(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0,V0m_2E0),V1g_2E0)))) ) ) ) ).

tff(thm_2Emeasure_2EINF__MEASURE__POS0,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))))] :
      ( ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3r_2E0: tyop_2Erealax_2Ereal] :
          ( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0,V0m_2E0),V1g_2E0),V3r_2E0))
        <=> ? [V4f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
              & ! [V5m_2E0: tyop_2Enum_2Enum,V6n_2E0: tyop_2Enum_2Enum] :
                  ( ( V5m_2E0 != V6n_2E0 )
                 => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,V5m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,V6n_2E0))) )
              & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1g_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))))
              & p(c_2Eseq_2Esums_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V4f_2E0),V3r_2E0)) ) )
     => ( ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3r_2E0: tyop_2Erealax_2Ereal] : ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0,V0m_2E0),V1g_2E0),V3r_2E0) = c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V3r_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0,V0m_2E0),V1g_2E0),V3r_2E0)) )
       => ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Erealax_2Ereal] :
            ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
              & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Erealax_2Ereal,V2x_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0,V0m_2E0),V1g_2E0)))) )
           => p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),V2x_2E0)) ) ) ) ).

tff(thm_2Emeasure_2EINF__MEASURE__POS,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1g_2E0,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0))) )
     => p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),c_2Emeasure_2Einf__measure_2E2(A_27a,V0m_2E0,V1g_2E0))) ) ).

tff(thm_2Emeasure_2EINCREASING,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Eincreasing_2E1(A_27a,V0m_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2t_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
     => p(c_2Ereal_2Ereal__lte_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V2t_2E0))) ) ).

tff(thm_2Emeasure_2EADDITIVE__INCREASING,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Eadditive_2E1(A_27a,V0m_2E0)) )
     => p(c_2Emeasure_2Eincreasing_2E1(A_27a,V0m_2E0)) ) ).

tff(thm_2Emeasure_2ECOUNTABLY__ADDITIVE__ADDITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Ecountably__additive_2E1(A_27a,V0m_2E0)) )
     => p(c_2Emeasure_2Eadditive_2E1(A_27a,V0m_2E0)) ) ).

tff(thm_2Emeasure_2ECOUNTABLY__ADDITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Ecountably__additive_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & ! [V3m_2E0: tyop_2Enum_2Enum,V4n_2E0: tyop_2Enum_2Enum] :
            ( ( V3m_2E0 != V4n_2E0 )
           => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,V3m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,V4n_2E0))) )
        & ( V1s_2E0 = c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) )
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
     => p(c_2Eseq_2Esums_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V2f_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0))) ) ).

tff(thm_2Emeasure_2EINF__MEASURE__AGREES,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Ecountably__additive_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
     => ( c_2Emeasure_2Einf__measure_2E2(A_27a,V0m_2E0,V1s_2E0) = c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0) ) ) ).

tff(thm_2Emeasure_2EMEASURE__DOWN,axiom,
    ! [A_27a: $tType,V0m0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1m1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m0_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m0_2E0))))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m0_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m1_2E0)))
        & ( c_2Emeasure_2Emeasure_2E1(A_27a,V0m0_2E0) = c_2Emeasure_2Emeasure_2E1(A_27a,V1m1_2E0) )
        & p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V1m1_2E0)) )
     => p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m0_2E0)) ) ).

tff(thm_2Emeasure_2ESIGMA__ALGEBRA__SIGMA,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1sts_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( p(c_2Emeasure_2Esubset__class_2E2(A_27a,V0sp_2E0,V1sts_2E0))
     => p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V1sts_2E0))) ) ).

tff(thm_2Emeasure_2EPOW__ALGEBRA,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,c_2Epred__set_2EPOW_2E1(A_27a,V0sp_2E0)))) ).

tff(thm_2Emeasure_2EPOW__SIGMA__ALGEBRA,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,c_2Epred__set_2EPOW_2E1(A_27a,V0sp_2E0)))) ).

tff(thm_2Emeasure_2EUNIV__SIGMA__ALGEBRA,axiom,
    ! [A_27a: $tType] : p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(A_27a),c_2Epred__set_2EUNIV_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))) ).

tff(thm_2Emeasure_2EINF__MEASURE__EMPTY,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0)) )
     => ( c_2Emeasure_2Einf__measure_2E2(A_27a,V0m_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).

tff(thm_2Emeasure_2EINF__MEASURE__POSITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0)) )
     => p(c_2Emeasure_2Epositive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Epred__set_2EPOW_2E1(A_27a,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0)),c_2Emeasure_2Einf__measure_2E1(A_27a,V0m_2E0))))) ) ).

tff(thm_2Emeasure_2EINF__MEASURE__INCREASING,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0)) )
     => p(c_2Emeasure_2Eincreasing_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Epred__set_2EPOW_2E1(A_27a,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0)),c_2Emeasure_2Einf__measure_2E1(A_27a,V0m_2E0))))) ) ).

tff(thm_2Emeasure_2EINF__MEASURE__LE,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))))] :
      ( ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3r_2E0: tyop_2Erealax_2Ereal] :
          ( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0,V0m_2E0),V1s_2E0),V3r_2E0))
        <=> ? [V4f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
              & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))))
              & p(c_2Eseq_2Esums_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V4f_2E0),V3r_2E0)) ) )
     => ( ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3r_2E0: tyop_2Erealax_2Ereal] : ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0,V0m_2E0),V1s_2E0),V3r_2E0) = c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V3r_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0,V0m_2E0),V1s_2E0),V3r_2E0)) )
       => ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Erealax_2Ereal] :
            ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
              & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
              & p(c_2Emeasure_2Eincreasing_2E1(A_27a,V0m_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Erealax_2Ereal,V2x_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0,V0m_2E0),V1s_2E0)))) )
           => p(c_2Ereal_2Ereal__lte_2E2(c_2Emeasure_2Einf__measure_2E2(A_27a,V0m_2E0,V1s_2E0),V2x_2E0)) ) ) ) ).

tff(thm_2Emeasure_2EINF__MEASURE__CLOSE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2e_2E0: tyop_2Erealax_2Ereal] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),V2e_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0))) )
     => ? [V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4l_2E0: tyop_2Erealax_2Ereal] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
          & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))))
          & ! [V5m_2E0: tyop_2Enum_2Enum,V6n_2E0: tyop_2Enum_2Enum] :
              ( ( V5m_2E0 != V6n_2E0 )
             => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0,V5m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0,V6n_2E0))) )
          & p(c_2Eseq_2Esums_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V3f_2E0),V4l_2E0))
          & p(c_2Ereal_2Ereal__lte_2E2(V4l_2E0,c_2Erealax_2Ereal__add_2E2(c_2Emeasure_2Einf__measure_2E2(A_27a,V0m_2E0,V1s_2E0),V2e_2E0))) ) ) ).

tff(thm_2Emeasure_2EINF__MEASURE__COUNTABLY__SUBADDITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Eincreasing_2E1(A_27a,V0m_2E0)) )
     => p(c_2Emeasure_2Ecountably__subadditive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Epred__set_2EPOW_2E1(A_27a,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0)),c_2Emeasure_2Einf__measure_2E1(A_27a,V0m_2E0))))) ) ).

tff(thm_2Emeasure_2EINF__MEASURE__OUTER,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Eincreasing_2E1(A_27a,V0m_2E0)) )
     => p(c_2Emeasure_2Eouter__measure__space_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Epred__set_2EPOW_2E1(A_27a,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0)),c_2Emeasure_2Einf__measure_2E1(A_27a,V0m_2E0))))) ) ).

tff(thm_2Emeasure_2ESIGMA__SUBSET,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1b_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V1b_2E0))) )
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V1b_2E0),V0a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1b_2E0))) ) ).

tff(thm_2Emeasure_2EALGEBRA__SUBSET__LAMBDA__SYSTEM,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Eincreasing_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Eadditive_2E1(A_27a,V0m_2E0)) )
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0),c_2Emeasure_2Elambda__system_2E2(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Epred__set_2EPOW_2E1(A_27a,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0))),c_2Emeasure_2Einf__measure_2E1(A_27a,V0m_2E0)))) ) ).

tff(thm_2Emeasure_2ECARATHEODORY,axiom,
    ! [A_27a: $tType,V0m0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m0_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m0_2E0))))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m0_2E0))
        & p(c_2Emeasure_2Ecountably__additive_2E1(A_27a,V0m0_2E0)) )
     => ? [V1m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
          ( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m0_2E0)))
             => ( c_2Emeasure_2Emeasure_2E2(A_27a,V1m_2E0,V2s_2E0) = c_2Emeasure_2Emeasure_2E2(A_27a,V0m0_2E0,V2s_2E0) ) )
          & ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)) = c_2Emeasure_2Esigma_2E2(A_27a,c_2Emeasure_2Em__space_2E1(A_27a,V0m0_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m0_2E0)) )
          & p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V1m_2E0)) ) ) ).

tff(thm_2Emeasure_2ESIGMA__SUBSET__SUBSETS,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V1a_2E0)))) ).

tff(thm_2Emeasure_2EIN__SIGMA,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0,V1a_2E0))
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V1a_2E0)))) ) ).

tff(thm_2Emeasure_2ESIGMA__ALGEBRA,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0p_2E0))
    <=> ( p(c_2Emeasure_2Esubset__class_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0p_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0)))
        & ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0p_2E0),V1s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))) )
        & ! [V2c_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
            ( ( p(c_2Epred__set_2Ecountable_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2c_2E0))
              & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2c_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,V2c_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0p_2E0))) ) ) ) ).

tff(thm_2Emeasure_2ESIGMA__ALGEBRA__COUNTABLE__UNION,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1c_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Epred__set_2Ecountable_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,V1c_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ).

tff(thm_2Emeasure_2ESIGMA__ALGEBRA__ENUM,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURE__COMPL,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
     => ( c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),V1s_2E0)) = c_2Ereal_2Ereal__sub_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0)),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0)) ) ) ).

tff(thm_2Emeasure_2ESIGMA__PROPERTY,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Esubset__class_2E2(A_27a,V0sp_2E0,V1p_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),V1p_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0,V1p_2E0))
        & ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0,c_2Epred__set_2EINTER_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V2a_2E0)))))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,V0sp_2E0,V3s_2E0),V1p_2E0)) )
        & ! [V4c_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
            ( ( p(c_2Epred__set_2Ecountable_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4c_2E0))
              & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4c_2E0,c_2Epred__set_2EINTER_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V2a_2E0))))) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,V4c_2E0),V1p_2E0)) ) )
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V2a_2E0)),V1p_2E0)) ) ).

tff(thm_2Emeasure_2EMEASURE__EMPTY,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
     => ( c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).

tff(thm_2Emeasure_2ESIGMA__SUBSET__MEASURABLE__SETS,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V1m_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0))) )
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0),V0a_2E0)),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0))) ) ).

tff(thm_2Emeasure_2ESIGMA__ALGEBRA__FN,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
    <=> ( p(c_2Emeasure_2Esubset__class_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),V1s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
        & ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2ESIGMA__ALGEBRA__FN__DISJOINT,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
    <=> ( p(c_2Emeasure_2Esubset__class_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),V1s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
        & ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
              & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(A_27a,V2s_2E0,V3t_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
        & ! [V4f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))))
              & ! [V5m_2E0: tyop_2Enum_2Enum,V6n_2E0: tyop_2Enum_2Enum] :
                  ( ( V5m_2E0 != V6n_2E0 )
                 => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,V5m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,V6n_2E0))) ) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2ESIGMA__PROPERTY__ALT,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Esubset__class_2E2(A_27a,V0sp_2E0,V1p_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),V1p_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0,V1p_2E0))
        & ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0,c_2Epred__set_2EINTER_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V2a_2E0)))))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,V0sp_2E0,V3s_2E0),V1p_2E0)) )
        & ! [V4f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EINTER_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V2a_2E0))))))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),V1p_2E0)) ) )
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V2a_2E0)),V1p_2E0)) ) ).

tff(thm_2Emeasure_2ESIGMA__PROPERTY__DISJOINT__WEAK,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,V2a_2E0)))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0,V1p_2E0))
        & p(c_2Emeasure_2Esubset__class_2E2(A_27a,V0sp_2E0,V1p_2E0))
        & ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0,V1p_2E0))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,V0sp_2E0,V3s_2E0),V1p_2E0)) )
        & ! [V4f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V1p_2E0)))
              & ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,c_2Enum_2E0_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
              & ! [V5n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,V5n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,c_2Enum_2ESUC_2E1(V5n_2E0)))) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),V1p_2E0)) )
        & ! [V6f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V6f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V1p_2E0)))
              & ! [V7m_2E0: tyop_2Enum_2Enum,V8n_2E0: tyop_2Enum_2Enum] :
                  ( ( V7m_2E0 != V8n_2E0 )
                 => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6f_2E0,V7m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6f_2E0,V8n_2E0))) ) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),V1p_2E0)) ) )
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V2a_2E0)),V1p_2E0)) ) ).

tff(thm_2Emeasure_2ESIGMA__PROPERTY__DISJOINT,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Ealgebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,V2a_2E0)))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0,V1p_2E0))
        & ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0,c_2Epred__set_2EINTER_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V2a_2E0)))))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,V0sp_2E0,V3s_2E0),V1p_2E0)) )
        & ! [V4f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EINTER_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V2a_2E0))))))
              & ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,c_2Enum_2E0_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
              & ! [V5n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,V5n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,c_2Enum_2ESUC_2E1(V5n_2E0)))) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),V1p_2E0)) )
        & ! [V6f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V6f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EINTER_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V2a_2E0))))))
              & ! [V7m_2E0: tyop_2Enum_2Enum,V8n_2E0: tyop_2Enum_2Enum] :
                  ( ( V7m_2E0 != V8n_2E0 )
                 => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6f_2E0,V7m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6f_2E0,V8n_2E0))) ) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),V1p_2E0)) ) )
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V2a_2E0)),V1p_2E0)) ) ).

tff(thm_2Emeasure_2EMEASURE__COUNTABLY__ADDITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & ! [V3m_2E0: tyop_2Enum_2Enum,V4n_2E0: tyop_2Enum_2Enum] :
            ( ( V3m_2E0 != V4n_2E0 )
           => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,V3m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,V4n_2E0))) )
        & ( V1s_2E0 = c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ) )
     => p(c_2Eseq_2Esums_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V2f_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__ADDITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
     => p(c_2Emeasure_2Eadditive_2E1(A_27a,V0m_2E0)) ) ).

tff(thm_2Emeasure_2EMEASURE__ADDITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
        & p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V1s_2E0,V2t_2E0))
        & ( V3u_2E0 = c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0) ) )
     => ( c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V3u_2E0) = c_2Erealax_2Ereal__add_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V2t_2E0)) ) ) ).

tff(thm_2Emeasure_2EMEASURE__COUNTABLE__INCREASING,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Enum_2E0_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
        & ! [V3n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,V3n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Enum_2ESUC_2E1(V3n_2E0))))
        & ( V1s_2E0 = c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ) )
     => p(c_2Eseq_2E_2D_2D_3E_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V2f_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__REDUCE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0))) = V0m_2E0 ) ).

tff(thm_2Emeasure_2ESPACE__SIGMA,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Espace_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V1a_2E0)) = V0sp_2E0 ) ).

tff(thm_2Emeasure_2EMONOTONE__CONVERGENCE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & ! [V3n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,V3n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Enum_2ESUC_2E1(V3n_2E0))))
        & ( V1s_2E0 = c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ) )
     => p(c_2Eseq_2E_2D_2D_3E_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V2f_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0))) ) ).

tff(thm_2Emeasure_2ESIGMA__REDUCE,axiom,
    ! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V1a_2E0))) = c_2Emeasure_2Esigma_2E2(A_27a,V0sp_2E0,V1a_2E0) ) ).

tff(thm_2Emeasure_2EMEASURABLE__SETS__SUBSET__SPACE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
     => p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__DIFF__PROPERTY,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Emeasure_2Esigma__algebra_2E1(A_27b,V1b_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Espace_2E1(A_27b,V1b_2E0))))
        & ! [V3s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_2E0,c_2Emeasure_2Esubsets_2E1(A_27b,V1b_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V2f_2E0,V3s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) )
     => ! [V4s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4s_2E0,c_2Emeasure_2Esubsets_2E1(A_27b,V1b_2E0)))
         => ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V2f_2E0,c_2Epred__set_2EDIFF_2E2(A_27b,c_2Emeasure_2Espace_2E1(A_27b,V1b_2E0),V4s_2E0)) = c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V2f_2E0,V4s_2E0)) ) ) ) ).

tff(thm_2Emeasure_2EMEASURABLE__BIGUNION__PROPERTY,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Emeasure_2Esigma__algebra_2E1(A_27b,V1b_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Espace_2E1(A_27b,V1b_2E0))))
        & ! [V3s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_2E0,c_2Emeasure_2Esubsets_2E1(A_27b,V1b_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V2f_2E0,V3s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) )
     => ! [V4c_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
          ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4c_2E0,c_2Emeasure_2Esubsets_2E1(A_27b,V1b_2E0)))
         => ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V2f_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27b,V4c_2E0)) = c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E1(A_27a,A_27b,V2f_2E0),V4c_2E0)) ) ) ) ).

tff(thm_2Emeasure_2EMEASUBABLE__BIGUNION__LEMMA,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Emeasure_2Esigma__algebra_2E1(A_27b,V1b_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Espace_2E1(A_27b,V1b_2E0))))
        & ! [V3s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_2E0,c_2Emeasure_2Esubsets_2E1(A_27b,V1b_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V2f_2E0,V3s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) )
     => ! [V4c_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
          ( ( p(c_2Epred__set_2Ecountable_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4c_2E0))
            & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4c_2E0,c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E1(A_27a,A_27b,V2f_2E0),c_2Emeasure_2Esubsets_2E1(A_27b,V1b_2E0)))) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,V4c_2E0),c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E1(A_27a,A_27b,V2f_2E0),c_2Emeasure_2Esubsets_2E1(A_27b,V1b_2E0)))) ) ) ).

tff(thm_2Emeasure_2EMEASURABLE__SIGMA__PREIMAGES,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Emeasure_2Esigma__algebra_2E1(A_27b,V1b_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Espace_2E1(A_27b,V1b_2E0))))
        & ! [V3s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_2E0,c_2Emeasure_2Esubsets_2E1(A_27b,V1b_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V2f_2E0,V3s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) )
     => p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E1(A_27a,A_27b,V2f_2E0),c_2Emeasure_2Esubsets_2E1(A_27b,V1b_2E0))))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,V0a_2E0,V1b_2E0)))
    <=> ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Emeasure_2Esigma__algebra_2E1(A_27b,V1b_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Espace_2E1(A_27b,V1b_2E0))))
        & ! [V3s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_2E0,c_2Emeasure_2Esubsets_2E1(A_27b,V1b_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V2f_2E0,V3s_2E0),c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2EMEASURABLE__SIGMA,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V2b_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3sp_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
        & p(c_2Emeasure_2Esubset__class_2E2(A_27b,V3sp_2E0,V2b_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0),V3sp_2E0)))
        & ! [V4s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4s_2E0,V2b_2E0))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V4s_2E0),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,V1a_2E0,c_2Emeasure_2Esigma_2E2(A_27b,V3sp_2E0,V2b_2E0)))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__SUBSET,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,A_27b),c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,V0a_2E0,V1b_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,V0a_2E0,c_2Emeasure_2Esigma_2E2(A_27b,c_2Emeasure_2Espace_2E1(A_27b,V1b_2E0),c_2Emeasure_2Esubsets_2E1(A_27b,V1b_2E0))))) ).

tff(thm_2Emeasure_2EMEASURABLE__LIFT,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V2b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,V1a_2E0,V2b_2E0)))
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,V1a_2E0,c_2Emeasure_2Esigma_2E2(A_27b,c_2Emeasure_2Espace_2E1(A_27b,V2b_2E0),c_2Emeasure_2Esubsets_2E1(A_27b,V2b_2E0))))) ) ).

tff(thm_2Emeasure_2EIN__MEASURE__PRESERVING,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0m1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1m2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,V0m1_2E0,V1m2_2E0)))
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m1_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m1_2E0)),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27b,V1m2_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27b,V1m2_2E0)))))
        & p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m1_2E0))
        & p(c_2Emeasure_2Emeasure__space_2E1(A_27b,V1m2_2E0))
        & ! [V3s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27b,V1m2_2E0)))
           => ( c_2Emeasure_2Emeasure_2E2(A_27a,V0m1_2E0,c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V2f_2E0,V3s_2E0),c_2Emeasure_2Em__space_2E1(A_27a,V0m1_2E0))) = c_2Emeasure_2Emeasure_2E2(A_27b,V1m2_2E0,V3s_2E0) ) ) ) ) ).

tff(thm_2Emeasure_2EMEASURE__PRESERVING__LIFT,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0m1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1m2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V2a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m1_2E0))
        & p(c_2Emeasure_2Emeasure__space_2E1(A_27b,V1m2_2E0))
        & ( c_2Emeasure_2Emeasurable__sets_2E1(A_27b,V1m2_2E0) = c_2Emeasure_2Esubsets_2E1(A_27b,c_2Emeasure_2Esigma_2E2(A_27b,c_2Emeasure_2Em__space_2E1(A_27b,V1m2_2E0),V2a_2E0)) )
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0,c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,V0m1_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Em__space_2E1(A_27b,V1m2_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V2a_2E0,c_2Emeasure_2Emeasure_2E1(A_27b,V1m2_2E0)))))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0,c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,V0m1_2E0,V1m2_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURE__PRESERVING__SUBSET,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0m1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1m2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V2a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m1_2E0))
        & p(c_2Emeasure_2Emeasure__space_2E1(A_27b,V1m2_2E0))
        & ( c_2Emeasure_2Emeasurable__sets_2E1(A_27b,V1m2_2E0) = c_2Emeasure_2Esubsets_2E1(A_27b,c_2Emeasure_2Esigma_2E2(A_27b,c_2Emeasure_2Em__space_2E1(A_27b,V1m2_2E0),V2a_2E0)) ) )
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,A_27b),c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,V0m1_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Em__space_2E1(A_27b,V1m2_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V2a_2E0,c_2Emeasure_2Emeasure_2E1(A_27b,V1m2_2E0)))),c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,V0m1_2E0,V1m2_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__I,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0(A_27a),c_2Emeasure_2Emeasurable_2E2(A_27a,A_27a,V0a_2E0,V0a_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__COMP,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V3b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V4c_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,V2a_2E0,V3b_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0,c_2Emeasure_2Emeasurable_2E2(A_27b,A_27c,V3b_2E0,V4c_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,V1g_2E0,V0f_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,A_27c,V2a_2E0,V4c_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__COMP__STRONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V3b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V4c_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,V2a_2E0,V3b_2E0)))
        & p(c_2Emeasure_2Esigma__algebra_2E1(A_27c,V4c_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0,c_2Epred__set_2EFUNSET_2E2(A_27b,A_27c,c_2Emeasure_2Espace_2E1(A_27b,V3b_2E0),c_2Emeasure_2Espace_2E1(A_27c,V4c_2E0))))
        & ! [V5x_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V5x_2E0,c_2Emeasure_2Esubsets_2E1(A_27c,V4c_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27b,c_2Epred__set_2EPREIMAGE_2E2(A_27b,A_27c,V1g_2E0,V5x_2E0),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Emeasure_2Espace_2E1(A_27a,V2a_2E0))),c_2Emeasure_2Esubsets_2E1(A_27b,V3b_2E0))) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,V1g_2E0,V0f_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,A_27c,V2a_2E0,V4c_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__COMP__STRONGER,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V3b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V4c_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V5t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,V2a_2E0,V3b_2E0)))
        & p(c_2Emeasure_2Esigma__algebra_2E1(A_27c,V4c_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0,c_2Epred__set_2EFUNSET_2E2(A_27b,A_27c,c_2Emeasure_2Espace_2E1(A_27b,V3b_2E0),c_2Emeasure_2Espace_2E1(A_27c,V4c_2E0))))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Emeasure_2Espace_2E1(A_27a,V2a_2E0)),V5t_2E0))
        & ! [V6s_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V6s_2E0,c_2Emeasure_2Esubsets_2E1(A_27c,V4c_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27b,c_2Epred__set_2EPREIMAGE_2E2(A_27b,A_27c,V1g_2E0,V6s_2E0),V5t_2E0),c_2Emeasure_2Esubsets_2E1(A_27b,V3b_2E0))) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,V1g_2E0,V0f_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,A_27c,V2a_2E0,V4c_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__UP__LIFT,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2b_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3c_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V4f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,V1a_2E0),V3c_2E0)))
        & p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,V2b_2E0)))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0,V2b_2E0)) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,V2b_2E0),V3c_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__UP__SUBSET,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2b_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3c_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0,V2b_2E0))
        & p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,V2b_2E0))) )
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,A_27b),c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,V1a_2E0),V3c_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0sp_2E0,V2b_2E0),V3c_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__UP__SIGMA,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,A_27b),c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,V0a_2E0,V1b_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,c_2Emeasure_2Esigma_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)),V1b_2E0))) ).

tff(thm_2Emeasure_2EMEASURE__PRESERVING__UP__LIFT,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1m1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V2m2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V1m1_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0,c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Em__space_2E1(A_27a,V1m1_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V0a_2E0,c_2Emeasure_2Emeasure_2E1(A_27a,V1m1_2E0))),V2m2_2E0)))
        & p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V1m1_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m1_2E0))))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m1_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0,c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,V1m1_2E0,V2m2_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURE__PRESERVING__UP__SUBSET,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1m1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V2m2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V1m1_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m1_2E0)))
        & p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V1m1_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m1_2E0)))) )
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,A_27b),c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Em__space_2E1(A_27a,V1m1_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V0a_2E0,c_2Emeasure_2Emeasure_2E1(A_27a,V1m1_2E0))),V2m2_2E0),c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,V1m1_2E0,V2m2_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURE__PRESERVING__UP__SIGMA,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0m1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1m2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V2a_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m1_2E0))
        & ( c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m1_2E0) = c_2Emeasure_2Esubsets_2E1(A_27a,c_2Emeasure_2Esigma_2E2(A_27a,c_2Emeasure_2Em__space_2E1(A_27a,V0m1_2E0),V2a_2E0)) ) )
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,A_27b),c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Em__space_2E1(A_27a,V0m1_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V2a_2E0,c_2Emeasure_2Emeasure_2E1(A_27a,V0m1_2E0))),V1m2_2E0),c_2Emeasure_2Emeasure__preserving_2E2(A_27a,A_27b,V0m1_2E0,V1m2_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__PROD__SIGMA,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1a1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V2a2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V3f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(A_27a,A_27b,tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2EFST_2E0(A_27b,A_27c),V3f_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,V0a_2E0,V1a1_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(A_27a,A_27c,tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2ESND_2E0(A_27b,A_27c),V3f_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,A_27c,V0a_2E0,V2a2_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V3f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),V0a_2E0,c_2Emeasure_2Esigma_2E2(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epred__set_2ECROSS_2E2(A_27b,A_27c,c_2Emeasure_2Espace_2E1(A_27b,V1a1_2E0),c_2Emeasure_2Espace_2E1(A_27c,V2a2_2E0)),c_2Eutil__prob_2Eprod__sets_2E2(A_27b,A_27c,c_2Emeasure_2Esubsets_2E1(A_27b,V1a1_2E0),c_2Emeasure_2Esubsets_2E1(A_27c,V2a2_2E0)))))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__RANGE__REDUCE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2s_2E0,c_2Epred__set_2EPOW_2E1(A_27b,V2s_2E0)))))
        & ( V2s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27b) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27b,V2s_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0))),c_2Epred__set_2EPOW_2E1(A_27b,c_2Epred__set_2EINTER_2E2(A_27b,V2s_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0)))))))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__POW__TO__POW,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & ( c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0) = c_2Epred__set_2EPOW_2E1(A_27a,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0)) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(A_27b),c_2Epred__set_2EPOW_2E1(A_27b,c_2Epred__set_2EUNIV_2E0(A_27b)))))) ) ).

tff(thm_2Emeasure_2EMEASURABLE__POW__TO__POW__IMAGE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & ( c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0) = c_2Epred__set_2EPOW_2E1(A_27a,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0)) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0)),c_2Epred__set_2EPOW_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0))))))) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__SUBSET,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2m_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] :
      ( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_27_2E0,V0s_2E0))
        & p(c_2Emeasure_2Emeasure__space_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),V0s_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Epred__set_2EPOW_2E1(A_27a,V0s_2E0),V2m_2E0)))) )
     => p(c_2Emeasure_2Emeasure__space_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),V1s_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Epred__set_2EPOW_2E1(A_27a,V1s_27_2E0),V2m_2E0)))) ) ).

tff(thm_2Emeasure_2ESTRONG__MEASURE__SPACE__SUBSET,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_27_2E0,c_2Emeasure_2Em__space_2E1(A_27a,V0s_2E0)))
        & p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(A_27a,V1s_27_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0s_2E0))) )
     => p(c_2Emeasure_2Emeasure__space_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),V1s_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Epred__set_2EPOW_2E1(A_27a,V1s_27_2E0),c_2Emeasure_2Emeasure_2E1(A_27a,V0s_2E0))))) ) ).

tff(thm_2Emeasure_2EMEASURE__REAL__SUM__IMAGE,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal))] :
      ( ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Erealax_2Ereal,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0m_2E0),V3x_2E0) = c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V3x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) )
     => ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
            & ! [V2x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
               => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
            & p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) )
         => ( c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0) = c_2Ereal__sigma_2EREAL__SUM__IMAGE_2E2(A_27a,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0m_2E0),V1s_2E0) ) ) ) ).

tff(thm_2Emeasure_2ESIGMA__POW,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Emeasure_2Esigma_2E2(A_27a,V0s_2E0,c_2Epred__set_2EPOW_2E1(A_27a,V0s_2E0)) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s_2E0,c_2Epred__set_2EPOW_2E1(A_27a,V0s_2E0)) ) ).

tff(thm_2Emeasure_2Efinite__additivity__sufficient__for__finite__spaces,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1m_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0s_2E0)))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0s_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0s_2E0),V1m_2E0))))
        & p(c_2Emeasure_2Eadditive_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0s_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0s_2E0),V1m_2E0)))) )
     => p(c_2Emeasure_2Emeasure__space_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Espace_2E1(A_27a,V0s_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Esubsets_2E1(A_27a,V0s_2E0),V1m_2E0)))) ) ).

tff(thm_2Emeasure_2Efinite__additivity__sufficient__for__finite__spaces2,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0)))
        & p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0))
        & p(c_2Emeasure_2Eadditive_2E1(A_27a,V0m_2E0)) )
     => p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0)) ) ).

tff(thm_2Emeasure_2EIMAGE__SING,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: A_27a] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) = c_2Epred__set_2EINSERT_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0),c_2Epred__set_2EEMPTY_2E0(A_27b)) ) ).

tff(thm_2Emeasure_2ESUBSET__BIGINTER,axiom,
    ! [A_27a: $tType,V0X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0X_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V1P_2E0)))
    <=> ! [V2Y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0,V1P_2E0))
         => p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0X_2E0,V2Y_2E0)) ) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__INCREASING,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
     => p(c_2Emeasure_2Eincreasing_2E1(A_27a,V0m_2E0)) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__POSITIVE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
     => p(c_2Emeasure_2Epositive_2E1(A_27a,V0m_2E0)) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__INTER,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__UNION,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__DIFF,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,V1s_2E0,V2t_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURE__COMPL__SUBSET,axiom,
    ! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V1m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0t_2E0,V2s_2E0)) )
     => ( c_2Emeasure_2Emeasure_2E2(A_27a,V1m_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V2s_2E0,V0t_2E0)) = c_2Ereal_2Ereal__sub_2E2(c_2Emeasure_2Emeasure_2E2(A_27a,V1m_2E0,V2s_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V1m_2E0,V0t_2E0)) ) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__BIGUNION,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & ! [V2n_2E0: tyop_2Enum_2Enum] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,V2n_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__IN__MSPACE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
     => ! [V2x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1A_2E0))
         => p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0))) ) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__SUBSET__MSPACE,axiom,
    ! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V1m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0))) )
     => p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0A_2E0,c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__EMPTY__MEASURABLE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__MSPACE__MEASURABLE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) ) ).

tff(thm_2Emeasure_2ESIGMA__ALGEBRA__FN__BIGINTER,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
     => ( p(c_2Emeasure_2Esubset__class_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),V1s_2E0),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
        & ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__BIGINTER,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & ! [V2n_2E0: tyop_2Enum_2Enum] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,V2n_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) ) ).

tff(thm_2Emeasure_2EMONOTONE__CONVERGENCE2,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & ! [V2n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V2n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Enum_2ESUC_2E1(V2n_2E0)))) )
     => p(c_2Eseq_2E_2D_2D_3E_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V1f_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))))) ) ).

tff(thm_2Emeasure_2EMONOTONE__CONVERGENCE__BIGINTER,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & ! [V3n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Enum_2ESUC_2E1(V3n_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,V3n_2E0)))
        & ( V1s_2E0 = c_2Epred__set_2EBIGINTER_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ) )
     => p(c_2Eseq_2E_2D_2D_3E_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V2f_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V1s_2E0))) ) ).

tff(thm_2Emeasure_2EMONOTONE__CONVERGENCE__BIGINTER2,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))))
        & ! [V2n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Enum_2ESUC_2E1(V2n_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V2n_2E0))) )
     => p(c_2Eseq_2E_2D_2D_3E_2E2(c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0),V1f_2E0),c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))))) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__RESTRICTED,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V1s_2E0),V2t_2E0) = c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0) )
     => ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0))) )
         => p(c_2Emeasure_2Emeasure__space_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),V1s_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V1s_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)),c_2Emeasure_2Emeasure_2E1(A_27a,V0m_2E0))))) ) ) ).

tff(thm_2Emeasure_2EMEASURE__SPACE__CMUL,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
      ( ! [V1c_2E0: tyop_2Erealax_2Ereal,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),F0_2E0,V1c_2E0),V0m_2E0),V2a_2E0) = c_2Erealax_2Ereal__mul_2E2(V1c_2E0,c_2Emeasure_2Emeasure_2E2(A_27a,V0m_2E0,V2a_2E0)) )
     => ! [V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1c_2E0: tyop_2Erealax_2Ereal] :
          ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
            & p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),V1c_2E0)) )
         => p(c_2Emeasure_2Emeasure__space_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)),F0_2E0,V1c_2E0),V0m_2E0))))) ) ) ).

tff(thm_2Emeasure_2EBIGUNION__IMAGE__Q,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0,c_2Epred__set_2EFUNSET_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eextreal_2EQ__set_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Eextreal_2EQ__set_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) ) ).

tff(thm_2Emeasure_2ESIGMA__ALGEBRA__BOREL,axiom,
    p(c_2Emeasure_2Esigma__algebra_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0)) ).

tff(thm_2Emeasure_2EMEASURABLE__BOREL,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))] :
      ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V3x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V2c_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V3x_2E0,c_2Eextreal_2Eextreal__lt_2E2(V3x_2E0,V2c_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
        <=> ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal))))
            & ! [V2c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V2c_2E0))),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2c_2E0: tyop_2Eextreal_2Eextreal,V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2c_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,c_2Eextreal_2Eextreal__lt_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0),V2c_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
        <=> ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal))))
            & ! [V2c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2c_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__NEGINF,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0f_2E0),V2x_2E0))
        <=> ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V2x_2E0) = c_2Eextreal_2ENegInf_2E0 ) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0f_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0f_2E0),V2x_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
           => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0f_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ALT1,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V2c_2E0),V0f_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,c_2Eextreal_2Eextreal__le_2E2(V2c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0))) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
        <=> ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal))))
            & ! [V2c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V2c_2E0),V0f_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ALT2,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2c_2E0: tyop_2Eextreal_2Eextreal,V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2c_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,c_2Eextreal_2Eextreal__le_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0),V2c_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
        <=> ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal))))
            & ! [V2c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2c_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ALT3,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V2c_2E0),V0f_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,c_2Eextreal_2Eextreal__lt_2E2(V2c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0))) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
        <=> ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal))))
            & ! [V2c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V2c_2E0),V0f_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ALT4,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
      ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V4x_2E0: A_27a,V3d_2E0: tyop_2Eextreal_2Eextreal] :
          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F1_2E0,V2c_2E0),V0f_2E0),V4x_2E0),V3d_2E0))
        <=> ( p(c_2Eextreal_2Eextreal__le_2E2(V2c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V4x_2E0)))
            & p(c_2Eextreal_2Eextreal__lt_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V4x_2E0),V3d_2E0)) ) )
     => ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3d_2E0: tyop_2Eextreal_2Eextreal,V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2c_2E0),V0f_2E0),V3d_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F1_2E0,V2c_2E0),V0f_2E0),V4x_2E0),V3d_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
          <=> ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal))))
              & ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V3d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2c_2E0),V0f_2E0),V3d_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ALT5,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
      ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V4x_2E0: A_27a,V3d_2E0: tyop_2Eextreal_2Eextreal] :
          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F1_2E0,V2c_2E0),V0f_2E0),V4x_2E0),V3d_2E0))
        <=> ( p(c_2Eextreal_2Eextreal__lt_2E2(V2c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V4x_2E0)))
            & p(c_2Eextreal_2Eextreal__le_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V4x_2E0),V3d_2E0)) ) )
     => ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3d_2E0: tyop_2Eextreal_2Eextreal,V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2c_2E0),V0f_2E0),V3d_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F1_2E0,V2c_2E0),V0f_2E0),V4x_2E0),V3d_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
          <=> ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal))))
              & ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V3d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2c_2E0),V0f_2E0),V3d_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ALT6,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
      ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V4x_2E0: A_27a,V3d_2E0: tyop_2Eextreal_2Eextreal] :
          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F1_2E0,V2c_2E0),V0f_2E0),V4x_2E0),V3d_2E0))
        <=> ( p(c_2Eextreal_2Eextreal__le_2E2(V2c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V4x_2E0)))
            & p(c_2Eextreal_2Eextreal__le_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V4x_2E0),V3d_2E0)) ) )
     => ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3d_2E0: tyop_2Eextreal_2Eextreal,V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2c_2E0),V0f_2E0),V3d_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F1_2E0,V2c_2E0),V0f_2E0),V4x_2E0),V3d_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
          <=> ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal))))
              & ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V3d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2c_2E0),V0f_2E0),V3d_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ALT7,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
      ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V4x_2E0: A_27a,V3d_2E0: tyop_2Eextreal_2Eextreal] :
          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F1_2E0,V2c_2E0),V0f_2E0),V4x_2E0),V3d_2E0))
        <=> ( p(c_2Eextreal_2Eextreal__lt_2E2(V2c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V4x_2E0)))
            & p(c_2Eextreal_2Eextreal__lt_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V4x_2E0),V3d_2E0)) ) )
     => ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3d_2E0: tyop_2Eextreal_2Eextreal,V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2c_2E0),V0f_2E0),V3d_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F1_2E0,V2c_2E0),V0f_2E0),V4x_2E0),V3d_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
           => ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal))))
              & ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V3d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2c_2E0),V0f_2E0),V3d_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ALT8,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3x_2E0: A_27a,V2c_2E0: tyop_2Eextreal_2Eextreal] :
          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0f_2E0),V3x_2E0),V2c_2E0))
        <=> ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0) = V2c_2E0 ) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2c_2E0: tyop_2Eextreal_2Eextreal,V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2c_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0f_2E0),V3x_2E0),V2c_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
           => ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal))))
              & ! [V2c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2c_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ALT9,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3x_2E0: A_27a,V2c_2E0: tyop_2Eextreal_2Eextreal] :
          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0f_2E0),V3x_2E0),V2c_2E0))
        <=> ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0) != V2c_2E0 ) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2c_2E0: tyop_2Eextreal_2Eextreal,V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2c_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0f_2E0),V3x_2E0),V2c_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
           => ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal))))
              & ! [V2c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2c_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ALL,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F15_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F9_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F14_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F8_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F13_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F4_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F12_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F6_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F11_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F5_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F10_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F7_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F3_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2c_2E0: tyop_2Eextreal_2Eextreal,V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2c_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,c_2Eextreal_2Eextreal__lt_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0),V2c_2E0)) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V6c_2E0: tyop_2Eextreal_2Eextreal,V7x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F2_2E0,V0f_2E0),V6c_2E0),V7x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V7x_2E0,c_2Eextreal_2Eextreal__le_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V7x_2E0),V6c_2E0)) )
       => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V25x_2E0: A_27a,V24c_2E0: tyop_2Eextreal_2Eextreal] :
              ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F15_2E0,V0f_2E0),V25x_2E0),V24c_2E0))
            <=> ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V25x_2E0) = V24c_2E0 ) )
         => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V24c_2E0: tyop_2Eextreal_2Eextreal,V25x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F9_2E0,V0f_2E0),V24c_2E0),V25x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V25x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F15_2E0,V0f_2E0),V25x_2E0),V24c_2E0)) )
           => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V23x_2E0: A_27a,V22c_2E0: tyop_2Eextreal_2Eextreal] :
                  ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F14_2E0,V0f_2E0),V23x_2E0),V22c_2E0))
                <=> ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V23x_2E0) != V22c_2E0 ) )
             => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V22c_2E0: tyop_2Eextreal_2Eextreal,V23x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F8_2E0,V0f_2E0),V22c_2E0),V23x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V23x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F14_2E0,V0f_2E0),V23x_2E0),V22c_2E0)) )
               => ( ! [V10c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V12x_2E0: A_27a,V11d_2E0: tyop_2Eextreal_2Eextreal] :
                      ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F13_2E0,V10c_2E0),V0f_2E0),V12x_2E0),V11d_2E0))
                    <=> ( p(c_2Eextreal_2Eextreal__lt_2E2(V10c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V12x_2E0)))
                        & p(c_2Eextreal_2Eextreal__lt_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V12x_2E0),V11d_2E0)) ) )
                 => ( ! [V10c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V11d_2E0: tyop_2Eextreal_2Eextreal,V12x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F4_2E0,V10c_2E0),V0f_2E0),V11d_2E0),V12x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V12x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F13_2E0,V10c_2E0),V0f_2E0),V12x_2E0),V11d_2E0)) )
                   => ( ! [V16c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V18x_2E0: A_27a,V17d_2E0: tyop_2Eextreal_2Eextreal] :
                          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F12_2E0,V16c_2E0),V0f_2E0),V18x_2E0),V17d_2E0))
                        <=> ( p(c_2Eextreal_2Eextreal__lt_2E2(V16c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V18x_2E0)))
                            & p(c_2Eextreal_2Eextreal__le_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V18x_2E0),V17d_2E0)) ) )
                     => ( ! [V16c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V17d_2E0: tyop_2Eextreal_2Eextreal,V18x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F6_2E0,V16c_2E0),V0f_2E0),V17d_2E0),V18x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V18x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F12_2E0,V16c_2E0),V0f_2E0),V18x_2E0),V17d_2E0)) )
                       => ( ! [V13c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V15x_2E0: A_27a,V14d_2E0: tyop_2Eextreal_2Eextreal] :
                              ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F11_2E0,V13c_2E0),V0f_2E0),V15x_2E0),V14d_2E0))
                            <=> ( p(c_2Eextreal_2Eextreal__le_2E2(V13c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V15x_2E0)))
                                & p(c_2Eextreal_2Eextreal__lt_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V15x_2E0),V14d_2E0)) ) )
                         => ( ! [V13c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V14d_2E0: tyop_2Eextreal_2Eextreal,V15x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F5_2E0,V13c_2E0),V0f_2E0),V14d_2E0),V15x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V15x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F11_2E0,V13c_2E0),V0f_2E0),V15x_2E0),V14d_2E0)) )
                           => ( ! [V19c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V21x_2E0: A_27a,V20d_2E0: tyop_2Eextreal_2Eextreal] :
                                  ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F10_2E0,V19c_2E0),V0f_2E0),V21x_2E0),V20d_2E0))
                                <=> ( p(c_2Eextreal_2Eextreal__le_2E2(V19c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V21x_2E0)))
                                    & p(c_2Eextreal_2Eextreal__le_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V21x_2E0),V20d_2E0)) ) )
                             => ( ! [V19c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V20d_2E0: tyop_2Eextreal_2Eextreal,V21x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F7_2E0,V19c_2E0),V0f_2E0),V20d_2E0),V21x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V21x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F10_2E0,V19c_2E0),V0f_2E0),V21x_2E0),V20d_2E0)) )
                               => ( ! [V8c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V9x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F3_2E0,V8c_2E0),V0f_2E0),V9x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V9x_2E0,c_2Eextreal_2Eextreal__lt_2E2(V8c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V9x_2E0))) )
                                 => ( ! [V4c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V4c_2E0),V0f_2E0),V5x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V5x_2E0,c_2Eextreal_2Eextreal__le_2E2(V4c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V5x_2E0))) )
                                   => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
                                        ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
                                       => ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2c_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0)))
                                          & ! [V4c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V4c_2E0),V0f_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0)))
                                          & ! [V6c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F2_2E0,V0f_2E0),V6c_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0)))
                                          & ! [V8c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F3_2E0,V8c_2E0),V0f_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0)))
                                          & ! [V10c_2E0: tyop_2Eextreal_2Eextreal,V11d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F4_2E0,V10c_2E0),V0f_2E0),V11d_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0)))
                                          & ! [V13c_2E0: tyop_2Eextreal_2Eextreal,V14d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F5_2E0,V13c_2E0),V0f_2E0),V14d_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0)))
                                          & ! [V16c_2E0: tyop_2Eextreal_2Eextreal,V17d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F6_2E0,V16c_2E0),V0f_2E0),V17d_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0)))
                                          & ! [V19c_2E0: tyop_2Eextreal_2Eextreal,V20d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F7_2E0,V19c_2E0),V0f_2E0),V20d_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0)))
                                          & ! [V22c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F8_2E0,V0f_2E0),V22c_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0)))
                                          & ! [V24c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F9_2E0,V0f_2E0),V24c_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V1a_2E0))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ALL__MEASURE,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F15_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F8_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F14_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F9_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F13_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F4_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F12_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F6_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F11_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F5_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F10_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F7_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F3_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2c_2E0: tyop_2Eextreal_2Eextreal,V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2c_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,c_2Eextreal_2Eextreal__lt_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0),V2c_2E0)) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V6c_2E0: tyop_2Eextreal_2Eextreal,V7x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F2_2E0,V0f_2E0),V6c_2E0),V7x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V7x_2E0,c_2Eextreal_2Eextreal__le_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V7x_2E0),V6c_2E0)) )
       => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V23x_2E0: A_27a,V22c_2E0: tyop_2Eextreal_2Eextreal] :
              ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F15_2E0,V0f_2E0),V23x_2E0),V22c_2E0))
            <=> ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V23x_2E0) = V22c_2E0 ) )
         => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V22c_2E0: tyop_2Eextreal_2Eextreal,V23x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F8_2E0,V0f_2E0),V22c_2E0),V23x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V23x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F15_2E0,V0f_2E0),V23x_2E0),V22c_2E0)) )
           => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V25x_2E0: A_27a,V24c_2E0: tyop_2Eextreal_2Eextreal] :
                  ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F14_2E0,V0f_2E0),V25x_2E0),V24c_2E0))
                <=> ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V25x_2E0) != V24c_2E0 ) )
             => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V24c_2E0: tyop_2Eextreal_2Eextreal,V25x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F9_2E0,V0f_2E0),V24c_2E0),V25x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V25x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F14_2E0,V0f_2E0),V25x_2E0),V24c_2E0)) )
               => ( ! [V10c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V12x_2E0: A_27a,V11d_2E0: tyop_2Eextreal_2Eextreal] :
                      ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F13_2E0,V10c_2E0),V0f_2E0),V12x_2E0),V11d_2E0))
                    <=> ( p(c_2Eextreal_2Eextreal__lt_2E2(V10c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V12x_2E0)))
                        & p(c_2Eextreal_2Eextreal__lt_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V12x_2E0),V11d_2E0)) ) )
                 => ( ! [V10c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V11d_2E0: tyop_2Eextreal_2Eextreal,V12x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F4_2E0,V10c_2E0),V0f_2E0),V11d_2E0),V12x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V12x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F13_2E0,V10c_2E0),V0f_2E0),V12x_2E0),V11d_2E0)) )
                   => ( ! [V16c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V18x_2E0: A_27a,V17d_2E0: tyop_2Eextreal_2Eextreal] :
                          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F12_2E0,V16c_2E0),V0f_2E0),V18x_2E0),V17d_2E0))
                        <=> ( p(c_2Eextreal_2Eextreal__lt_2E2(V16c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V18x_2E0)))
                            & p(c_2Eextreal_2Eextreal__le_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V18x_2E0),V17d_2E0)) ) )
                     => ( ! [V16c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V17d_2E0: tyop_2Eextreal_2Eextreal,V18x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F6_2E0,V16c_2E0),V0f_2E0),V17d_2E0),V18x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V18x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F12_2E0,V16c_2E0),V0f_2E0),V18x_2E0),V17d_2E0)) )
                       => ( ! [V13c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V15x_2E0: A_27a,V14d_2E0: tyop_2Eextreal_2Eextreal] :
                              ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F11_2E0,V13c_2E0),V0f_2E0),V15x_2E0),V14d_2E0))
                            <=> ( p(c_2Eextreal_2Eextreal__le_2E2(V13c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V15x_2E0)))
                                & p(c_2Eextreal_2Eextreal__lt_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V15x_2E0),V14d_2E0)) ) )
                         => ( ! [V13c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V14d_2E0: tyop_2Eextreal_2Eextreal,V15x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F5_2E0,V13c_2E0),V0f_2E0),V14d_2E0),V15x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V15x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F11_2E0,V13c_2E0),V0f_2E0),V15x_2E0),V14d_2E0)) )
                           => ( ! [V19c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V21x_2E0: A_27a,V20d_2E0: tyop_2Eextreal_2Eextreal] :
                                  ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F10_2E0,V19c_2E0),V0f_2E0),V21x_2E0),V20d_2E0))
                                <=> ( p(c_2Eextreal_2Eextreal__le_2E2(V19c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V21x_2E0)))
                                    & p(c_2Eextreal_2Eextreal__le_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V21x_2E0),V20d_2E0)) ) )
                             => ( ! [V19c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V20d_2E0: tyop_2Eextreal_2Eextreal,V21x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F7_2E0,V19c_2E0),V0f_2E0),V20d_2E0),V21x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V21x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F10_2E0,V19c_2E0),V0f_2E0),V21x_2E0),V20d_2E0)) )
                               => ( ! [V8c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V9x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F3_2E0,V8c_2E0),V0f_2E0),V9x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V9x_2E0,c_2Eextreal_2Eextreal__lt_2E2(V8c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V9x_2E0))) )
                                 => ( ! [V4c_2E0: tyop_2Eextreal_2Eextreal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V4c_2E0),V0f_2E0),V5x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V5x_2E0,c_2Eextreal_2Eextreal__le_2E2(V4c_2E0,app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V5x_2E0))) )
                                   => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
                                        ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)),c_2Emeasure_2EBorel_2E0)))
                                       => ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2c_2E0)),c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0)),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)))
                                          & ! [V4c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V4c_2E0),V0f_2E0)),c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0)),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)))
                                          & ! [V6c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F2_2E0,V0f_2E0),V6c_2E0)),c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0)),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)))
                                          & ! [V8c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F3_2E0,V8c_2E0),V0f_2E0)),c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0)),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)))
                                          & ! [V10c_2E0: tyop_2Eextreal_2Eextreal,V11d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F4_2E0,V10c_2E0),V0f_2E0),V11d_2E0)),c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0)),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)))
                                          & ! [V13c_2E0: tyop_2Eextreal_2Eextreal,V14d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F5_2E0,V13c_2E0),V0f_2E0),V14d_2E0)),c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0)),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)))
                                          & ! [V16c_2E0: tyop_2Eextreal_2Eextreal,V17d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F6_2E0,V16c_2E0),V0f_2E0),V17d_2E0)),c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0)),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)))
                                          & ! [V19c_2E0: tyop_2Eextreal_2Eextreal,V20d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F7_2E0,V19c_2E0),V0f_2E0),V20d_2E0)),c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0)),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)))
                                          & ! [V22c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F8_2E0,V0f_2E0),V22c_2E0)),c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0)),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0)))
                                          & ! [V24c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F9_2E0,V0f_2E0),V24c_2E0)),c_2Emeasure_2Em__space_2E1(A_27a,V1m_2E0)),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V1m_2E0))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__LT,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1g_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,c_2Eextreal_2Eextreal__lt_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1g_2E0,V3x_2E0))) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2a_2E0,c_2Emeasure_2EBorel_2E0)))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1g_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2a_2E0,c_2Emeasure_2EBorel_2E0))) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1g_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V2a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V2a_2E0))) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__LE,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1g_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,c_2Eextreal_2Eextreal__le_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1g_2E0,V3x_2E0))) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2a_2E0,c_2Emeasure_2EBorel_2E0)))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1g_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2a_2E0,c_2Emeasure_2EBorel_2E0))) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1g_2E0)),c_2Emeasure_2Espace_2E1(A_27a,V2a_2E0)),c_2Emeasure_2Esubsets_2E1(A_27a,V2a_2E0))) ) ) ).

tff(thm_2Emeasure_2ESPACE__BOREL,axiom,
    c_2Emeasure_2Espace_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0) = c_2Epred__set_2EUNIV_2E0(tyop_2Eextreal_2Eextreal) ).

tff(thm_2Emeasure_2EBOREL__MEASURABLE__SETS1,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))] :
      ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V0c_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V1x_2E0,c_2Eextreal_2Eextreal__lt_2E2(V1x_2E0,V0c_2E0)) )
     => ! [V0c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V0c_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EBOREL__MEASURABLE__SETS2,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))] :
      ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V0c_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V1x_2E0,c_2Eextreal_2Eextreal__le_2E2(V0c_2E0,V1x_2E0)) )
     => ! [V0c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V0c_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EBOREL__MEASURABLE__SETS3,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))] :
      ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V0c_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V1x_2E0,c_2Eextreal_2Eextreal__le_2E2(V1x_2E0,V0c_2E0)) )
     => ! [V0c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V0c_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EBOREL__MEASURABLE__SETS4,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))] :
      ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V0c_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V1x_2E0,c_2Eextreal_2Eextreal__lt_2E2(V0c_2E0,V1x_2E0)) )
     => ! [V0c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V0c_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EBOREL__MEASURABLE__SETS5,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))))] :
      ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V2x_2E0: tyop_2Eextreal_2Eextreal,V1d_2E0: tyop_2Eextreal_2Eextreal] :
          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0c_2E0),V2x_2E0),V1d_2E0))
        <=> ( p(c_2Eextreal_2Eextreal__le_2E2(V0c_2E0,V2x_2E0))
            & p(c_2Eextreal_2Eextreal__lt_2E2(V2x_2E0,V1d_2E0)) ) )
     => ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1d_2E0: tyop_2Eextreal_2Eextreal,V2x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0,V0c_2E0),V1d_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0c_2E0),V2x_2E0),V1d_2E0)) )
       => ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0,V0c_2E0),V1d_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0))) ) ) ).

tff(thm_2Emeasure_2EBOREL__MEASURABLE__SETS6,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))))] :
      ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V2x_2E0: tyop_2Eextreal_2Eextreal,V1d_2E0: tyop_2Eextreal_2Eextreal] :
          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0c_2E0),V2x_2E0),V1d_2E0))
        <=> ( p(c_2Eextreal_2Eextreal__lt_2E2(V0c_2E0,V2x_2E0))
            & p(c_2Eextreal_2Eextreal__le_2E2(V2x_2E0,V1d_2E0)) ) )
     => ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1d_2E0: tyop_2Eextreal_2Eextreal,V2x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0,V0c_2E0),V1d_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0c_2E0),V2x_2E0),V1d_2E0)) )
       => ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0,V0c_2E0),V1d_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0))) ) ) ).

tff(thm_2Emeasure_2EBOREL__MEASURABLE__SETS7,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))))] :
      ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V2x_2E0: tyop_2Eextreal_2Eextreal,V1d_2E0: tyop_2Eextreal_2Eextreal] :
          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0c_2E0),V2x_2E0),V1d_2E0))
        <=> ( p(c_2Eextreal_2Eextreal__le_2E2(V0c_2E0,V2x_2E0))
            & p(c_2Eextreal_2Eextreal__le_2E2(V2x_2E0,V1d_2E0)) ) )
     => ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1d_2E0: tyop_2Eextreal_2Eextreal,V2x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0,V0c_2E0),V1d_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0c_2E0),V2x_2E0),V1d_2E0)) )
       => ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0,V0c_2E0),V1d_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0))) ) ) ).

tff(thm_2Emeasure_2EBOREL__MEASURABLE__SETS8,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))))] :
      ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V2x_2E0: tyop_2Eextreal_2Eextreal,V1d_2E0: tyop_2Eextreal_2Eextreal] :
          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0c_2E0),V2x_2E0),V1d_2E0))
        <=> ( p(c_2Eextreal_2Eextreal__lt_2E2(V0c_2E0,V2x_2E0))
            & p(c_2Eextreal_2Eextreal__lt_2E2(V2x_2E0,V1d_2E0)) ) )
     => ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1d_2E0: tyop_2Eextreal_2Eextreal,V2x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0,V0c_2E0),V1d_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V0c_2E0),V2x_2E0),V1d_2E0)) )
       => ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0,V0c_2E0),V1d_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0))) ) ) ).

tff(thm_2Emeasure_2EBOREL__MEASURABLE__SETS9,axiom,
    ! [V0c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(tyop_2Eextreal_2Eextreal,V0c_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Eextreal_2Eextreal)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0))) ).

tff(thm_2Emeasure_2EBOREL__MEASURABLE__SETS10,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))] :
      ( ! [V1x_2E0: tyop_2Eextreal_2Eextreal,V0c_2E0: tyop_2Eextreal_2Eextreal] :
          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),F1_2E0,V1x_2E0),V0c_2E0))
        <=> ( V1x_2E0 != V0c_2E0 ) )
     => ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V0c_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V1x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),F1_2E0,V1x_2E0),V0c_2E0)) )
       => ! [V0c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V0c_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0))) ) ) ).

tff(thm_2Emeasure_2EBOREL__MEASURABLE__SETS,axiom,
    ! [F2_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F3_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F13_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F8_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F12_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F4_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F11_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F6_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F10_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F5_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F9_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F7_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))))] :
      ( ! [V4c_2E0: tyop_2Eextreal_2Eextreal,V5x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F2_2E0,V4c_2E0),V5x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V5x_2E0,c_2Eextreal_2Eextreal__lt_2E2(V4c_2E0,V5x_2E0)) )
     => ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal,V1x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V0c_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V1x_2E0,c_2Eextreal_2Eextreal__lt_2E2(V1x_2E0,V0c_2E0)) )
       => ( ! [V2c_2E0: tyop_2Eextreal_2Eextreal,V3x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V2c_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V3x_2E0,c_2Eextreal_2Eextreal__le_2E2(V2c_2E0,V3x_2E0)) )
         => ( ! [V6c_2E0: tyop_2Eextreal_2Eextreal,V7x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F3_2E0,V6c_2E0),V7x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V7x_2E0,c_2Eextreal_2Eextreal__le_2E2(V7x_2E0,V6c_2E0)) )
           => ( ! [V22x_2E0: tyop_2Eextreal_2Eextreal,V21c_2E0: tyop_2Eextreal_2Eextreal] :
                  ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),F13_2E0,V22x_2E0),V21c_2E0))
                <=> ( V22x_2E0 != V21c_2E0 ) )
             => ( ! [V21c_2E0: tyop_2Eextreal_2Eextreal,V22x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F8_2E0,V21c_2E0),V22x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V22x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),F13_2E0,V22x_2E0),V21c_2E0)) )
               => ( ! [V8c_2E0: tyop_2Eextreal_2Eextreal,V10x_2E0: tyop_2Eextreal_2Eextreal,V9d_2E0: tyop_2Eextreal_2Eextreal] :
                      ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F12_2E0,V8c_2E0),V10x_2E0),V9d_2E0))
                    <=> ( p(c_2Eextreal_2Eextreal__lt_2E2(V8c_2E0,V10x_2E0))
                        & p(c_2Eextreal_2Eextreal__lt_2E2(V10x_2E0,V9d_2E0)) ) )
                 => ( ! [V8c_2E0: tyop_2Eextreal_2Eextreal,V9d_2E0: tyop_2Eextreal_2Eextreal,V10x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F4_2E0,V8c_2E0),V9d_2E0),V10x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V10x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F12_2E0,V8c_2E0),V10x_2E0),V9d_2E0)) )
                   => ( ! [V14c_2E0: tyop_2Eextreal_2Eextreal,V16x_2E0: tyop_2Eextreal_2Eextreal,V15d_2E0: tyop_2Eextreal_2Eextreal] :
                          ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F11_2E0,V14c_2E0),V16x_2E0),V15d_2E0))
                        <=> ( p(c_2Eextreal_2Eextreal__lt_2E2(V14c_2E0,V16x_2E0))
                            & p(c_2Eextreal_2Eextreal__le_2E2(V16x_2E0,V15d_2E0)) ) )
                     => ( ! [V14c_2E0: tyop_2Eextreal_2Eextreal,V15d_2E0: tyop_2Eextreal_2Eextreal,V16x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F6_2E0,V14c_2E0),V15d_2E0),V16x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V16x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F11_2E0,V14c_2E0),V16x_2E0),V15d_2E0)) )
                       => ( ! [V11c_2E0: tyop_2Eextreal_2Eextreal,V13x_2E0: tyop_2Eextreal_2Eextreal,V12d_2E0: tyop_2Eextreal_2Eextreal] :
                              ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F10_2E0,V11c_2E0),V13x_2E0),V12d_2E0))
                            <=> ( p(c_2Eextreal_2Eextreal__le_2E2(V11c_2E0,V13x_2E0))
                                & p(c_2Eextreal_2Eextreal__lt_2E2(V13x_2E0,V12d_2E0)) ) )
                         => ( ! [V11c_2E0: tyop_2Eextreal_2Eextreal,V12d_2E0: tyop_2Eextreal_2Eextreal,V13x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F5_2E0,V11c_2E0),V12d_2E0),V13x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V13x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F10_2E0,V11c_2E0),V13x_2E0),V12d_2E0)) )
                           => ( ! [V17c_2E0: tyop_2Eextreal_2Eextreal,V19x_2E0: tyop_2Eextreal_2Eextreal,V18d_2E0: tyop_2Eextreal_2Eextreal] :
                                  ( p(app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F9_2E0,V17c_2E0),V19x_2E0),V18d_2E0))
                                <=> ( p(c_2Eextreal_2Eextreal__le_2E2(V17c_2E0,V19x_2E0))
                                    & p(c_2Eextreal_2Eextreal__le_2E2(V19x_2E0,V18d_2E0)) ) )
                             => ( ! [V17c_2E0: tyop_2Eextreal_2Eextreal,V18d_2E0: tyop_2Eextreal_2Eextreal,V19x_2E0: tyop_2Eextreal_2Eextreal] : ( app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F7_2E0,V17c_2E0),V18d_2E0),V19x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,V19x_2E0,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F9_2E0,V17c_2E0),V19x_2E0),V18d_2E0)) )
                               => ( ! [V0c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F0_2E0,V0c_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0)))
                                  & ! [V2c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F1_2E0,V2c_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0)))
                                  & ! [V4c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F2_2E0,V4c_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0)))
                                  & ! [V6c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F3_2E0,V6c_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0)))
                                  & ! [V8c_2E0: tyop_2Eextreal_2Eextreal,V9d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F4_2E0,V8c_2E0),V9d_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0)))
                                  & ! [V11c_2E0: tyop_2Eextreal_2Eextreal,V12d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F5_2E0,V11c_2E0),V12d_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0)))
                                  & ! [V14c_2E0: tyop_2Eextreal_2Eextreal,V15d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F6_2E0,V14c_2E0),V15d_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0)))
                                  & ! [V17c_2E0: tyop_2Eextreal_2Eextreal,V18d_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),F7_2E0,V17c_2E0),V18d_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0)))
                                  & ! [V20c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(tyop_2Eextreal_2Eextreal,V20c_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Eextreal_2Eextreal)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0)))
                                  & ! [V21c_2E0: tyop_2Eextreal_2Eextreal] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),F8_2E0,V21c_2E0)),c_2Emeasure_2Esubsets_2E1(tyop_2Eextreal_2Eextreal,c_2Emeasure_2EBorel_2E0))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__CONST,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1k_2E0: tyop_2Eextreal_2Eextreal,V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & ! [V3x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)))
           => ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2f_2E0,V3x_2E0) = V1k_2E0 ) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__INDICATOR,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0)))
        & ! [V3x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)))
           => ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2f_2E0,V3x_2E0) = c_2Emeasure_2Eindicator__fn_2E2(A_27a,V1A_2E0,V3x_2E0) ) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__CMUL,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3z_2E0: tyop_2Erealax_2Ereal] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
        & ! [V4x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)))
           => ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2g_2E0,V4x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(c_2Eextreal_2ENormal_2E1(V3z_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V4x_2E0)) ) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ABS,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
        & ! [V3x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)))
           => ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2g_2E0,V3x_2E0) = c_2Eextreal_2Eextreal__abs_2E1(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V3x_2E0)) ) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__SQR,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
        & ! [V3x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)))
           => ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2g_2E0,V3x_2E0) = c_2Eextreal_2Eextreal__pow_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V3x_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__ADD,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3h_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
        & ! [V4x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)))
           => ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V3h_2E0,V4x_2E0) = c_2Eextreal_2Eextreal__add_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V4x_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2g_2E0,V4x_2E0)) ) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3h_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__SUB,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3h_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
        & ! [V4x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)))
           => ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V3h_2E0,V4x_2E0) = c_2Eextreal_2Eextreal__sub_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V4x_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2g_2E0,V4x_2E0)) ) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3h_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__MUL,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3h_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
        & ! [V4x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)))
           => ( ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V4x_2E0) != c_2Eextreal_2ENegInf_2E0 )
              & ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V4x_2E0) != c_2Eextreal_2EPosInf_2E0 )
              & ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2g_2E0,V4x_2E0) != c_2Eextreal_2ENegInf_2E0 )
              & ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2g_2E0,V4x_2E0) != c_2Eextreal_2EPosInf_2E0 ) ) )
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
        & ! [V5x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)))
           => ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V3h_2E0,V5x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V5x_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2g_2E0,V5x_2E0)) ) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3h_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__SUM,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal)))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V5x_2E0: A_27a,V6i_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Eextreal_2Eextreal,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal)),F0_2E0,V1f_2E0),V5x_2E0),V6i_2E0) = app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,V6i_2E0),V5x_2E0) )
     => ! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( ( p(c_2Epred__set_2EFINITE_2E1(A_27b,V3s_2E0))
            & p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
            & ! [V4i_2E0: A_27b] :
                ( p(c_2Ebool_2EIN_2E2(A_27b,V4i_2E0,V3s_2E0))
               => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,V4i_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) )
            & ! [V5x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0)))
               => ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2g_2E0,V5x_2E0) = c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2(A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal)),F0_2E0,V1f_2E0),V5x_2E0),V3s_2E0) ) ) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__CMUL__INDICATOR,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)))] :
      ( ! [V1z_2E0: tyop_2Erealax_2Ereal,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V1z_2E0),V2s_2E0),V3x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(c_2Eextreal_2ENormal_2E1(V1z_2E0),c_2Emeasure_2Eindicator__fn_2E2(A_27a,V2s_2E0,V3x_2E0)) )
     => ! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1z_2E0: tyop_2Erealax_2Ereal,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V1z_2E0),V2s_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__MUL__INDICATOR,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V1f_2E0),V2s_2E0),V3x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V3x_2E0),c_2Emeasure_2Eindicator__fn_2E2(A_27a,V2s_2E0,V3x_2E0)) )
     => ! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,c_2Emeasure_2Esubsets_2E1(A_27a,V0a_2E0))) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V1f_2E0),V2s_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__MUL__INDICATOR__EQ,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V1f_2E0),V0a_2E0),V2x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V2x_2E0),c_2Emeasure_2Eindicator__fn_2E2(A_27a,c_2Emeasure_2Espace_2E1(A_27a,V0a_2E0),V2x_2E0)) )
     => ! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
          ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
         => ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)) = c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V1f_2E0),V0a_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)) ) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__POS__SIMPLE__FN,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V0m_2E0))
        & ? [V2s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4x_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)] : p(c_2Emeasure_2Epos__simple__fn_2E5(A_27a,V0m_2E0,V1f_2E0,V2s_2E0,V3a_2E0,V4x_2E0)) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(A_27a,V0m_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V0m_2E0)),c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__POW,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)))] :
      ( ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0n_2E0: tyop_2Enum_2Enum,V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V2f_2E0),V0n_2E0),V4x_2E0) = c_2Eextreal_2Eextreal__pow_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2f_2E0,V4x_2E0),V0n_2E0) )
     => ! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
          ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V1a_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0)))
            & ! [V3x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V1a_2E0)))
               => ( ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2f_2E0,V3x_2E0) != c_2Eextreal_2ENegInf_2E0 )
                  & ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2f_2E0,V3x_2E0) != c_2Eextreal_2EPosInf_2E0 ) ) ) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V2f_2E0),V0n_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1a_2E0,c_2Emeasure_2EBorel_2E0))) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__MAX,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V1f_2E0),V2g_2E0),V3x_2E0) = c_2Eextreal_2Eextreal__max_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2g_2E0,V3x_2E0)) )
     => ! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
          ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V0a_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2g_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V1f_2E0),V2g_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__MONO__SUP,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)))] :
      ( ! [V0fn_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V6x_2E0: A_27a,V7n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)),F0_2E0,V0fn_2E0),V6x_2E0),V7n_2E0) = app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0fn_2E0,V7n_2E0),V6x_2E0) )
     => ! [V0fn_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
          ( ( p(c_2Emeasure_2Esigma__algebra_2E1(A_27a,V2a_2E0))
            & ! [V3n_2E0: tyop_2Enum_2Enum] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0fn_2E0,V3n_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2a_2E0,c_2Emeasure_2EBorel_2E0)))
            & ! [V4n_2E0: tyop_2Enum_2Enum,V5x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V2a_2E0)))
               => p(c_2Eextreal_2Eextreal__le_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0fn_2E0,V4n_2E0),V5x_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V0fn_2E0,c_2Enum_2ESUC_2E1(V4n_2E0)),V5x_2E0))) )
            & ! [V6x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,c_2Emeasure_2Espace_2E1(A_27a,V2a_2E0)))
               => ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1f_2E0,V6x_2E0) = c_2Eextreal_2Eextreal__sup_2E1(c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)),F0_2E0,V0fn_2E0),V6x_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ) ) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V2a_2E0,c_2Emeasure_2EBorel_2E0))) ) ) ).

tff(thm_2Emeasure_2EFN__PLUS__POS,axiom,
    ! [A_27a: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1x_2E0: A_27a] : p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__of__num_2E1(c_2Enum_2E0_2E0),c_2Emeasure_2Efn__plus_2E2(A_27a,V0g_2E0,V1x_2E0))) ).

tff(thm_2Emeasure_2EFN__MINUS__POS,axiom,
    ! [A_27a: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1x_2E0: A_27a] : p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__of__num_2E1(c_2Enum_2E0_2E0),c_2Emeasure_2Efn__minus_2E2(A_27a,V0g_2E0,V1x_2E0))) ).

tff(thm_2Emeasure_2EFN__PLUS__POS__ID,axiom,
    ! [A_27a: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( ! [V1x_2E0: A_27a] : p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__of__num_2E1(c_2Enum_2E0_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0g_2E0,V1x_2E0)))
     => ( c_2Emeasure_2Efn__plus_2E1(A_27a,V0g_2E0) = V0g_2E0 ) ) ).

tff(thm_2Emeasure_2EFN__MINUS__POS__ZERO,axiom,
    ! [A_27a: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( ! [V1x_2E0: A_27a] : p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__of__num_2E1(c_2Enum_2E0_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0g_2E0,V1x_2E0)))
     => ! [V2x_2E0: A_27a] : ( c_2Emeasure_2Efn__minus_2E2(A_27a,V0g_2E0,V2x_2E0) = c_2Eextreal_2Eextreal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).

tff(thm_2Emeasure_2EFN__PLUS__CMUL,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal))),F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)))] :
      ( ! [V1c_2E0: tyop_2Erealax_2Ereal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F1_2E0,V1c_2E0),V0f_2E0),V5x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(c_2Eextreal_2ENormal_2E1(V1c_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V5x_2E0)) )
     => ( ! [V1c_2E0: tyop_2Erealax_2Ereal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V1c_2E0),V0f_2E0),V3x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(c_2Eextreal_2ENormal_2E1(V1c_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1c_2E0: tyop_2Erealax_2Ereal] :
            ( ( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),V1c_2E0))
             => ! [V2x_2E0: A_27a] : ( c_2Emeasure_2Efn__plus_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V1c_2E0),V0f_2E0),V2x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(c_2Eextreal_2ENormal_2E1(V1c_2E0),c_2Emeasure_2Efn__plus_2E2(A_27a,V0f_2E0,V2x_2E0)) ) )
            & ( p(c_2Ereal_2Ereal__lte_2E2(V1c_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)))
             => ! [V4x_2E0: A_27a] : ( c_2Emeasure_2Efn__plus_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F1_2E0,V1c_2E0),V0f_2E0),V4x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(c_2Eextreal_2Eextreal__ainv_2E1(c_2Eextreal_2ENormal_2E1(V1c_2E0)),c_2Emeasure_2Efn__minus_2E2(A_27a,V0f_2E0,V4x_2E0)) ) ) ) ) ) ).

tff(thm_2Emeasure_2EFN__MINUS__CMUL,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal))),F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)))] :
      ( ! [V1c_2E0: tyop_2Erealax_2Ereal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F1_2E0,V1c_2E0),V0f_2E0),V5x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(c_2Eextreal_2ENormal_2E1(V1c_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V5x_2E0)) )
     => ( ! [V1c_2E0: tyop_2Erealax_2Ereal,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V1c_2E0),V0f_2E0),V3x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(c_2Eextreal_2ENormal_2E1(V1c_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1c_2E0: tyop_2Erealax_2Ereal] :
            ( ( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),V1c_2E0))
             => ! [V2x_2E0: A_27a] : ( c_2Emeasure_2Efn__minus_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V1c_2E0),V0f_2E0),V2x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(c_2Eextreal_2ENormal_2E1(V1c_2E0),c_2Emeasure_2Efn__minus_2E2(A_27a,V0f_2E0,V2x_2E0)) ) )
            & ( p(c_2Ereal_2Ereal__lte_2E2(V1c_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)))
             => ! [V4x_2E0: A_27a] : ( c_2Emeasure_2Efn__minus_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F1_2E0,V1c_2E0),V0f_2E0),V4x_2E0) = c_2Eextreal_2Eextreal__mul_2E2(c_2Eextreal_2Eextreal__ainv_2E1(c_2Eextreal_2ENormal_2E1(V1c_2E0)),c_2Emeasure_2Efn__plus_2E2(A_27a,V0f_2E0,V4x_2E0)) ) ) ) ) ) ).

tff(thm_2Emeasure_2EFN__PLUS__ADD__LE,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V0f_2E0),V1g_2E0),V3x_2E0) = c_2Eextreal_2Eextreal__add_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1g_2E0,V3x_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2x_2E0: A_27a] : p(c_2Eextreal_2Eextreal__le_2E2(c_2Emeasure_2Efn__plus_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V0f_2E0),V1g_2E0),V2x_2E0),c_2Eextreal_2Eextreal__add_2E2(c_2Emeasure_2Efn__plus_2E2(A_27a,V0f_2E0,V2x_2E0),c_2Emeasure_2Efn__plus_2E2(A_27a,V1g_2E0,V2x_2E0)))) ) ).

tff(thm_2Emeasure_2EFN__MINUS__ADD__LE,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eextreal_2Eextreal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V0f_2E0),V1g_2E0),V3x_2E0) = c_2Eextreal_2Eextreal__add_2E2(app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Eextreal_2Eextreal,V1g_2E0,V3x_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2x_2E0: A_27a] : p(c_2Eextreal_2Eextreal__le_2E2(c_2Emeasure_2Efn__minus_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),F0_2E0,V0f_2E0),V1g_2E0),V2x_2E0),c_2Eextreal_2Eextreal__add_2E2(c_2Emeasure_2Efn__minus_2E2(A_27a,V0f_2E0,V2x_2E0),c_2Emeasure_2Efn__minus_2E2(A_27a,V1g_2E0,V2x_2E0)))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__FN__PLUS,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Emeasure_2Efn__plus_2E1(A_27a,V1f_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__FN__MINUS,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
     => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Emeasure_2Efn__minus_2E1(A_27a,V1f_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ).

tff(thm_2Emeasure_2EIN__MEASURABLE__BOREL__PLUS__MINUS,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0,c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Emeasure_2Efn__plus_2E1(A_27a,V1f_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Emeasure_2Efn__minus_2E1(A_27a,V1f_2E0),c_2Emeasure_2Emeasurable_2E2(A_27a,tyop_2Eextreal_2Eextreal,V0a_2E0,c_2Emeasure_2EBorel_2E0))) ) ) ).

tff(thm_2Emeasure_2EINDICATOR__FN__MUL__INTER,axiom,
    ! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( c_2Eextreal_2Eextreal__mul_2E2(c_2Emeasure_2Eindicator__fn_2E2(A_27a,V0A_2E0,V2x_2E0),c_2Emeasure_2Eindicator__fn_2E2(A_27a,V1B_2E0,V2x_2E0)) = c_2Emeasure_2Eindicator__fn_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0A_2E0,V1B_2E0),V2x_2E0) ) ).

tff(thm_2Emeasure_2Eindicator__fn__split,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal))))] :
      ( ! [V5a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V6x_2E0: A_27a,V7i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal))),F0_2E0,V5a_2E0),V2b_2E0),V6x_2E0),V7i_2E0) = c_2Emeasure_2Eindicator__fn_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V5a_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2b_2E0,V7i_2E0)),V6x_2E0) )
     => ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
          ( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0r_2E0))
            & ( c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2b_2E0,V0r_2E0)) = V1s_2E0 )
            & ! [V3i_2E0: tyop_2Enum_2Enum,V4j_2E0: tyop_2Enum_2Enum] :
                ( ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V3i_2E0,V0r_2E0))
                  & p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V4j_2E0,V0r_2E0))
                  & ( V3i_2E0 != V4j_2E0 ) )
               => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2b_2E0,V3i_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2b_2E0,V4j_2E0))) ) )
         => ! [V5a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V5a_2E0,V1s_2E0))
             => ! [V6x_2E0: A_27a] : ( c_2Emeasure_2Eindicator__fn_2E2(A_27a,V5a_2E0,V6x_2E0) = c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2(tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal))),F0_2E0,V5a_2E0),V2b_2E0),V6x_2E0),V0r_2E0) ) ) ) ) ).

tff(thm_2Emeasure_2Eindicator__fn__suminf,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)))] :
      ( ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V4i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)),F0_2E0,V0a_2E0),V1x_2E0),V4i_2E0) = c_2Emeasure_2Eindicator__fn_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0,V4i_2E0),V1x_2E0) )
     => ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a] :
          ( ! [V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
              ( ( V2m_2E0 != V3n_2E0 )
             => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0,V2m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0,V3n_2E0))) )
         => ( c_2Eextreal_2Eext__suminf_2E1(app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)),F0_2E0,V0a_2E0),V1x_2E0)) = c_2Emeasure_2Eindicator__fn_2E2(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),V1x_2E0) ) ) ) ).

tff(thm_2Emeasure_2Emeasure__split,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))))] :
      ( ! [V2m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V6a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V7i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),F0_2E0,V2m_2E0),V6a_2E0),V1b_2E0),V7i_2E0) = c_2Emeasure_2Emeasure_2E2(A_27a,V2m_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V6a_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0,V7i_2E0))) )
     => ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2m_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal)))] :
          ( ( p(c_2Emeasure_2Emeasure__space_2E1(A_27a,V2m_2E0))
            & p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0r_2E0))
            & ( c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0,V0r_2E0)) = c_2Emeasure_2Em__space_2E1(A_27a,V2m_2E0) )
            & ! [V3i_2E0: tyop_2Enum_2Enum,V4j_2E0: tyop_2Enum_2Enum] :
                ( ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V3i_2E0,V0r_2E0))
                  & p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V4j_2E0,V0r_2E0))
                  & ( V3i_2E0 != V4j_2E0 ) )
               => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0,V3i_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0,V4j_2E0))) )
            & ! [V5i_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V5i_2E0,V0r_2E0))
               => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0,V5i_2E0),c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V2m_2E0))) ) )
         => ! [V6a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6a_2E0,c_2Emeasure_2Emeasurable__sets_2E1(A_27a,V2m_2E0)))
             => ( c_2Emeasure_2Emeasure_2E2(A_27a,V2m_2E0,V6a_2E0) = c_2Ereal__sigma_2EREAL__SUM__IMAGE_2E2(tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),F0_2E0,V2m_2E0),V6a_2E0),V1b_2E0),V0r_2E0) ) ) ) ) ).

%------------------------------------------------------------------------------