%------------------------------------------------------------------------------
% File     : ITP024_3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Problem  : HOL4 syntactic export of thm_2Ereal__topology_2ECLOSED__UNION__COMPACT__SUBSETS.p, bushy 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    : thm_2Ereal__topology_2ECLOSED__UNION__COMPACT__SUBSETS.p [Gau19]
%          : HL411501_3.p [TPAP]

% Status   : Theorem
% Rating   : 1.00 v7.5.0
% Syntax   : Number of formulae    :  286 ( 106 unt; 107 typ;   0 def)
%            Number of atoms       :  487 ( 204 equ)
%            Maximal formula atoms :   40 (   1 avg)
%            Number of connectives :  359 (  51   ~;  37   |; 126   &)
%                                         (  80 <=>;  65  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   37 (   5 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   74 (  50   >;  24   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  103 ( 103 usr;  40 con; 0-4 aty)
%            Number of variables   :  569 ( 510   !;  22   ?; 569   :)
%                                         (  37  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_THM_EQU_NAR

% Comments : 
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
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_2Earithmetic_2E_2A_2E0,type,
    c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2A_2E2,type,
    c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

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_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2D_2E2,type,
    c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

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_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Earithmetic_2E_3C_3D_2E2,type,
    c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

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_2Earithmetic_2E_3E_2E0,type,
    c_2Earithmetic_2E_3E_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Earithmetic_2E_3E_2E2,type,
    c_2Earithmetic_2E_3E_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2E_3E_3D_2E0,type,
    c_2Earithmetic_2E_3E_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Earithmetic_2E_3E_3D_2E2,type,
    c_2Earithmetic_2E_3E_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > 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_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_2Ereal__topology_2EClosed_2E0,type,
    c_2Ereal__topology_2EClosed_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ereal__topology_2EClosed_2E1,type,
    c_2Ereal__topology_2EClosed_2E1: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ).

tff(c_2Ereal__topology_2EDist_2E0,type,
    c_2Ereal__topology_2EDist_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal) ).

tff(c_2Ereal__topology_2EDist_2E1,type,
    c_2Ereal__topology_2EDist_2E1: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) > tyop_2Erealax_2Ereal ).

tff(c_2Earithmetic_2EEVEN_2E0,type,
    c_2Earithmetic_2EEVEN_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2Earithmetic_2EEVEN_2E1,type,
    c_2Earithmetic_2EEVEN_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2EEXP_2E0,type,
    c_2Earithmetic_2EEXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2EEXP_2E2,type,
    c_2Earithmetic_2EEXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: 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_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_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_2Earithmetic_2EODD_2E0,type,
    c_2Earithmetic_2EODD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2Earithmetic_2EODD_2E1,type,
    c_2Earithmetic_2EODD_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).

tff(c_2Eprim__rec_2EPRE_2E0,type,
    c_2Eprim__rec_2EPRE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Eprim__rec_2EPRE_2E1,type,
    c_2Eprim__rec_2EPRE_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

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_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_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_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).

tff(c_2Epair_2EUNCURRY_2E1,type,
    c_2Epair_2EUNCURRY_2E1: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) ) ).

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_2Ereal_2Eabs_2E0,type,
    c_2Ereal_2Eabs_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).

tff(c_2Ereal_2Eabs_2E1,type,
    c_2Ereal_2Eabs_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).

tff(c_2Ereal__topology_2Eball_2E0,type,
    c_2Ereal__topology_2Eball_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).

tff(c_2Ereal__topology_2Eball_2E1,type,
    c_2Ereal__topology_2Eball_2E1: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) > tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool) ).

tff(c_2Ereal__topology_2Ebounded__def_2E0,type,
    c_2Ereal__topology_2Ebounded__def_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ereal__topology_2Ebounded__def_2E1,type,
    c_2Ereal__topology_2Ebounded__def_2E1: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ).

tff(c_2Ereal__topology_2Ecball_2E0,type,
    c_2Ereal__topology_2Ecball_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).

tff(c_2Ereal__topology_2Ecball_2E1,type,
    c_2Ereal__topology_2Ecball_2E1: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) > tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool) ).

tff(c_2Ereal__topology_2Ecompact_2E0,type,
    c_2Ereal__topology_2Ecompact_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ereal__topology_2Ecompact_2E1,type,
    c_2Ereal__topology_2Ecompact_2E1: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ).

tff(c_2Enumeral_2EiDUB_2E0,type,
    c_2Enumeral_2EiDUB_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Enumeral_2EiDUB_2E1,type,
    c_2Enumeral_2EiDUB_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Enumeral_2EiZ_2E0,type,
    c_2Enumeral_2EiZ_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Enumeral_2EiZ_2E1,type,
    c_2Enumeral_2EiZ_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Enumeral_2EiiSUC_2E0,type,
    c_2Enumeral_2EiiSUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Enumeral_2EiiSUC_2E1,type,
    c_2Enumeral_2EiiSUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

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_2Ereal_2Ereal__ge_2E0,type,
    c_2Ereal_2Ereal__ge_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).

tff(c_2Ereal_2Ereal__ge_2E2,type,
    c_2Ereal_2Ereal__ge_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).

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_2Erealax_2Ereal__neg_2E0,type,
    c_2Erealax_2Ereal__neg_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).

tff(c_2Erealax_2Ereal__neg_2E1,type,
    c_2Erealax_2Ereal__neg_2E1: 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_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_2Earithmetic_2E_2A_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : c_2Epair_2E_2C_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2E_2C_2E0(A_27a,A_27b),X0_2E0),X1_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_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27b,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27e_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27e: $tType,X0_2E0: A_27e,X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(A_27e,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27e,tyop_2Emin_2Ebool),app_2E2(A_27e,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27e,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27e,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27i_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27i: $tType,X0_2E0: A_27i,X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(A_27i,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27i,tyop_2Emin_2Ebool),app_2E2(A_27i,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27i,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27i,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_2Emin_2Ebool,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(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_2Ebool,tyop_2Epair_2Eprod(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_2Ebool),X0_2E0),X1_2E0) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27e_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27i_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27i: $tType,X0_2E0: tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E0(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),X1_2E0) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_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_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_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(arityeq2_2Ec_2Earithmetic_2E_3E_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_2E0,X0_2E0),X1_2E0) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_3D_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_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_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27e,axiom,
    ! [A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : c_2Epred__set_2EBIGUNION_2E1(A_27e,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27e),X0_2E0) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27i,axiom,
    ! [A_27i: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : c_2Epred__set_2EBIGUNION_2E1(A_27i,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27i),X0_2E0) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : c_2Epred__set_2EBIGUNION_2E1(tyop_2Erealax_2Ereal,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(tyop_2Erealax_2Ereal),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(arityeq1_2Ec_2Ereal__topology_2EClosed_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] : c_2Ereal__topology_2EClosed_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ereal__topology_2EClosed_2E0,X0_2E0) ).

tff(arityeq1_2Ec_2Ereal__topology_2EDist_2E1,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] : c_2Ereal__topology_2EDist_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal,c_2Ereal__topology_2EDist_2E0,X0_2E0) ).

tff(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEVEN_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E0,X0_2E0) ).

tff(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP_2E0,X0_2E0),X1_2E0) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a),X0_2E0) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27a,A_27b),X0_2E0) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27b,A_27b),X0_2E0) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27e_20mono_2EA_27e,axiom,
    ! [A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27e,tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(A_27e,A_27e,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27e,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27e,A_27e),X0_2E0) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27i_20mono_2EA_27i,axiom,
    ! [A_27i: $tType,X0_2E0: tyop_2Emin_2Efun(A_27i,tyop_2Epair_2Eprod(A_27i,tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(A_27i,A_27i,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27i,tyop_2Epair_2Eprod(A_27i,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27i,A_27i),X0_2E0) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),X0_2E0) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27e_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27d_29,axiom,
    ! [A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(A_27c,A_27d)),X0_2E0) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27i_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28A_27f_2Ctyop_2Epair_2Eprod_28A_27g_2CA_27h_29_29,axiom,
    ! [A_27f: $tType,A_27g: $tType,A_27h: $tType,A_27i: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27f,tyop_2Epair_2Eprod(A_27g,A_27h)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(A_27f,tyop_2Epair_2Eprod(A_27g,A_27h)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27f,tyop_2Epair_2Eprod(A_27g,A_27h)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(A_27f,tyop_2Epair_2Eprod(A_27g,A_27h))),X0_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_2EA_27e,axiom,
    ! [A_27e: $tType,X0_2E0: A_27e,X1_2E0: tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool)] : c_2Ebool_2EIN_2E2(A_27e,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27e,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27e),X0_2E0),X1_2E0) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27i,axiom,
    ! [A_27i: $tType,X0_2E0: A_27i,X1_2E0: tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)] : c_2Ebool_2EIN_2E2(A_27i,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27i,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27i),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_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_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] : c_2Epred__set_2EINTER_2E2(tyop_2Erealax_2Ereal,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Epred__set_2EINTER_2E0(tyop_2Erealax_2Ereal),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_2Earithmetic_2EODD_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EODD_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E0,X0_2E0) ).

tff(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2EPRE_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E0,X0_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_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] : c_2Epred__set_2ESUBSET_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_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Erealax_2Ereal),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(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27c_20mono_2EA_27d_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27e_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] : c_2Epair_2EUNCURRY_2E1(A_27c,A_27d,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27c,A_27d,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27f_20mono_2Etyop_2Epair_2Eprod_28A_27g_2CA_27h_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27i_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27f: $tType,A_27g: $tType,A_27h: $tType,A_27i: $tType,X0_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] : c_2Epair_2EUNCURRY_2E1(A_27f,tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27f,tyop_2Epair_2Eprod(A_27g,A_27h)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27f,tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27g_20mono_2EA_27h_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27i_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27g: $tType,A_27h: $tType,A_27i: $tType,X0_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] : c_2Epair_2EUNCURRY_2E1(A_27g,A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27g,A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_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_2Ereal_2Eabs_2E1,axiom,
    ! [X0_2E0: tyop_2Erealax_2Ereal] : c_2Ereal_2Eabs_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E0,X0_2E0) ).

tff(arityeq1_2Ec_2Ereal__topology_2Eball_2E1,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] : c_2Ereal__topology_2Eball_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E0,X0_2E0) ).

tff(arityeq1_2Ec_2Ereal__topology_2Ebounded__def_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] : c_2Ereal__topology_2Ebounded__def_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E0,X0_2E0) ).

tff(arityeq1_2Ec_2Ereal__topology_2Ecball_2E1,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] : c_2Ereal__topology_2Ecball_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E0,X0_2E0) ).

tff(arityeq1_2Ec_2Ereal__topology_2Ecompact_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] : c_2Ereal__topology_2Ecompact_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ereal__topology_2Ecompact_2E0,X0_2E0) ).

tff(arityeq1_2Ec_2Enumeral_2EiDUB_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : c_2Enumeral_2EiDUB_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E0,X0_2E0) ).

tff(arityeq1_2Ec_2Enumeral_2EiZ_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : c_2Enumeral_2EiZ_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E0,X0_2E0) ).

tff(arityeq1_2Ec_2Enumeral_2EiiSUC_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : c_2Enumeral_2EiiSUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E0,X0_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_2Ereal_2Ereal__ge_2E2,axiom,
    ! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : c_2Ereal_2Ereal__ge_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__ge_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_2Erealax_2Ereal__neg_2E1,axiom,
    ! [X0_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__neg_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,X0_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(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_2Earithmetic_2EZERO__LESS__EQ,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2E0_2E0,V0n_2E0)) ).

tff(thm_2Earithmetic_2ENOT__LESS__EQUAL,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
      ( ~ p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0))
    <=> p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,V0m_2E0)) ) ).

tff(thm_2Earithmetic_2EADD__EQ__0,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0) = c_2Enum_2E0_2E0 )
    <=> ( ( V0m_2E0 = c_2Enum_2E0_2E0 )
        & ( V1n_2E0 = c_2Enum_2E0_2E0 ) ) ) ).

tff(thm_2Earithmetic_2ELE,axiom,
    ( ! [V0n_2E0: tyop_2Enum_2Enum] :
        ( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Enum_2E0_2E0))
      <=> ( V0n_2E0 = c_2Enum_2E0_2E0 ) )
    & ! [V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
        ( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,c_2Enum_2ESUC_2E1(V2n_2E0)))
      <=> ( ( V1m_2E0 = c_2Enum_2ESUC_2E1(V2n_2E0) )
          | p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V2n_2E0)) ) ) ) ).

tff(thm_2Ebool_2EIN__DEF,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1x_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1x_27_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V1x_27_2E0,V0x_2E0) ).

tff(thm_2Ebool_2ETRUTH,axiom,
    p(c_2Ebool_2ET_2E0) ).

tff(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
    ! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V0t1_2E0)
       => p(V1t2_2E0) )
     => ( ( p(V1t2_2E0)
         => p(V0t1_2E0) )
       => ( V0t1_2E0 = V1t2_2E0 ) ) ) ).

tff(thm_2Ebool_2EFORALL__SIMP,axiom,
    ! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Ebool] :
      ( ! [V1x_2E0: A_27a] : p(V0t_2E0)
    <=> p(V0t_2E0) ) ).

tff(thm_2Ebool_2EIMP__F,axiom,
    ! [V0t_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V0t_2E0)
       => p(c_2Ebool_2EF_2E0) )
     => ~ p(V0t_2E0) ) ).

tff(thm_2Ebool_2EF__IMP,axiom,
    ! [V0t_2E0: tyop_2Emin_2Ebool] :
      ( ~ p(V0t_2E0)
     => ( p(V0t_2E0)
       => p(c_2Ebool_2EF_2E0) ) ) ).

tff(thm_2Ebool_2EAND__CLAUSES,axiom,
    ! [V0t_2E0: tyop_2Emin_2Ebool] :
      ( ( ( p(c_2Ebool_2ET_2E0)
          & p(V0t_2E0) )
      <=> p(V0t_2E0) )
      & ( ( p(V0t_2E0)
          & p(c_2Ebool_2ET_2E0) )
      <=> p(V0t_2E0) )
      & ( ( p(c_2Ebool_2EF_2E0)
          & p(V0t_2E0) )
      <=> p(c_2Ebool_2EF_2E0) )
      & ( ( p(V0t_2E0)
          & p(c_2Ebool_2EF_2E0) )
      <=> p(c_2Ebool_2EF_2E0) )
      & ( ( p(V0t_2E0)
          & p(V0t_2E0) )
      <=> p(V0t_2E0) ) ) ).

tff(thm_2Ebool_2EIMP__CLAUSES,axiom,
    ! [V0t_2E0: tyop_2Emin_2Ebool] :
      ( ( ( p(c_2Ebool_2ET_2E0)
         => p(V0t_2E0) )
      <=> p(V0t_2E0) )
      & ( ( p(V0t_2E0)
         => p(c_2Ebool_2ET_2E0) )
      <=> p(c_2Ebool_2ET_2E0) )
      & ( ( p(c_2Ebool_2EF_2E0)
         => p(V0t_2E0) )
      <=> p(c_2Ebool_2ET_2E0) )
      & ( ( p(V0t_2E0)
         => p(V0t_2E0) )
      <=> p(c_2Ebool_2ET_2E0) )
      & ( ( p(V0t_2E0)
         => p(c_2Ebool_2EF_2E0) )
      <=> ~ p(V0t_2E0) ) ) ).

tff(thm_2Ebool_2ENOT__CLAUSES,axiom,
    ( ! [V0t_2E0: tyop_2Emin_2Ebool] :
        ( ~ ~ p(V0t_2E0)
      <=> p(V0t_2E0) )
    & ( ~ p(c_2Ebool_2ET_2E0)
    <=> p(c_2Ebool_2EF_2E0) )
    & ( ~ p(c_2Ebool_2EF_2E0)
    <=> p(c_2Ebool_2ET_2E0) ) ) ).

tff(thm_2Ebool_2EREFL__CLAUSE,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] :
      ( ( V0x_2E0 = V0x_2E0 )
    <=> p(c_2Ebool_2ET_2E0) ) ).

tff(thm_2Ebool_2EEQ__SYM__EQ,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
      ( ( V0x_2E0 = V1y_2E0 )
    <=> ( V1y_2E0 = V0x_2E0 ) ) ).

tff(thm_2Ebool_2EEQ__CLAUSES,axiom,
    ! [V0t_2E0: tyop_2Emin_2Ebool] :
      ( ( ( c_2Ebool_2ET_2E0 = V0t_2E0 )
      <=> p(V0t_2E0) )
      & ( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
      <=> p(V0t_2E0) )
      & ( ( c_2Ebool_2EF_2E0 = V0t_2E0 )
      <=> ~ p(V0t_2E0) )
      & ( ( V0t_2E0 = c_2Ebool_2EF_2E0 )
      <=> ~ p(V0t_2E0) ) ) ).

tff(thm_2Ebool_2ENOT__EXISTS__THM,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0))
    <=> ! [V2x_2E0: A_27a] : ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) ) ).

tff(thm_2Ebool_2ELEFT__OR__EXISTS__THM,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
      ( ( ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
        | p(V1Q_2E0) )
    <=> ? [V3x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
          | p(V1Q_2E0) ) ) ).

tff(thm_2Ebool_2ELEFT__EXISTS__AND__THM,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
      ( ? [V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
          & p(V1Q_2E0) )
    <=> ( ? [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
        & p(V1Q_2E0) ) ) ).

tff(thm_2Ebool_2ERIGHT__EXISTS__AND__THM,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ? [V2x_2E0: A_27a] :
          ( p(V0P_2E0)
          & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
    <=> ( p(V0P_2E0)
        & ? [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) ) ).

tff(thm_2Ebool_2EDE__MORGAN__THM,axiom,
    ! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool] :
      ( ( ~ ( p(V0A_2E0)
            & p(V1B_2E0) )
      <=> ( ~ p(V0A_2E0)
          | ~ p(V1B_2E0) ) )
      & ( ~ ( p(V0A_2E0)
            | p(V1B_2E0) )
      <=> ( ~ p(V0A_2E0)
          & ~ p(V1B_2E0) ) ) ) ).

tff(thm_2Ebool_2EAND__IMP__INTRO,axiom,
    ! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool,V2t3_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V0t1_2E0)
       => ( p(V1t2_2E0)
         => p(V2t3_2E0) ) )
    <=> ( ( p(V0t1_2E0)
          & p(V1t2_2E0) )
       => p(V2t3_2E0) ) ) ).

tff(thm_2Ebool_2EIMP__CONG,axiom,
    ! [V0x_2E0: tyop_2Emin_2Ebool,V1x_27_2E0: tyop_2Emin_2Ebool,V2y_2E0: tyop_2Emin_2Ebool,V3y_27_2E0: tyop_2Emin_2Ebool] :
      ( ( ( V0x_2E0 = V1x_27_2E0 )
        & ( p(V1x_27_2E0)
         => ( V2y_2E0 = V3y_27_2E0 ) ) )
     => ( ( p(V0x_2E0)
         => p(V2y_2E0) )
      <=> ( p(V1x_27_2E0)
         => p(V3y_27_2E0) ) ) ) ).

tff(thm_2Ebool_2EUNWIND__THM2,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0: A_27a] :
      ( ? [V2x_2E0: A_27a] :
          ( ( V2x_2E0 = V1a_2E0 )
          & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
    <=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1a_2E0)) ) ).

tff(thm_2Ebool_2ESKOLEM__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( ! [V1x_2E0: A_27a] :
        ? [V2y_2E0: A_27b] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V1x_2E0),V2y_2E0))
    <=> ? [V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
        ! [V4x_2E0: A_27a] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V4x_2E0),app_2E2(A_27a,A_27b,V3f_2E0,V4x_2E0))) ) ).

tff(thm_2Ecardinal_2ECONJ__EQ__IMP,axiom,
    ! [V0r_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool,V2q_2E0: tyop_2Emin_2Ebool] :
      ( ( ( p(V1p_2E0)
          & p(V2q_2E0) )
       => p(V0r_2E0) )
    <=> ( p(V1p_2E0)
       => ( p(V2q_2E0)
         => p(V0r_2E0) ) ) ) ).

tff(thm_2Eiterate_2ESIMP__REAL__ARCH,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal] :
    ? [V1n_2E0: tyop_2Enum_2Enum] : p(c_2Ereal_2Ereal__lte_2E2(V0x_2E0,c_2Ereal_2Ereal__of__num_2E1(V1n_2E0))) ).

tff(thm_2Enumeral_2Enumeral__distrib,axiom,
    ( ! [V0n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2B_2E2(c_2Enum_2E0_2E0,V0n_2E0) = V0n_2E0
    & ! [V1n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2B_2E2(V1n_2E0,c_2Enum_2E0_2E0) = V1n_2E0
    & ! [V2n_2E0: tyop_2Enum_2Enum,V3m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(V2n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V3m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(V2n_2E0,V3m_2E0)))
    & ! [V4n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2A_2E2(c_2Enum_2E0_2E0,V4n_2E0) = c_2Enum_2E0_2E0
    & ! [V5n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2A_2E2(V5n_2E0,c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0
    & ! [V6n_2E0: tyop_2Enum_2Enum,V7m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(V6n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V7m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2E_2A_2E2(V6n_2E0,V7m_2E0))
    & ! [V8n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2D_2E2(c_2Enum_2E0_2E0,V8n_2E0) = c_2Enum_2E0_2E0
    & ! [V9n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2D_2E2(V9n_2E0,c_2Enum_2E0_2E0) = V9n_2E0
    & ! [V10n_2E0: tyop_2Enum_2Enum,V11m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V10n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V11m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2E_2D_2E2(V10n_2E0,V11m_2E0))
    & ! [V12n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEXP_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V12n_2E0))) = c_2Enum_2E0_2E0
    & ! [V13n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEXP_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V13n_2E0))) = c_2Enum_2E0_2E0
    & ! [V14n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEXP_2E2(V14n_2E0,c_2Enum_2E0_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))
    & ! [V15n_2E0: tyop_2Enum_2Enum,V16m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(V15n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V16m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EEXP_2E2(V15n_2E0,V16m_2E0))
    & ( c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
    & ! [V17n_2E0: tyop_2Enum_2Enum] : c_2Enum_2ESUC_2E1(c_2Earithmetic_2ENUMERAL_2E1(V17n_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Enum_2ESUC_2E1(V17n_2E0))
    & ( c_2Eprim__rec_2EPRE_2E1(c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0 )
    & ! [V18n_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2ENUMERAL_2E1(V18n_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Eprim__rec_2EPRE_2E1(V18n_2E0))
    & ! [V19n_2E0: tyop_2Enum_2Enum] :
        ( ( c_2Earithmetic_2ENUMERAL_2E1(V19n_2E0) = c_2Enum_2E0_2E0 )
      <=> ( V19n_2E0 = c_2Earithmetic_2EZERO_2E0 ) )
    & ! [V20n_2E0: tyop_2Enum_2Enum] :
        ( ( c_2Enum_2E0_2E0 = c_2Earithmetic_2ENUMERAL_2E1(V20n_2E0) )
      <=> ( V20n_2E0 = c_2Earithmetic_2EZERO_2E0 ) )
    & ! [V21n_2E0: tyop_2Enum_2Enum,V22m_2E0: tyop_2Enum_2Enum] :
        ( ( c_2Earithmetic_2ENUMERAL_2E1(V21n_2E0) = c_2Earithmetic_2ENUMERAL_2E1(V22m_2E0) )
      <=> ( V21n_2E0 = V22m_2E0 ) )
    & ! [V23n_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2E_3C_2E2(V23n_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2EF_2E0
    & ! [V24n_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(V24n_2E0)) = c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EZERO_2E0,V24n_2E0)
    & ! [V25n_2E0: tyop_2Enum_2Enum,V26m_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(V25n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V26m_2E0)) = c_2Eprim__rec_2E_3C_2E2(V25n_2E0,V26m_2E0)
    & ! [V27n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_2E2(c_2Enum_2E0_2E0,V27n_2E0) = c_2Ebool_2EF_2E0
    & ! [V28n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_2E2(c_2Earithmetic_2ENUMERAL_2E1(V28n_2E0),c_2Enum_2E0_2E0) = c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EZERO_2E0,V28n_2E0)
    & ! [V29n_2E0: tyop_2Enum_2Enum,V30m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_2E2(c_2Earithmetic_2ENUMERAL_2E1(V29n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V30m_2E0)) = c_2Eprim__rec_2E_3C_2E2(V30m_2E0,V29n_2E0)
    & ! [V31n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2E0_2E0,V31n_2E0) = c_2Ebool_2ET_2E0
    & ! [V32n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V32n_2E0),c_2Enum_2E0_2E0) = c_2Earithmetic_2E_3C_3D_2E2(V32n_2E0,c_2Earithmetic_2EZERO_2E0)
    & ! [V33n_2E0: tyop_2Enum_2Enum,V34m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V33n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V34m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V33n_2E0,V34m_2E0)
    & ! [V35n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_3D_2E2(V35n_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2ET_2E0
    & ! [V36n_2E0: tyop_2Enum_2Enum] :
        ( p(c_2Earithmetic_2E_3E_3D_2E2(c_2Enum_2E0_2E0,V36n_2E0))
      <=> ( V36n_2E0 = c_2Enum_2E0_2E0 ) )
    & ! [V37n_2E0: tyop_2Enum_2Enum,V38m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V37n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V38m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V38m_2E0,V37n_2E0)
    & ! [V39n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EODD_2E1(c_2Earithmetic_2ENUMERAL_2E1(V39n_2E0)) = c_2Earithmetic_2EODD_2E1(V39n_2E0)
    & ! [V40n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEVEN_2E1(c_2Earithmetic_2ENUMERAL_2E1(V40n_2E0)) = c_2Earithmetic_2EEVEN_2E1(V40n_2E0)
    & ~ p(c_2Earithmetic_2EODD_2E1(c_2Enum_2E0_2E0))
    & p(c_2Earithmetic_2EEVEN_2E1(c_2Enum_2E0_2E0)) ) ).

tff(thm_2Enumeral_2Enumeral__add,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
      ( ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0)) = V0n_2E0 )
      & ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0)) = V0n_2E0 )
      & ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
      & ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
      & ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
      & ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
      & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0)) = c_2Enum_2ESUC_2E1(V0n_2E0) )
      & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0)) = c_2Enum_2ESUC_2E1(V0n_2E0) )
      & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
      & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
      & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
      & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
      & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0)) = c_2Enumeral_2EiiSUC_2E1(V0n_2E0) )
      & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0)) = c_2Enumeral_2EiiSUC_2E1(V0n_2E0) )
      & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
      & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
      & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
      & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) ) ) ).

tff(thm_2Enumeral_2EiDUB__removal,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum] :
      ( ( c_2Enumeral_2EiDUB_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)) = c_2Earithmetic_2EBIT2_2E1(c_2Enumeral_2EiDUB_2E1(V0n_2E0)) )
      & ( c_2Enumeral_2EiDUB_2E1(c_2Earithmetic_2EBIT2_2E1(V0n_2E0)) = c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)) )
      & ( c_2Enumeral_2EiDUB_2E1(c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EZERO_2E0 ) ) ).

tff(thm_2Enumeral_2Enumeral__mult,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0) = c_2Earithmetic_2EZERO_2E0 )
      & ( c_2Earithmetic_2E_2A_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EZERO_2E0 )
      & ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),V1m_2E0) = c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Enumeral_2EiDUB_2E1(c_2Earithmetic_2E_2A_2E2(V0n_2E0,V1m_2E0)),V1m_2E0)) )
      & ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),V1m_2E0) = c_2Enumeral_2EiDUB_2E1(c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(V0n_2E0,V1m_2E0),V1m_2E0))) ) ) ).

tff(thm_2Epair_2ECLOSED__PAIR__EQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b,V2a_2E0: A_27a,V3b_2E0: A_27b] :
      ( ( c_2Epair_2E_2C_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27b,V2a_2E0,V3b_2E0) )
    <=> ( ( V0x_2E0 = V2a_2E0 )
        & ( V1y_2E0 = V3b_2E0 ) ) ) ).

tff(thm_2Epred__set_2EEXTENSION,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( V0s_2E0 = V1t_2E0 )
    <=> ! [V2x_2E0: A_27a] : c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0) = c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0) ) ).

tff(thm_2Epred__set_2EGSPECIFICATION,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V1v_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V1v_2E0,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27b,V0f_2E0)))
    <=> ? [V2x_2E0: A_27b] : c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V1v_2E0,c_2Ebool_2ET_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),V0f_2E0,V2x_2E0) ) ).

tff(thm_2Epred__set_2EIN__UNIV,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2EUNIV_2E0(A_27a))) ).

tff(thm_2Epred__set_2ESUBSET__DEF,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
    <=> ! [V2x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
         => p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) ) ).

tff(thm_2Epred__set_2ESUBSET__TRANS,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1t_2E0,V2u_2E0)) )
     => p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V2u_2E0)) ) ).

tff(thm_2Epred__set_2EIN__INTER,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0)))
    <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) ) ).

tff(thm_2Epred__set_2EINTER__SUBSET,axiom,
    ! [A_27a: $tType] :
      ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0),V0s_2E0))
      & ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V3t_2E0,V2s_2E0),V2s_2E0)) ) ).

tff(thm_2Epred__set_2ESUBSET__INTER,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1t_2E0,V2u_2E0)))
    <=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V2u_2E0)) ) ) ).

tff(thm_2Ereal_2EREAL__ADD__SYM,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__add_2E2(V0x_2E0,V1y_2E0) = c_2Erealax_2Ereal__add_2E2(V1y_2E0,V0x_2E0) ).

tff(thm_2Ereal_2EREAL__ADD__ASSOC,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2z_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__add_2E2(V0x_2E0,c_2Erealax_2Ereal__add_2E2(V1y_2E0,V2z_2E0)) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__add_2E2(V0x_2E0,V1y_2E0),V2z_2E0) ).

tff(thm_2Ereal_2EREAL__ADD__LID,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),V0x_2E0) = V0x_2E0 ).

tff(thm_2Ereal_2EREAL__ADD__LINV,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__neg_2E1(V0x_2E0),V0x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ).

tff(thm_2Ereal_2EREAL__LT__TRANS,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2z_2E0: tyop_2Erealax_2Ereal] :
      ( ( p(c_2Erealax_2Ereal__lt_2E2(V0x_2E0,V1y_2E0))
        & p(c_2Erealax_2Ereal__lt_2E2(V1y_2E0,V2z_2E0)) )
     => p(c_2Erealax_2Ereal__lt_2E2(V0x_2E0,V2z_2E0)) ) ).

tff(thm_2Ereal_2EREAL__MUL__LID,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0x_2E0) = V0x_2E0 ).

tff(thm_2Ereal_2Ereal__ge,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal] : c_2Ereal_2Ereal__ge_2E2(V0x_2E0,V1y_2E0) = c_2Ereal_2Ereal__lte_2E2(V1y_2E0,V0x_2E0) ).

tff(thm_2Ereal_2EREAL__ADD__RID,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__add_2E2(V0x_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) = V0x_2E0 ).

tff(thm_2Ereal_2EREAL__ADD__RINV,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__add_2E2(V0x_2E0,c_2Erealax_2Ereal__neg_2E1(V0x_2E0)) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ).

tff(thm_2Ereal_2EREAL__MUL__RID,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__mul_2E2(V0x_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = V0x_2E0 ).

tff(thm_2Ereal_2EREAL__NEG__ADD,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__neg_2E1(c_2Erealax_2Ereal__add_2E2(V0x_2E0,V1y_2E0)) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__neg_2E1(V0x_2E0),c_2Erealax_2Ereal__neg_2E1(V1y_2E0)) ).

tff(thm_2Ereal_2EREAL__MUL__LZERO,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),V0x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ).

tff(thm_2Ereal_2EREAL__LT__LADD,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2z_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(V0x_2E0,V1y_2E0),c_2Erealax_2Ereal__add_2E2(V0x_2E0,V2z_2E0)) = c_2Erealax_2Ereal__lt_2E2(V1y_2E0,V2z_2E0) ).

tff(thm_2Ereal_2EREAL__LTE__TRANS,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2z_2E0: tyop_2Erealax_2Ereal] :
      ( ( p(c_2Erealax_2Ereal__lt_2E2(V0x_2E0,V1y_2E0))
        & p(c_2Ereal_2Ereal__lte_2E2(V1y_2E0,V2z_2E0)) )
     => p(c_2Erealax_2Ereal__lt_2E2(V0x_2E0,V2z_2E0)) ) ).

tff(thm_2Ereal_2EREAL__LET__TRANS,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2z_2E0: tyop_2Erealax_2Ereal] :
      ( ( p(c_2Ereal_2Ereal__lte_2E2(V0x_2E0,V1y_2E0))
        & p(c_2Erealax_2Ereal__lt_2E2(V1y_2E0,V2z_2E0)) )
     => p(c_2Erealax_2Ereal__lt_2E2(V0x_2E0,V2z_2E0)) ) ).

tff(thm_2Ereal_2EREAL__LE__TRANS,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2z_2E0: tyop_2Erealax_2Ereal] :
      ( ( p(c_2Ereal_2Ereal__lte_2E2(V0x_2E0,V1y_2E0))
        & p(c_2Ereal_2Ereal__lte_2E2(V1y_2E0,V2z_2E0)) )
     => p(c_2Ereal_2Ereal__lte_2E2(V0x_2E0,V2z_2E0)) ) ).

tff(thm_2Ereal_2EREAL__LE__ANTISYM,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal] :
      ( ( p(c_2Ereal_2Ereal__lte_2E2(V0x_2E0,V1y_2E0))
        & p(c_2Ereal_2Ereal__lte_2E2(V1y_2E0,V0x_2E0)) )
    <=> ( V0x_2E0 = V1y_2E0 ) ) ).

tff(thm_2Ereal_2EREAL__ADD,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(V0m_2E0),c_2Ereal_2Ereal__of__num_2E1(V1n_2E0)) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0)) ).

tff(thm_2Ereal_2EREAL__MUL__RNEG,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__mul_2E2(V0x_2E0,c_2Erealax_2Ereal__neg_2E1(V1y_2E0)) = c_2Erealax_2Ereal__neg_2E1(c_2Erealax_2Ereal__mul_2E2(V0x_2E0,V1y_2E0)) ).

tff(thm_2Ereal_2EREAL__MUL__LNEG,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V0x_2E0),V1y_2E0) = c_2Erealax_2Ereal__neg_2E1(c_2Erealax_2Ereal__mul_2E2(V0x_2E0,V1y_2E0)) ).

tff(thm_2Ereal_2Ereal__lt,axiom,
    ! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal] :
      ( p(c_2Erealax_2Ereal__lt_2E2(V1x_2E0,V0y_2E0))
    <=> ~ p(c_2Ereal_2Ereal__lte_2E2(V0y_2E0,V1x_2E0)) ) ).

tff(thm_2Ereal_2EREAL__LE__LADD__IMP,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2z_2E0: tyop_2Erealax_2Ereal] :
      ( p(c_2Ereal_2Ereal__lte_2E2(V1y_2E0,V2z_2E0))
     => p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V0x_2E0,V1y_2E0),c_2Erealax_2Ereal__add_2E2(V0x_2E0,V2z_2E0))) ) ).

tff(thm_2Ereal_2EREAL__LE__LNEG,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal] : c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__neg_2E1(V0x_2E0),V1y_2E0) = c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),c_2Erealax_2Ereal__add_2E2(V0x_2E0,V1y_2E0)) ).

tff(thm_2Ereal_2EREAL__LE__NEG2,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal] : c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__neg_2E1(V0x_2E0),c_2Erealax_2Ereal__neg_2E1(V1y_2E0)) = c_2Ereal_2Ereal__lte_2E2(V1y_2E0,V0x_2E0) ).

tff(thm_2Ereal_2EREAL__NEG__NEG,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__neg_2E1(c_2Erealax_2Ereal__neg_2E1(V0x_2E0)) = V0x_2E0 ).

tff(thm_2Ereal_2EREAL__LE__RNEG,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal] : c_2Ereal_2Ereal__lte_2E2(V0x_2E0,c_2Erealax_2Ereal__neg_2E1(V1y_2E0)) = c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V0x_2E0,V1y_2E0),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) ).

tff(thm_2Ereal_2EREAL__ADD__RDISTRIB,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2z_2E0: tyop_2Erealax_2Ereal] : c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__add_2E2(V0x_2E0,V1y_2E0),V2z_2E0) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V0x_2E0,V2z_2E0),c_2Erealax_2Ereal__mul_2E2(V1y_2E0,V2z_2E0)) ).

tff(thm_2Ereal_2EREAL__OF__NUM__ADD,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(V0m_2E0),c_2Ereal_2Ereal__of__num_2E1(V1n_2E0)) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0)) ).

tff(thm_2Ereal_2EREAL__OF__NUM__LE,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(V0m_2E0),c_2Ereal_2Ereal__of__num_2E1(V1n_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0) ).

tff(thm_2Ereal_2EREAL__OF__NUM__MUL,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Ereal__of__num_2E1(V0m_2E0),c_2Ereal_2Ereal__of__num_2E1(V1n_2E0)) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2E_2A_2E2(V0m_2E0,V1n_2E0)) ).

tff(thm_2Ereal__topology_2EREAL__OF__NUM__GE,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : c_2Ereal_2Ereal__ge_2E2(c_2Ereal_2Ereal__of__num_2E1(V0m_2E0),c_2Ereal_2Ereal__of__num_2E1(V1n_2E0)) = c_2Earithmetic_2E_3E_3D_2E2(V0m_2E0,V1n_2E0) ).

tff(thm_2Ereal__topology_2EDIST__REFL,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal] : c_2Ereal__topology_2EDist_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V0x_2E0,V0x_2E0)) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ).

tff(thm_2Ereal__topology_2EIN__CBALL__0,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1e_2E0: tyop_2Erealax_2Ereal] : c_2Ebool_2EIN_2E2(tyop_2Erealax_2Ereal,V0x_2E0,c_2Ereal__topology_2Ecball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),V1e_2E0))) = c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V0x_2E0),V1e_2E0) ).

tff(thm_2Ereal__topology_2EBOUNDED__SUBSET__CBALL,axiom,
    ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Erealax_2Ereal] :
      ( p(c_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0))
     => ? [V2r_2E0: tyop_2Erealax_2Ereal] :
          ( p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),V2r_2E0))
          & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,V0s_2E0,c_2Ereal__topology_2Ecball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V1x_2E0,V2r_2E0)))) ) ) ).

tff(thm_2Ereal__topology_2ESUBSET__BALLS,axiom,
    ( ! [V0a_2E0: tyop_2Erealax_2Ereal,V1a_27_2E0: tyop_2Erealax_2Ereal,V2r_2E0: tyop_2Erealax_2Ereal,V3r_27_2E0: tyop_2Erealax_2Ereal] :
        ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,c_2Ereal__topology_2Eball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V0a_2E0,V2r_2E0)),c_2Ereal__topology_2Eball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V1a_27_2E0,V3r_27_2E0))))
      <=> ( p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Ereal__topology_2EDist_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V0a_2E0,V1a_27_2E0)),V2r_2E0),V3r_27_2E0))
          | p(c_2Ereal_2Ereal__lte_2E2(V2r_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) ) )
    & ! [V4a_2E0: tyop_2Erealax_2Ereal,V5a_27_2E0: tyop_2Erealax_2Ereal,V6r_2E0: tyop_2Erealax_2Ereal,V7r_27_2E0: tyop_2Erealax_2Ereal] :
        ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,c_2Ereal__topology_2Eball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V4a_2E0,V6r_2E0)),c_2Ereal__topology_2Ecball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V5a_27_2E0,V7r_27_2E0))))
      <=> ( p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Ereal__topology_2EDist_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V4a_2E0,V5a_27_2E0)),V6r_2E0),V7r_27_2E0))
          | p(c_2Ereal_2Ereal__lte_2E2(V6r_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) ) )
    & ! [V8a_2E0: tyop_2Erealax_2Ereal,V9a_27_2E0: tyop_2Erealax_2Ereal,V10r_2E0: tyop_2Erealax_2Ereal,V11r_27_2E0: tyop_2Erealax_2Ereal] :
        ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,c_2Ereal__topology_2Ecball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V8a_2E0,V10r_2E0)),c_2Ereal__topology_2Eball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V9a_27_2E0,V11r_27_2E0))))
      <=> ( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Ereal__topology_2EDist_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V8a_2E0,V9a_27_2E0)),V10r_2E0),V11r_27_2E0))
          | p(c_2Erealax_2Ereal__lt_2E2(V10r_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) ) )
    & ! [V12a_2E0: tyop_2Erealax_2Ereal,V13a_27_2E0: tyop_2Erealax_2Ereal,V14r_2E0: tyop_2Erealax_2Ereal,V15r_27_2E0: tyop_2Erealax_2Ereal] :
        ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,c_2Ereal__topology_2Ecball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V12a_2E0,V14r_2E0)),c_2Ereal__topology_2Ecball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V13a_27_2E0,V15r_27_2E0))))
      <=> ( p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Ereal__topology_2EDist_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V12a_2E0,V13a_27_2E0)),V14r_2E0),V15r_27_2E0))
          | p(c_2Erealax_2Ereal__lt_2E2(V14r_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) ) ) ) ).

tff(thm_2Ereal__topology_2ECOMPACT__IMP__BOUNDED,axiom,
    ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
      ( p(c_2Ereal__topology_2Ecompact_2E1(V0s_2E0))
     => p(c_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) ) ).

tff(thm_2Ereal__topology_2ECLOSED__INTER__COMPACT,axiom,
    ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ereal__topology_2EClosed_2E1(V0s_2E0))
        & p(c_2Ereal__topology_2Ecompact_2E1(V1t_2E0)) )
     => p(c_2Ereal__topology_2Ecompact_2E1(c_2Epred__set_2EINTER_2E2(tyop_2Erealax_2Ereal,V0s_2E0,V1t_2E0))) ) ).

tff(thm_2Ereal__topology_2ECOMPACT__CBALL,axiom,
    ! [V0x_2E0: tyop_2Erealax_2Ereal,V1e_2E0: tyop_2Erealax_2Ereal] : p(c_2Ereal__topology_2Ecompact_2E1(c_2Ereal__topology_2Ecball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,V0x_2E0,V1e_2E0)))) ).

tff(thm_2Ereal__topology_2EBIGUNION__GSPEC,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,A_27g: $tType,A_27h: $tType,A_27i: $tType,F9_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))))),F4_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))),F8_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool))),F5_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27i,tyop_2Epair_2Eprod(A_27i,tyop_2Emin_2Ebool)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))),F7_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool))),F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27e,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F6_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))))] :
      ( ! [V13f_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),V14x_2E0: A_27f,V12P_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),V15y_2E0: A_27g,V16z_2E0: A_27h] : app_2E2(A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(A_27f,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))),F9_2E0,V13f_2E0),V14x_2E0),V12P_2E0),V15y_2E0),V16z_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),app_2E2(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)),app_2E2(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool))),V13f_2E0,V14x_2E0),V15y_2E0),V16z_2E0),app_2E2(A_27h,tyop_2Emin_2Ebool,app_2E2(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool),app_2E2(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V12P_2E0,V14x_2E0),V15y_2E0),V16z_2E0))
     => ( ! [V13f_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),V12P_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),V14x_2E0: A_27f] : app_2E2(A_27f,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F4_2E0,V13f_2E0),V12P_2E0),V14x_2E0) = c_2Epair_2EUNCURRY_2E1(A_27g,A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(A_27f,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))),F9_2E0,V13f_2E0),V14x_2E0),V12P_2E0))
       => ( ! [V12P_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),V17a_2E0: A_27i,V13f_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool))))] :
              ( p(app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool,app_2E2(A_27i,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool)),F8_2E0,V12P_2E0),V17a_2E0),V13f_2E0))
            <=> ? [V18x_2E0: A_27f,V19y_2E0: A_27g,V20z_2E0: A_27h] :
                  ( p(app_2E2(A_27h,tyop_2Emin_2Ebool,app_2E2(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool),app_2E2(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V12P_2E0,V18x_2E0),V19y_2E0),V20z_2E0))
                  & p(c_2Ebool_2EIN_2E2(A_27i,V17a_2E0,app_2E2(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),app_2E2(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)),app_2E2(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool))),V13f_2E0,V18x_2E0),V19y_2E0),V20z_2E0))) ) )
         => ( ! [V12P_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),V13f_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),V17a_2E0: A_27i] : app_2E2(A_27i,tyop_2Epair_2Eprod(A_27i,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27i,tyop_2Epair_2Eprod(A_27i,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27i,tyop_2Epair_2Eprod(A_27i,tyop_2Emin_2Ebool))),F5_2E0,V12P_2E0),V13f_2E0),V17a_2E0) = c_2Epair_2E_2C_2E2(A_27i,tyop_2Emin_2Ebool,V17a_2E0,app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool,app_2E2(A_27i,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool)),F8_2E0,V12P_2E0),V17a_2E0),V13f_2E0))
           => ( ! [V6f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),V5P_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V7x_2E0: A_27c,V8y_2E0: A_27d] : app_2E2(A_27d,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F2_2E0,V6f_2E0),V5P_2E0),V7x_2E0),V8y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool)),V6f_2E0,V7x_2E0),V8y_2E0),app_2E2(A_27d,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V5P_2E0,V7x_2E0),V8y_2E0))
             => ( ! [V5P_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V9a_2E0: A_27e,V6f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool)))] :
                    ( p(app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(A_27e,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),F7_2E0,V5P_2E0),V9a_2E0),V6f_2E0))
                  <=> ? [V10x_2E0: A_27c,V11y_2E0: A_27d] :
                        ( p(app_2E2(A_27d,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V5P_2E0,V10x_2E0),V11y_2E0))
                        & p(c_2Ebool_2EIN_2E2(A_27e,V9a_2E0,app_2E2(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool)),V6f_2E0,V10x_2E0),V11y_2E0))) ) )
               => ( ! [V5P_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V6f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),V9a_2E0: A_27e] : app_2E2(A_27e,tyop_2Epair_2Eprod(A_27e,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27e,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27e,tyop_2Emin_2Ebool))),F3_2E0,V5P_2E0),V6f_2E0),V9a_2E0) = c_2Epair_2E_2C_2E2(A_27e,tyop_2Emin_2Ebool,V9a_2E0,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(A_27e,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),F7_2E0,V5P_2E0),V9a_2E0),V6f_2E0))
                 => ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V1f_2E0),V0P_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1f_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
                   => ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
                          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),F6_2E0,V0P_2E0),V3a_2E0),V1f_2E0))
                        <=> ? [V4x_2E0: A_27a] :
                              ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0))
                              & p(c_2Ebool_2EIN_2E2(A_27b,V3a_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1f_2E0,V4x_2E0))) ) )
                     => ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3a_2E0: A_27b] : app_2E2(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F1_2E0,V0P_2E0),V1f_2E0),V3a_2E0) = c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,V3a_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),F6_2E0,V0P_2E0),V3a_2E0),V1f_2E0))
                       => ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : c_2Epred__set_2EBIGUNION_2E1(A_27b,c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V1f_2E0),V0P_2E0))) = c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F1_2E0,V0P_2E0),V1f_2E0))
                          & ! [V5P_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V6f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool)))] : c_2Epred__set_2EBIGUNION_2E1(A_27e,c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2EUNCURRY_2E1(A_27c,A_27d,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F2_2E0,V6f_2E0),V5P_2E0)))) = c_2Epred__set_2EGSPEC_2E1(A_27e,A_27e,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27e,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27e,tyop_2Emin_2Ebool))),F3_2E0,V5P_2E0),V6f_2E0))
                          & ! [V12P_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),V13f_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool))))] : c_2Epred__set_2EBIGUNION_2E1(A_27i,c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(A_27f,tyop_2Epair_2Eprod(A_27g,A_27h)),c_2Epair_2EUNCURRY_2E1(A_27f,tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F4_2E0,V13f_2E0),V12P_2E0)))) = c_2Epred__set_2EGSPEC_2E1(A_27i,A_27i,app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27i,tyop_2Epair_2Eprod(A_27i,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27i,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27i,tyop_2Epair_2Eprod(A_27i,tyop_2Emin_2Ebool))),F5_2E0,V12P_2E0),V13f_2E0)) ) ) ) ) ) ) ) ) ) ) ) ).

tff(thm_2Esat_2ENOT__NOT,axiom,
    ! [V0t_2E0: tyop_2Emin_2Ebool] :
      ( ~ ~ p(V0t_2E0)
    <=> p(V0t_2E0) ) ).

tff(thm_2Esat_2EAND__INV__IMP,axiom,
    ! [V0A_2E0: tyop_2Emin_2Ebool] :
      ( p(V0A_2E0)
     => ( ~ p(V0A_2E0)
       => p(c_2Ebool_2EF_2E0) ) ) ).

tff(thm_2Esat_2EOR__DUAL2,axiom,
    ! [V0B_2E0: tyop_2Emin_2Ebool,V1A_2E0: tyop_2Emin_2Ebool] :
      ( ( ~ ( p(V1A_2E0)
            | p(V0B_2E0) )
       => p(c_2Ebool_2EF_2E0) )
    <=> ( ( p(V1A_2E0)
         => p(c_2Ebool_2EF_2E0) )
       => ( ~ p(V0B_2E0)
         => p(c_2Ebool_2EF_2E0) ) ) ) ).

tff(thm_2Esat_2EOR__DUAL3,axiom,
    ! [V0B_2E0: tyop_2Emin_2Ebool,V1A_2E0: tyop_2Emin_2Ebool] :
      ( ( ~ ( ~ p(V1A_2E0)
            | p(V0B_2E0) )
       => p(c_2Ebool_2EF_2E0) )
    <=> ( p(V1A_2E0)
       => ( ~ p(V0B_2E0)
         => p(c_2Ebool_2EF_2E0) ) ) ) ).

tff(thm_2Esat_2EAND__INV2,axiom,
    ! [V0A_2E0: tyop_2Emin_2Ebool] :
      ( ( ~ p(V0A_2E0)
       => p(c_2Ebool_2EF_2E0) )
     => ( ( p(V0A_2E0)
         => p(c_2Ebool_2EF_2E0) )
       => p(c_2Ebool_2EF_2E0) ) ) ).

tff(thm_2Esat_2Edc__eq,axiom,
    ! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V2p_2E0)
      <=> ( V1q_2E0 = V0r_2E0 ) )
    <=> ( ( p(V2p_2E0)
          | p(V1q_2E0)
          | p(V0r_2E0) )
        & ( p(V2p_2E0)
          | ~ p(V0r_2E0)
          | ~ p(V1q_2E0) )
        & ( p(V1q_2E0)
          | ~ p(V0r_2E0)
          | ~ p(V2p_2E0) )
        & ( p(V0r_2E0)
          | ~ p(V1q_2E0)
          | ~ p(V2p_2E0) ) ) ) ).

tff(thm_2Esat_2Edc__conj,axiom,
    ! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V2p_2E0)
      <=> ( p(V1q_2E0)
          & p(V0r_2E0) ) )
    <=> ( ( p(V2p_2E0)
          | ~ p(V1q_2E0)
          | ~ p(V0r_2E0) )
        & ( p(V1q_2E0)
          | ~ p(V2p_2E0) )
        & ( p(V0r_2E0)
          | ~ p(V2p_2E0) ) ) ) ).

tff(thm_2Esat_2Edc__disj,axiom,
    ! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V2p_2E0)
      <=> ( p(V1q_2E0)
          | p(V0r_2E0) ) )
    <=> ( ( p(V2p_2E0)
          | ~ p(V1q_2E0) )
        & ( p(V2p_2E0)
          | ~ p(V0r_2E0) )
        & ( p(V1q_2E0)
          | p(V0r_2E0)
          | ~ p(V2p_2E0) ) ) ) ).

tff(thm_2Esat_2Edc__imp,axiom,
    ! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V2p_2E0)
      <=> ( p(V1q_2E0)
         => p(V0r_2E0) ) )
    <=> ( ( p(V2p_2E0)
          | p(V1q_2E0) )
        & ( p(V2p_2E0)
          | ~ p(V0r_2E0) )
        & ( ~ p(V1q_2E0)
          | p(V0r_2E0)
          | ~ p(V2p_2E0) ) ) ) ).

tff(thm_2Esat_2Edc__neg,axiom,
    ! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V1p_2E0)
      <=> ~ p(V0q_2E0) )
    <=> ( ( p(V1p_2E0)
          | p(V0q_2E0) )
        & ( ~ p(V0q_2E0)
          | ~ p(V1p_2E0) ) ) ) ).

tff(thm_2Ereal__topology_2ECLOSED__UNION__COMPACT__SUBSETS,conjecture,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),V5n_2E0: tyop_2Enum_2Enum] : app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V1f_2E0),V5n_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1f_2E0,V5n_2E0),c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V5n_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))
     => ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
          ( p(c_2Ereal__topology_2EClosed_2E1(V0s_2E0))
         => ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))] :
              ( ! [V2n_2E0: tyop_2Enum_2Enum] : p(c_2Ereal__topology_2Ecompact_2E1(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1f_2E0,V2n_2E0)))
              & ! [V3n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1f_2E0,V3n_2E0),V0s_2E0))
              & ! [V4n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1f_2E0,V4n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1f_2E0,c_2Earithmetic_2E_2B_2E2(V4n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
              & ( c_2Epred__set_2EBIGUNION_2E1(tyop_2Erealax_2Ereal,c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V1f_2E0))) = V0s_2E0 )
              & ! [V6k_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
                  ( ( p(c_2Ereal__topology_2Ecompact_2E1(V6k_2E0))
                    & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,V6k_2E0,V0s_2E0)) )
                 => ? [V7N_2E0: tyop_2Enum_2Enum] :
                    ! [V8n_2E0: tyop_2Enum_2Enum] :
                      ( p(c_2Earithmetic_2E_3E_3D_2E2(V8n_2E0,V7N_2E0))
                     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,V6k_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1f_2E0,V8n_2E0))) ) ) ) ) ) ).

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