%------------------------------------------------------------------------------
% File     : ITP033_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : set_relation.ax [Gau19]
%          : HL4033_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  526 ( 193 unt; 190 typ;   0 def)
%            Number of atoms       :  795 ( 317 equ)
%            Maximal formula atoms :   25 (   1 avg)
%            Number of connectives :  490 (  31   ~;  12   |; 191   &)
%                                         (  62 <=>; 194  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   41 (   6 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  144 (  92   >;  52   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  187 ( 187 usr;  14 con; 0-5 aty)
%            Number of variables   : 1599 (1344   !;  41   ?;1599   :)
%                                         ( 214  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
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_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: $tType > $tType ).

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

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

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

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

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

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

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

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

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

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

tff(c_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_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_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_2Epred__set_2ECHOICE_2E0,type,
    c_2Epred__set_2ECHOICE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).

tff(c_2Epred__set_2ECHOICE_2E1,type,
    c_2Epred__set_2ECHOICE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).

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

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

tff(c_2Epair_2ECURRY_2E0,type,
    c_2Epair_2ECURRY_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))) ).

tff(c_2Epred__set_2EDELETE_2E0,type,
    c_2Epred__set_2EDELETE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EDELETE_2E2,type,
    c_2Epred__set_2EDELETE_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

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

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

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

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

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

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

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

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

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

tff(c_2Epair_2EFST_2E1,type,
    c_2Epair_2EFST_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27a ) ).

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_2Epred__set_2EIMAGE_2E0,type,
    c_2Epred__set_2EIMAGE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).

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

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

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

tff(c_2Epred__set_2EINJ_2E0,type,
    c_2Epred__set_2EINJ_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EINJ_2E3,type,
    c_2Epred__set_2EINJ_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

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

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

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

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

tff(c_2Ebool_2ELET_2E0,type,
    c_2Ebool_2ELET_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).

tff(c_2Ebool_2ELET_2E2,type,
    c_2Ebool_2ELET_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: 
      !>[A_27a: $tType] : tyop_2Eoption_2Eoption(A_27a) ).

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_2Erelation_2EO_2E0,type,
    c_2Erelation_2EO_2E0: 
      !>[A_27g: $tType,A_27h: $tType,A_27k: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)))) ).

tff(c_2Erelation_2EO_2E2,type,
    c_2Erelation_2EO_2E2: 
      !>[A_27g: $tType,A_27h: $tType,A_27k: $tType] : ( ( tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)) ) ).

tff(c_2Erelation_2ERDOM_2E0,type,
    c_2Erelation_2ERDOM_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Erelation_2ERDOM_2E1,type,
    c_2Erelation_2ERDOM_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EREL__RESTRICT_2E0,type,
    c_2Epred__set_2EREL__RESTRICT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).

tff(c_2Epred__set_2EREL__RESTRICT_2E2,type,
    c_2Epred__set_2EREL__RESTRICT_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).

tff(c_2Erelation_2ERRANGE_2E0,type,
    c_2Erelation_2ERRANGE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ).

tff(c_2Erelation_2ERRANGE_2E1,type,
    c_2Erelation_2ERRANGE_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2ERREFL__EXP_2E0,type,
    c_2Eset__relation_2ERREFL__EXP_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).

tff(c_2Eset__relation_2ERREFL__EXP_2E2,type,
    c_2Eset__relation_2ERREFL__EXP_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).

tff(c_2Eset__relation_2ERRUNIV_2E0,type,
    c_2Eset__relation_2ERRUNIV_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Eset__relation_2ERRUNIV_2E1,type,
    c_2Eset__relation_2ERRUNIV_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).

tff(c_2Eset__relation_2ERRUNIV_2E3,type,
    c_2Eset__relation_2ERRUNIV_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Erelation_2ERSUBSET_2E0,type,
    c_2Erelation_2ERSUBSET_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : 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_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)) ).

tff(c_2Erelation_2ERSUBSET_2E2,type,
    c_2Erelation_2ERSUBSET_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Erelation_2ERUNION_2E0,type,
    c_2Erelation_2ERUNION_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : 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_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))) ).

tff(c_2Erelation_2ERUNION_2E2,type,
    c_2Erelation_2ERUNION_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) ).

tff(c_2Epred__set_2ESING_2E0,type,
    c_2Epred__set_2ESING_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Epred__set_2ESING_2E1,type,
    c_2Epred__set_2ESING_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

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

tff(c_2Epair_2ESND_2E1,type,
    c_2Epair_2ESND_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27b ) ).

tff(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)) ).

tff(c_2Eoption_2ESOME_2E1,type,
    c_2Eoption_2ESOME_2E1: 
      !>[A_27a: $tType] : ( A_27a > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Erelation_2ESTRORD_2E0,type,
    c_2Erelation_2ESTRORD_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Erelation_2ESTRORD_2E1,type,
    c_2Erelation_2ESTRORD_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).

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_2Epair_2ESWAP_2E0,type,
    c_2Epair_2ESWAP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27a,A_27b)) ).

tff(c_2Erelation_2EStrongLinearOrder_2E0,type,
    c_2Erelation_2EStrongLinearOrder_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Erelation_2EStrongLinearOrder_2E1,type,
    c_2Erelation_2EStrongLinearOrder_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(c_2Erelation_2ETC_2E0,type,
    c_2Erelation_2ETC_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Erelation_2ETC_2E1,type,
    c_2Erelation_2ETC_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).

tff(c_2Eoption_2ETHE_2E0,type,
    c_2Eoption_2ETHE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a) ).

tff(c_2Eoption_2ETHE_2E1,type,
    c_2Eoption_2ETHE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Eoption_2Eoption(A_27a) > A_27a ) ).

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_2EUNION_2E0,type,
    c_2Epred__set_2EUNION_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

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

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

tff(c_2Erelation_2EWF_2E0,type,
    c_2Erelation_2EWF_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Erelation_2EWF_2E1,type,
    c_2Erelation_2EWF_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Erelation_2EWeakLinearOrder_2E0,type,
    c_2Erelation_2EWeakLinearOrder_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Erelation_2EWeakLinearOrder_2E1,type,
    c_2Erelation_2EWeakLinearOrder_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Erelation_2EWeakOrder_2E0,type,
    c_2Erelation_2EWeakOrder_2E0: 
      !>[A_27g: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Erelation_2EWeakOrder_2E1,type,
    c_2Erelation_2EWeakOrder_2E1: 
      !>[A_27g: $tType] : ( tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)) > 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_2Eset__relation_2Eacyclic_2E0,type,
    c_2Eset__relation_2Eacyclic_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Eset__relation_2Eacyclic_2E1,type,
    c_2Eset__relation_2Eacyclic_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Eall__choices_2E0,type,
    c_2Eset__relation_2Eall__choices_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Eall__choices_2E1,type,
    c_2Eset__relation_2Eall__choices_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Eantisym_2E0,type,
    c_2Eset__relation_2Eantisym_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Eset__relation_2Eantisym_2E1,type,
    c_2Eset__relation_2Eantisym_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Erelation_2Eantisymmetric_2E0,type,
    c_2Erelation_2Eantisymmetric_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Erelation_2Eantisymmetric_2E1,type,
    c_2Erelation_2Eantisymmetric_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Echain_2E0,type,
    c_2Eset__relation_2Echain_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Echain_2E2,type,
    c_2Eset__relation_2Echain_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

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

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

tff(c_2Eset__relation_2Edomain_2E0,type,
    c_2Eset__relation_2Edomain_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Edomain_2E1,type,
    c_2Eset__relation_2Edomain_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Efchains_2E0,type,
    c_2Eset__relation_2Efchains_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Efchains_2E1,type,
    c_2Eset__relation_2Efchains_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Efinite__prefixes_2E0,type,
    c_2Eset__relation_2Efinite__prefixes_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Efinite__prefixes_2E2,type,
    c_2Eset__relation_2Efinite__prefixes_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Eget__min_2E0,type,
    c_2Eset__relation_2Eget__min_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(A_27a))) ).

tff(c_2Eset__relation_2Eget__min_2E2,type,
    c_2Eset__relation_2Eget__min_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)) ) > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Erelation_2Eirreflexive_2E0,type,
    c_2Erelation_2Eirreflexive_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Erelation_2Eirreflexive_2E1,type,
    c_2Erelation_2Eirreflexive_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Eirreflexive_2E0,type,
    c_2Eset__relation_2Eirreflexive_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Eirreflexive_2E2,type,
    c_2Eset__relation_2Eirreflexive_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Elinear__order_2E0,type,
    c_2Eset__relation_2Elinear__order_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Elinear__order_2E2,type,
    c_2Eset__relation_2Elinear__order_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Emaximal__elements_2E0,type,
    c_2Eset__relation_2Emaximal__elements_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Eset__relation_2Emaximal__elements_2E2,type,
    c_2Eset__relation_2Emaximal__elements_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Eminimal__elements_2E0,type,
    c_2Eset__relation_2Eminimal__elements_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Eset__relation_2Eminimal__elements_2E2,type,
    c_2Eset__relation_2Eminimal__elements_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Enth__min_2E0,type,
    c_2Eset__relation_2Enth__min_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))) ).

tff(c_2Eset__relation_2Enth__min_2E3,type,
    c_2Eset__relation_2Enth__min_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)) * tyop_2Enum_2Enum ) > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Eset__relation_2Enum__order_2E0,type,
    c_2Eset__relation_2Enum__order_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))) ).

tff(c_2Eset__relation_2Enum__order_2E2,type,
    c_2Eset__relation_2Enum__order_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Epartial__order_2E0,type,
    c_2Eset__relation_2Epartial__order_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Epartial__order_2E2,type,
    c_2Eset__relation_2Epartial__order_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Eper_2E0,type,
    c_2Eset__relation_2Eper_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Eper_2E2,type,
    c_2Eset__relation_2Eper_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Eper__restrict_2E0,type,
    c_2Eset__relation_2Eper__restrict_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).

tff(c_2Eset__relation_2Eper__restrict_2E2,type,
    c_2Eset__relation_2Eper__restrict_2E2: 
      !>[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) ) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Erange_2E0,type,
    c_2Eset__relation_2Erange_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Erange_2E1,type,
    c_2Eset__relation_2Erange_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Ercomp_2E0,type,
    c_2Eset__relation_2Ercomp_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))) ).

tff(c_2Eset__relation_2Ercomp_2E2,type,
    c_2Eset__relation_2Ercomp_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).

tff(c_2Erelation_2Ereflexive_2E0,type,
    c_2Erelation_2Ereflexive_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Erelation_2Ereflexive_2E1,type,
    c_2Erelation_2Ereflexive_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Ereflexive_2E0,type,
    c_2Eset__relation_2Ereflexive_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Ereflexive_2E2,type,
    c_2Eset__relation_2Ereflexive_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Erel__to__reln_2E0,type,
    c_2Eset__relation_2Erel__to__reln_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Erel__to__reln_2E1,type,
    c_2Eset__relation_2Erel__to__reln_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Ereln__to__rel_2E0,type,
    c_2Eset__relation_2Ereln__to__rel_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).

tff(c_2Eset__relation_2Ereln__to__rel_2E1,type,
    c_2Eset__relation_2Ereln__to__rel_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) ).

tff(c_2Eset__relation_2Ereln__to__rel_2E3,type,
    c_2Eset__relation_2Ereln__to__rel_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) * A_27a * A_27b ) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Errestrict_2E0,type,
    c_2Eset__relation_2Errestrict_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))) ).

tff(c_2Eset__relation_2Errestrict_2E2,type,
    c_2Eset__relation_2Errestrict_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Estrict_2E0,type,
    c_2Eset__relation_2Estrict_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Estrict_2E1,type,
    c_2Eset__relation_2Estrict_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Estrict__linear__order_2E0,type,
    c_2Eset__relation_2Estrict__linear__order_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Estrict__linear__order_2E2,type,
    c_2Eset__relation_2Estrict__linear__order_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Etc_2E0,type,
    c_2Eset__relation_2Etc_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Etc_2E1,type,
    c_2Eset__relation_2Etc_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Etc_2E2,type,
    c_2Eset__relation_2Etc_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Epair_2Eprod(A_27a,A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Erelation_2Etransitive_2E0,type,
    c_2Erelation_2Etransitive_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Erelation_2Etransitive_2E1,type,
    c_2Erelation_2Etransitive_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Etransitive_2E0,type,
    c_2Eset__relation_2Etransitive_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Eset__relation_2Etransitive_2E1,type,
    c_2Eset__relation_2Etransitive_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Euniv__reln_2E0,type,
    c_2Eset__relation_2Euniv__reln_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Euniv__reln_2E1,type,
    c_2Eset__relation_2Euniv__reln_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Eupper__bounds_2E0,type,
    c_2Eset__relation_2Eupper__bounds_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Eset__relation_2Eupper__bounds_2E2,type,
    c_2Eset__relation_2Eupper__bounds_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2E_2C_2E0(A_27a,A_27a),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_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: A_27a,X1_2E0: A_27c] : ( c_2Epair_2E_2C_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Epair_2E_2C_2E0(A_27a,A_27c),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_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epair_2E_2C_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27b,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27b,A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,A_27b)),c_2Epair_2E_2C_2E0(A_27b,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: A_27b,X1_2E0: A_27c] : ( c_2Epair_2E_2C_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),c_2Epair_2E_2C_2E0(A_27b,A_27c),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_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: A_27c,X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Epair_2E_2C_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27b),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),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_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(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_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),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_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECHOICE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Epred__set_2ECHOICE_2E0(A_27a),X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Epred__set_2EDELETE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EDELETE_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDELETE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDELETE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

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

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

tff(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDISJOINT_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EDISJOINT_2E0(A_27b),X0_2E0),X1_2E0) ) ).

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

tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27a)] : ( c_2Epair_2EFST_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2EFST_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),X0_2E0) ) ).

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

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a),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_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),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)),c_2Epred__set_2EIMAGE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).

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

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

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27c),X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).

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

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

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

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Ebool_2ELET_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),X1_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Ebool_2ELET_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ebool_2ELET_2E0(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),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(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2EO_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2ERDOM_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERDOM_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EREL__RESTRICT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EREL__RESTRICT_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2ERRANGE_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERRANGE_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERRANGE_2E0(A_27b,A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2ERREFL__EXP_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2ERREFL__EXP_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eset__relation_2ERREFL__EXP_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2ERRUNIV_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2ERRUNIV_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERRUNIV_2E0(A_27a),X0_2E0) ) ).

tff(arityeq3_2Ec_2Eset__relation_2ERRUNIV_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Eset__relation_2ERRUNIV_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERRUNIV_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERSUBSET_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2ERSUBSET_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2ERUNION_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERUNION_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERUNION_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2ESING_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESING_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27a)] : ( c_2Epair_2ESND_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,c_2Epair_2ESND_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2ESND_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Eoption_2ESOME_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2ESTRORD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ESTRORD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E0(A_27a),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_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),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_2Erelation_2EStrongLinearOrder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EStrongLinearOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ETC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Eoption_2ETHE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),A_27a,c_2Eoption_2ETHE_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27b_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWeakLinearOrder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWeakLinearOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWeakLinearOrder_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWeakOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E0(A_27a),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_2Eset__relation_2Eacyclic_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eacyclic_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Eall__choices_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eall__choices_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eall__choices_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Eantisym_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eantisym_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2Eantisymmetric_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eantisymmetric_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Echain_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Echain_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Echain_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(A_27a),X0_2E0) ) ).

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

tff(arityeq1_2Ec_2Eset__relation_2Edomain_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Edomain_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Edomain_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Efchains_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Efchains_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Efchains_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Efinite__prefixes_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Efinite__prefixes_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Efinite__prefixes_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Efinite__prefixes_2E2(A_27b,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Efinite__prefixes_2E0(A_27b,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Efinite__prefixes_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Efinite__prefixes_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Eget__min_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))] : ( c_2Eset__relation_2Eget__min_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(A_27a)),c_2Eset__relation_2Eget__min_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eirreflexive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Eirreflexive_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eirreflexive_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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eirreflexive_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Elinear__order_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Elinear__order_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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Elinear__order_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Emaximal__elements_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Emaximal__elements_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Emaximal__elements_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Eminimal__elements_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eminimal__elements_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Eminimal__elements_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Eset__relation_2Enth__min_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X2_2E0: tyop_2Enum_2Enum] : ( c_2Eset__relation_2Enth__min_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),c_2Eset__relation_2Enth__min_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Enum__order_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Enum__order_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Enum__order_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Epartial__order_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Epartial__order_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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Epartial__order_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Eper_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eper_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eper_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Eper__restrict_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eper__restrict_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Eper__restrict_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Erange_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Erange_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E0(A_27b,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Erange_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Ercomp_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ercomp_2E2(A_27a,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool)),c_2Eset__relation_2Ercomp_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Ercomp_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ercomp_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Eset__relation_2Ercomp_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Ereflexive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Ereflexive_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ereflexive_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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Ereflexive_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Erel__to__reln_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Erel__to__reln_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq3_2Ec_2Eset__relation_2Ereln__to__rel_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: A_27a,X2_2E0: A_27b] : ( c_2Eset__relation_2Ereln__to__rel_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E0(A_27a,A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ereln__to__rel_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E0(A_27b,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ereln__to__rel_2E1(A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E0(A_27c,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Errestrict_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Errestrict_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Errestrict_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Estrict_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Estrict_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Estrict__linear__order_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Estrict__linear__order_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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict__linear__order_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Etc_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Etc_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Etc_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(A_27a,A_27a)] : ( c_2Eset__relation_2Etc_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Etransitive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Euniv__reln_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Euniv__reln_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Euniv__reln_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Eupper__bounds_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eupper__bounds_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Eupper__bounds_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Eupper__bounds_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eupper__bounds_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Eupper__bounds_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

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

tff(thm_2Eset__relation_2Edomain__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V1x_2E0: A_27a,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1x_2E0),V0r_2E0))
        <=> ? [V2y_2E0: A_27b] : p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0),V0r_2E0)) )
     => ( ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0r_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V1x_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1x_2E0),V0r_2E0)) )
       => ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Edomain_2E1(A_27a,A_27b,V0r_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0r_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Erange__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V1y_2E0: A_27a,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1y_2E0),V0r_2E0))
        <=> ? [V2x_2E0: A_27b] : p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(A_27b,A_27a,V2x_2E0,V1y_2E0),V0r_2E0)) )
     => ( ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0r_2E0),V1y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V1y_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1y_2E0),V0r_2E0)) )
       => ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Erange_2E1(A_27a,A_27b,V0r_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0r_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Errestrict__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))))] :
      ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V3y_2E0),V0r_2E0),V1s_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V0r_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0)) ) )
     => ( ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F0_2E0,V0r_2E0),V1s_2E0),V2x_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V3y_2E0),V0r_2E0),V1s_2E0)) )
       => ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Errestrict_2E2(A_27a,V0r_2E0,V1s_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F0_2E0,V0r_2E0),V1s_2E0))) ) ) ) ).

tff(thm_2Eset__relation_2Ercomp__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))))] :
      ( ! [V2x_2E0: A_27a,V0r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V3y_2E0: A_27b,V1r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V0r1_2E0),V3y_2E0),V1r2_2E0))
        <=> ? [V4z_2E0: A_27c] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(A_27a,A_27c,V2x_2E0,V4z_2E0),V0r1_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(A_27c,A_27b,V4z_2E0,V3y_2E0),V1r2_2E0)) ) )
     => ( ! [V0r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V1r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0,V0r1_2E0),V1r2_2E0),V2x_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V0r1_2E0),V3y_2E0),V1r2_2E0)) )
       => ! [V0r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V1r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ercomp_2E2(A_27a,A_27b,A_27c,V0r1_2E0,V1r2_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0,V0r1_2E0),V1r2_2E0))) ) ) ) ).

tff(thm_2Eset__relation_2Estrict__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))] :
      ( ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V1x_2E0),V2y_2E0),V0r_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),V0r_2E0))
            & ( V1x_2E0 != V2y_2E0 ) ) )
     => ( ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0,V0r_2E0),V1x_2E0),V2y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V1x_2E0),V2y_2E0),V0r_2E0)) )
       => ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Estrict_2E1(A_27a,V0r_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0,V0r_2E0))) ) ) ) ).

tff(thm_2Eset__relation_2Euniv__reln__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))] :
      ( ! [V1x1_2E0: A_27a,V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x2_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V1x1_2E0),V0xs_2E0),V2x2_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V1x1_2E0,V0xs_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27a,V2x2_2E0,V0xs_2E0)) ) )
     => ( ! [V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x1_2E0: A_27a,V2x2_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0,V0xs_2E0),V1x1_2E0),V2x2_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x1_2E0,V2x2_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V1x1_2E0),V0xs_2E0),V2x2_2E0)) )
       => ! [V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Euniv__reln_2E1(A_27a,V0xs_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0,V0xs_2E0))) ) ) ) ).

tff(thm_2Eset__relation_2Efinite__prefixes__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V2e_2E0: A_27b,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V3e_27_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V2e_2E0),V0r_2E0),V3e_27_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3e_27_2E0,c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V3e_27_2E0,V2e_2E0),V0r_2E0)) )
     => ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,V0r_2E0,V1s_2E0))
        <=> ! [V2e_2E0: A_27b] :
              ( p(c_2Ebool_2EIN_2E2(A_27b,V2e_2E0,V1s_2E0))
             => p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V2e_2E0),V0r_2E0)))) ) ) ) ).

tff(thm_2Eset__relation_2Etc__def,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1x_27_2E0: tyop_2Epair_2Eprod(A_27a,A_27a)] :
      ( p(c_2Eset__relation_2Etc_2E2(A_27a,V0x_2E0,V1x_27_2E0))
    <=> ! [V2tc_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
          ( ! [V3a0_2E0: tyop_2Epair_2Eprod(A_27a,A_27a)] :
              ( ( ? [V4x_2E0: A_27a,V5y_2E0: A_27a] :
                    ( ( V3a0_2E0 = c_2Epair_2E_2C_2E2(A_27a,A_27a,V4x_2E0,V5y_2E0) )
                    & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0x_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V4x_2E0,V5y_2E0))) )
                | ? [V6x_2E0: A_27a,V7y_2E0: A_27a] :
                    ( ( V3a0_2E0 = c_2Epair_2E_2C_2E2(A_27a,A_27a,V6x_2E0,V7y_2E0) )
                    & ? [V8z_2E0: A_27a] :
                        ( p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V2tc_27_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V6x_2E0,V8z_2E0)))
                        & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V2tc_27_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V8z_2E0,V7y_2E0))) ) ) )
             => p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V2tc_27_2E0,V3a0_2E0)) )
         => p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V2tc_27_2E0,V1x_27_2E0)) ) ) ).

tff(thm_2Eset__relation_2Eacyclic__def,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V0r_2E0))
    <=> ! [V1x_2E0: A_27a] : ~ p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V1x_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0))) ) ).

tff(thm_2Eset__relation_2Ereflexive__def,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Ereflexive_2E2(A_27a,V0r_2E0,V1s_2E0))
    <=> ! [V2x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
         => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V2x_2E0),V0r_2E0)) ) ) ).

tff(thm_2Eset__relation_2Eirreflexive__def,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Eirreflexive_2E2(A_27a,V0r_2E0,V1s_2E0))
    <=> ! [V2x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
         => ~ p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V2x_2E0),V0r_2E0)) ) ) ).

tff(thm_2Eset__relation_2Etransitive__def,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Etransitive_2E1(A_27a,V0r_2E0))
    <=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),V0r_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2y_2E0,V3z_2E0),V0r_2E0)) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V3z_2E0),V0r_2E0)) ) ) ).

tff(thm_2Eset__relation_2Eantisym__def,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Eantisym_2E1(A_27a,V0r_2E0))
    <=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),V0r_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2y_2E0,V1x_2E0),V0r_2E0)) )
         => ( V1x_2E0 = V2y_2E0 ) ) ) ).

tff(thm_2Eset__relation_2Epartial__order__def,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Epartial__order_2E2(A_27a,V0r_2E0,V1s_2E0))
    <=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V0r_2E0),V1s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V0r_2E0),V1s_2E0))
        & p(c_2Eset__relation_2Etransitive_2E1(A_27a,V0r_2E0))
        & p(c_2Eset__relation_2Ereflexive_2E2(A_27a,V0r_2E0,V1s_2E0))
        & p(c_2Eset__relation_2Eantisym_2E1(A_27a,V0r_2E0)) ) ) ).

tff(thm_2Eset__relation_2Elinear__order__def,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0r_2E0,V1s_2E0))
    <=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V0r_2E0),V1s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V0r_2E0),V1s_2E0))
        & p(c_2Eset__relation_2Etransitive_2E1(A_27a,V0r_2E0))
        & p(c_2Eset__relation_2Eantisym_2E1(A_27a,V0r_2E0))
        & ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
              & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0)) )
           => ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V0r_2E0))
              | p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V3y_2E0,V2x_2E0),V0r_2E0)) ) ) ) ) ).

tff(thm_2Eset__relation_2Estrict__linear__order__def,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,V0r_2E0,V1s_2E0))
    <=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V0r_2E0),V1s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V0r_2E0),V1s_2E0))
        & p(c_2Eset__relation_2Etransitive_2E1(A_27a,V0r_2E0))
        & ! [V2x_2E0: A_27a] : ~ p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V2x_2E0),V0r_2E0))
        & ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
              & p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V1s_2E0))
              & ( V3x_2E0 != V4y_2E0 ) )
           => ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V3x_2E0,V4y_2E0),V0r_2E0))
              | p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V4y_2E0,V3x_2E0),V0r_2E0)) ) ) ) ) ).

tff(thm_2Eset__relation_2Ereln__to__rel__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2x_27_2E0: A_27b] : ( c_2Eset__relation_2Ereln__to__rel_2E3(A_27a,A_27b,V0r_2E0,V1x_2E0,V2x_27_2E0) = c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2x_27_2E0),V0r_2E0) ) ).

tff(thm_2Eset__relation_2Erel__to__reln__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))] :
      ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0R_2E0),V1x_2E0),V2y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0),app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0)) )
     => ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,V0R_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0R_2E0))) ) ) ).

tff(thm_2Eset__relation_2ERRUNIV__def,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2x_27_2E0: A_27a] :
      ( p(c_2Eset__relation_2ERRUNIV_2E3(A_27a,V0s_2E0,V1x_2E0,V2x_27_2E0))
    <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V2x_27_2E0,V0s_2E0)) ) ) ).

tff(thm_2Eset__relation_2ERREFL__EXP__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V1s_2E0),V2x_2E0),V3y_2E0))
        <=> ( ( V2x_2E0 = V3y_2E0 )
            & ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0)) ) )
     => ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2ERREFL__EXP_2E2(A_27a,V0R_2E0,V1s_2E0) = c_2Erelation_2ERUNION_2E2(A_27a,A_27a,V0R_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V1s_2E0)) ) ) ).

tff(thm_2Eset__relation_2Emaximal__elements__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V2x_2E0: A_27a,V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2x_2E0),V0xs_2E0),V1r_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0xs_2E0))
            & ! [V3x_27_2E0: A_27a] :
                ( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_27_2E0,V0xs_2E0))
                  & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3x_27_2E0),V1r_2E0)) )
               => ( V2x_2E0 = V3x_27_2E0 ) ) ) )
     => ( ! [V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0xs_2E0),V1r_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2x_2E0),V0xs_2E0),V1r_2E0)) )
       => ! [V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V0xs_2E0,V1r_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0xs_2E0),V1r_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Eminimal__elements__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V2x_2E0: A_27a,V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2x_2E0),V0xs_2E0),V1r_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0xs_2E0))
            & ! [V3x_27_2E0: A_27a] :
                ( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_27_2E0,V0xs_2E0))
                  & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V3x_27_2E0,V2x_2E0),V1r_2E0)) )
               => ( V2x_2E0 = V3x_27_2E0 ) ) ) )
     => ( ! [V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0xs_2E0),V1r_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2x_2E0),V0xs_2E0),V1r_2E0)) )
       => ! [V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0xs_2E0,V1r_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0xs_2E0),V1r_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Echain__def,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Echain_2E2(A_27a,V0s_2E0,V1r_2E0))
    <=> ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
          ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V0s_2E0)) )
         => ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V1r_2E0))
            | p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V3y_2E0,V2x_2E0),V1r_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Eupper__bounds__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V2x_2E0: A_27a,V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2x_2E0),V1r_2E0),V0s_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Erange_2E1(A_27a,A_27b,V1r_2E0)))
            & ! [V3y_2E0: A_27b] :
                ( p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V0s_2E0))
               => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(A_27b,A_27a,V3y_2E0,V2x_2E0),V1r_2E0)) ) ) )
     => ( ! [V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1r_2E0),V0s_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2x_2E0),V1r_2E0),V0s_2E0)) )
       => ! [V0s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eupper__bounds_2E2(A_27a,A_27b,V0s_2E0,V1r_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1r_2E0),V0s_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Efchains__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
      ( ! [V1k_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1k_2E0),V0r_2E0))
        <=> ( p(c_2Eset__relation_2Echain_2E2(A_27a,V1k_2E0,V0r_2E0))
            & ( V1k_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) )
            & ! [V2C_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                ( ( p(c_2Eset__relation_2Echain_2E2(A_27a,V2C_2E0,V0r_2E0))
                  & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2C_2E0,V1k_2E0))
                  & ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,c_2Eset__relation_2Eupper__bounds_2E2(A_27a,A_27a,V2C_2E0,V0r_2E0),V2C_2E0),V1k_2E0) != c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
               => p(c_2Ebool_2EIN_2E2(A_27a,c_2Epred__set_2ECHOICE_2E1(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,c_2Eset__relation_2Eupper__bounds_2E2(A_27a,A_27a,V2C_2E0,V0r_2E0),V2C_2E0)),c_2Eset__relation_2Eminimal__elements_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,c_2Eset__relation_2Eupper__bounds_2E2(A_27a,A_27a,V2C_2E0,V0r_2E0),V2C_2E0),V1k_2E0),V0r_2E0))) ) ) )
     => ( ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1k_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0r_2E0),V1k_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1k_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1k_2E0),V0r_2E0)) )
       => ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Efchains_2E1(A_27a,V0r_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0r_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Eper__def,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1xss_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Eper_2E2(A_27a,V0xs_2E0,V1xss_2E0))
    <=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V1xss_2E0),V0xs_2E0))
        & ~ p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),V1xss_2E0))
        & ! [V2xs1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3xs2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2xs1_2E0,V1xss_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3xs2_2E0,V1xss_2E0))
              & ( V2xs1_2E0 != V3xs2_2E0 ) )
           => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V2xs1_2E0,V3xs2_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Eper__restrict__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))] :
      ( ! [V1xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xss_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2xs_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V1xs_2E0),V0xss_2E0),V2xs_27_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EINTER_2E2(A_27a,V2xs_27_2E0,V1xs_2E0),c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2xs_27_2E0,V0xss_2E0)) )
     => ! [V0xss_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eper__restrict_2E2(A_27a,V0xss_2E0,V1xs_2E0) = c_2Epred__set_2EDELETE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V1xs_2E0),V0xss_2E0)),c_2Epred__set_2EEMPTY_2E0(A_27a)) ) ) ).

tff(thm_2Eset__relation_2Eall__choices__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
      ( ! [V0xss_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1choice_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Ebool),F1_2E0,V0xss_2E0),V1choice_2E0))
        <=> ! [V2xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2xs_2E0,V0xss_2E0))
             => p(c_2Ebool_2EIN_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,V1choice_2E0,V2xs_2E0),V2xs_2E0)) ) )
     => ( ! [V0xss_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1choice_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a)] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0xss_2E0),V1choice_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,V1choice_2E0,V0xss_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Ebool),F1_2E0,V0xss_2E0),V1choice_2E0)) )
       => ! [V0xss_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eall__choices_2E1(A_27a,V0xss_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0xss_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Enum__order__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))))] :
      ( ! [V2x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3y_2E0: A_27a,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V1s_2E0),V3y_2E0),V0f_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0))
            & p(c_2Earithmetic_2E_3C_3D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V3y_2E0))) ) )
     => ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2x_2E0: A_27a,V3y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F0_2E0,V1s_2E0),V0f_2E0),V2x_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V1s_2E0),V3y_2E0),V0f_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Enum__order_2E2(A_27a,V0f_2E0,V1s_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F0_2E0,V1s_2E0),V0f_2E0))) ) ) ) ).

tff(thm_2Eset__relation_2Eget__min__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))] :
      ( ! [V3mins_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a),F0_2E0,V3mins_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ESING_2E1(A_27a,V3mins_2E0),c_2Eoption_2ESOME_2E1(A_27a,c_2Epred__set_2ECHOICE_2E1(A_27a,V3mins_2E0)),c_2Eoption_2ENONE_2E0(A_27a)) )
     => ! [V0r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eget__min_2E2(A_27a,V0r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0,V2r_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a),F0_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V1s_2E0,V2r_2E0),V0r_27_2E0)) ) ) ).

tff(thm_2Eset__relation_2Eacyclic__bigunion,axiom,
    ! [A_27a: $tType,V0rs_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( ! [V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0,V0rs_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0,V0rs_2E0))
              & ( V1r_2E0 != V2r_27_2E0 ) )
           => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V1r_2E0),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V1r_2E0)),c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V2r_27_2E0),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V2r_27_2E0)))) )
        & ! [V3r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r_2E0,V0rs_2E0))
           => p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V3r_2E0)) ) )
     => p(c_2Eset__relation_2Eacyclic_2E1(A_27a,c_2Epred__set_2EBIGUNION_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),V0rs_2E0))) ) ).

tff(thm_2Eset__relation_2Eacyclic__SWAP,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eacyclic_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2ESWAP_2E0(A_27a,A_27a),V0r_2E0)) = c_2Eset__relation_2Eacyclic_2E1(A_27a,V0r_2E0) ) ).

tff(thm_2Eset__relation_2Eacyclic__irreflexive,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1x_2E0: A_27a] :
      ( p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V0r_2E0))
     => ~ p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V1x_2E0),V0r_2E0)) ) ).

tff(thm_2Eset__relation_2Eacyclic__rrestrict,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V0r_2E0))
     => p(c_2Eset__relation_2Eacyclic_2E1(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V0r_2E0,V1s_2E0))) ) ).

tff(thm_2Eset__relation_2Etc__mono,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V1r_2E0,V0s_2E0))
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Eset__relation_2Etc_2E1(A_27a,V1r_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0s_2E0))) ) ).

tff(thm_2Eset__relation_2Etc__idemp,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Etc_2E1(A_27a,c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)) = c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0) ) ).

tff(thm_2Eset__relation_2Esubset__tc,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0r_2E0,c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0))) ).

tff(thm_2Eset__relation_2Etc__closure,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V1r_2E0,c_2Eset__relation_2Etc_2E1(A_27a,V0s_2E0)))
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Eset__relation_2Etc_2E1(A_27a,V1r_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0s_2E0))) ) ).

tff(thm_2Eset__relation_2Etc__ind,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1tc_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V0r_2E0))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V2x_2E0),V3y_2E0)) )
        & ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
            ( ? [V6z_2E0: A_27a] :
                ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V4x_2E0),V6z_2E0))
                & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V6z_2E0),V5y_2E0)) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V4x_2E0),V5y_2E0)) ) )
     => ! [V7x_2E0: A_27a,V8y_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V7x_2E0,V8y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V7x_2E0),V8y_2E0)) ) ) ).

tff(thm_2Eset__relation_2Erextension,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
      ( ( V0s_2E0 = V1t_2E0 )
    <=> ! [V2x_2E0: A_27a,V3y_2E0: A_27b] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0),V0s_2E0) = c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0),V1t_2E0) ) ) ).

tff(thm_2Eset__relation_2Ein__domain,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Eset__relation_2Edomain_2E1(A_27a,A_27b,V1r_2E0)))
    <=> ? [V2y_2E0: A_27b] : p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V0x_2E0,V2y_2E0),V1r_2E0)) ) ).

tff(thm_2Eset__relation_2Ein__range,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27a,V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,c_2Eset__relation_2Erange_2E1(A_27a,A_27b,V1r_2E0)))
    <=> ? [V2x_2E0: A_27b] : p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(A_27b,A_27a,V2x_2E0,V0y_2E0),V1r_2E0)) ) ).

tff(thm_2Eset__relation_2Ein__dom__rg,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a,V2r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0),V2r_2E0))
     => ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Eset__relation_2Edomain_2E1(A_27a,A_27b,V2r_2E0)))
        & p(c_2Ebool_2EIN_2E2(A_27b,V0y_2E0,c_2Eset__relation_2Erange_2E1(A_27b,A_27a,V2r_2E0))) ) ) ).

tff(thm_2Eset__relation_2Edomain__mono,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1r_2E0,V0r_27_2E0))
     => p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27b,V1r_2E0),c_2Eset__relation_2Edomain_2E1(A_27a,A_27b,V0r_27_2E0))) ) ).

tff(thm_2Eset__relation_2Erange__mono,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1r_2E0,V0r_27_2E0))
     => p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Eset__relation_2Erange_2E1(A_27b,A_27a,V1r_2E0),c_2Eset__relation_2Erange_2E1(A_27b,A_27a,V0r_27_2E0))) ) ).

tff(thm_2Eset__relation_2Ein__rrestrict,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a,V2r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0x_2E0,V1y_2E0),c_2Eset__relation_2Errestrict_2E2(A_27a,V2r_2E0,V3s_2E0)))
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0x_2E0,V1y_2E0),V2r_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V3s_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V1y_2E0,V3s_2E0)) ) ) ).

tff(thm_2Eset__relation_2Ein__rrestrict__alt,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Epair_2Eprod(A_27a,A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0x_2E0,c_2Eset__relation_2Errestrict_2E2(A_27a,V2r_2E0,V1s_2E0)))
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0x_2E0,V2r_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,c_2Epair_2EFST_2E1(A_27a,A_27a,V0x_2E0),V1s_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,c_2Epair_2ESND_2E1(A_27a,A_27a,V0x_2E0),V1s_2E0)) ) ) ).

tff(thm_2Eset__relation_2Errestrict__SUBSET,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0s_2E0),V1r_2E0)) ).

tff(thm_2Eset__relation_2Errestrict__union,axiom,
    ! [A_27a: $tType,V0r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Errestrict_2E2(A_27a,c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0r1_2E0,V1r2_2E0),V2s_2E0) = c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Eset__relation_2Errestrict_2E2(A_27a,V0r1_2E0,V2s_2E0),c_2Eset__relation_2Errestrict_2E2(A_27a,V1r2_2E0,V2s_2E0)) ) ).

tff(thm_2Eset__relation_2Errestrict__rrestrict,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Errestrict_2E2(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V0r_2E0,V1x_2E0),V2y_2E0) = c_2Eset__relation_2Errestrict_2E2(A_27a,V0r_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1x_2E0,V2y_2E0)) ) ).

tff(thm_2Eset__relation_2Edomain__rrestrict__SUBSET,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0s_2E0)),V0s_2E0)) ).

tff(thm_2Eset__relation_2Erange__rrestrict__SUBSET,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Erange_2E1(A_27a,A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0s_2E0)),V0s_2E0)) ).

tff(thm_2Eset__relation_2Estrict__rrestrict,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Estrict_2E1(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V0r_2E0,V1s_2E0)) = c_2Eset__relation_2Errestrict_2E2(A_27a,c_2Eset__relation_2Estrict_2E1(A_27a,V0r_2E0),V1s_2E0) ) ).

tff(thm_2Eset__relation_2Efinite__prefixes__subset__s,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,V0r_2E0,V1s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27b,V2s_27_2E0,V1s_2E0)) )
     => p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,V0r_2E0,V2s_27_2E0)) ) ).

tff(thm_2Eset__relation_2Efinite__prefixes__subset__r,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,V0r_2E0,V2s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1r_27_2E0,V0r_2E0)) )
     => p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,V1r_27_2E0,V2s_2E0)) ) ).

tff(thm_2Eset__relation_2Efinite__prefixes__subset__rs,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V3s_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,V0r_2E0,V1s_2E0))
     => ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V2r_27_2E0,V0r_2E0))
       => ( p(c_2Epred__set_2ESUBSET_2E2(A_27b,V3s_27_2E0,V1s_2E0))
         => p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,V2r_27_2E0,V3s_27_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Efinite__prefixes__subset,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,V0r_2E0,V1s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2s_27_2E0,V1s_2E0)) )
     => ( p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,V0r_2E0,V2s_27_2E0))
        & p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V0r_2E0,V2s_27_2E0),V2s_27_2E0)) ) ) ).

tff(thm_2Eset__relation_2Efinite__prefixes__union,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2s1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,V0r1_2E0,V2s1_2E0))
        & p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,V1r2_2E0,V3s2_2E0)) )
     => p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0r1_2E0,V1r2_2E0),c_2Epred__set_2EINTER_2E2(A_27b,V2s1_2E0,V3s2_2E0))) ) ).

tff(thm_2Eset__relation_2Efinite__prefixes__comp,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))))] :
      ( ! [V3s2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4x_2E0: A_27b,V1r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V3s2_2E0),V4x_2E0),V1r2_2E0))
        <=> ? [V5y_2E0: A_27c] :
              ( p(c_2Ebool_2EIN_2E2(A_27c,V5y_2E0,V3s2_2E0))
              & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(A_27b,A_27c,V4x_2E0,V5y_2E0),V1r2_2E0)) ) )
     => ( ! [V3s2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V1r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V4x_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V3s2_2E0),V1r2_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,V4x_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V3s2_2E0),V4x_2E0),V1r2_2E0)) )
       => ! [V0r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V2s1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
            ( ( p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,V0r1_2E0,V2s1_2E0))
              & p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27b,A_27c,V1r2_2E0,V3s2_2E0))
              & p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V3s2_2E0),V1r2_2E0)),V2s1_2E0)) )
           => p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27c,c_2Eset__relation_2Ercomp_2E2(A_27a,A_27c,A_27b,V0r1_2E0,V1r2_2E0),V3s2_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Efinite__prefixes__inj__image,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5x_2E0: A_27a,V6y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)))),F0_2E0,V0f_2E0),V1r_2E0),V5x_2E0),V6y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27b,A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0),app_2E2(A_27a,A_27b,V0f_2E0,V6y_2E0)),c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V5x_2E0,V6y_2E0),V1r_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
                ( ( app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V4y_2E0) )
               => ( V3x_2E0 = V4y_2E0 ) )
            & p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,V1r_2E0,V2s_2E0)) )
         => p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27b,A_27b,c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)))),F0_2E0,V0f_2E0),V1r_2E0))),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2s_2E0))) ) ) ).

tff(thm_2Eset__relation_2Efinite__prefixes__range,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,V0r_2E0,V1s_2E0))
        & p(c_2Epred__set_2EDISJOINT_2E2(A_27b,V2t_2E0,c_2Eset__relation_2Erange_2E1(A_27b,A_27a,V0r_2E0))) )
     => p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27b,V0r_2E0,c_2Epred__set_2EUNION_2E2(A_27b,V1s_2E0,V2t_2E0))) ) ).

tff(thm_2Eset__relation_2Etc__rules,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),V0r_2E0))
         => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0))) )
      & ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
          ( ? [V5z_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V3x_2E0,V5z_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
              & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V5z_2E0,V4y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0))) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V3x_2E0,V4y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0))) ) ) ).

tff(thm_2Eset__relation_2Etc__cases,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2y_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),V0r_2E0))
        | ? [V3z_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V3z_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
            & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V3z_2E0,V2y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0))) ) ) ) ).

tff(thm_2Eset__relation_2Etc__strongind,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1tc_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V0r_2E0))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V2x_2E0),V3y_2E0)) )
        & ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
            ( ? [V6z_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V4x_2E0,V6z_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
                & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V4x_2E0),V6z_2E0))
                & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V6z_2E0,V5y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
                & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V6z_2E0),V5y_2E0)) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V4x_2E0),V5y_2E0)) ) )
     => ! [V7x_2E0: A_27a,V8y_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V7x_2E0,V8y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V7x_2E0),V8y_2E0)) ) ) ).

tff(thm_2Eset__relation_2Etc__cases__right,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2y_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),V0r_2E0))
        | ? [V3z_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V3z_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
            & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V3z_2E0,V2y_2E0),V0r_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Etc__cases__left,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2y_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),V0r_2E0))
        | ? [V3z_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V3z_2E0),V0r_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V3z_2E0,V2y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0))) ) ) ) ).

tff(thm_2Eset__relation_2Etc__ind__left,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1tc_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V0r_2E0))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V2x_2E0),V3y_2E0)) )
        & ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
            ( ? [V6z_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V4x_2E0,V6z_2E0),V0r_2E0))
                & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V6z_2E0),V5y_2E0)) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V4x_2E0),V5y_2E0)) ) )
     => ! [V7x_2E0: A_27a,V8y_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V7x_2E0,V8y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V7x_2E0),V8y_2E0)) ) ) ).

tff(thm_2Eset__relation_2Etc__strongind__left,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1tc_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V0r_2E0))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V2x_2E0),V3y_2E0)) )
        & ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
            ( ? [V6z_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V4x_2E0,V6z_2E0),V0r_2E0))
                & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V6z_2E0,V5y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
                & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V6z_2E0),V5y_2E0)) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V4x_2E0),V5y_2E0)) ) )
     => ! [V7x_2E0: A_27a,V8y_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V7x_2E0,V8y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V7x_2E0),V8y_2E0)) ) ) ).

tff(thm_2Eset__relation_2Etc__ind__right,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1tc_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V0r_2E0))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V2x_2E0),V3y_2E0)) )
        & ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
            ( ? [V6z_2E0: A_27a] :
                ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V4x_2E0),V6z_2E0))
                & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V6z_2E0,V5y_2E0),V0r_2E0)) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V4x_2E0),V5y_2E0)) ) )
     => ! [V7x_2E0: A_27a,V8y_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V7x_2E0,V8y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V7x_2E0),V8y_2E0)) ) ) ).

tff(thm_2Eset__relation_2Ertc__ind__right,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1tc_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( ! [V2x_2E0: A_27a] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V0r_2E0)))
              | p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V0r_2E0))) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V2x_2E0),V2x_2E0)) )
        & ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
            ( ? [V5z_2E0: A_27a] :
                ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V3x_2E0),V5z_2E0))
                & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V5z_2E0,V4y_2E0),V0r_2E0)) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V3x_2E0),V4y_2E0)) ) )
     => ! [V6x_2E0: A_27a,V7y_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V6x_2E0,V7y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V6x_2E0),V7y_2E0)) ) ) ).

tff(thm_2Eset__relation_2Etc__strongind__right,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1tc_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V0r_2E0))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V2x_2E0),V3y_2E0)) )
        & ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
            ( ? [V6z_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V4x_2E0,V6z_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
                & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V4x_2E0),V6z_2E0))
                & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V6z_2E0,V5y_2E0),V0r_2E0)) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V4x_2E0),V5y_2E0)) ) )
     => ! [V7x_2E0: A_27a,V8y_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V7x_2E0,V8y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1tc_27_2E0,V7x_2E0),V8y_2E0)) ) ) ).

tff(thm_2Eset__relation_2Etc__union,axiom,
    ! [A_27a: $tType,V0r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2y_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r1_2E0)))
     => ! [V3r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0r1_2E0,V3r2_2E0)))) ) ).

tff(thm_2Eset__relation_2Etc__implication,axiom,
    ! [A_27a: $tType,V0r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V0r1_2E0))
         => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V1r2_2E0)) )
     => ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V4x_2E0,V5y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r1_2E0)))
         => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V4x_2E0,V5y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V1r2_2E0))) ) ) ).

tff(thm_2Eset__relation_2Etc__empty,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] : ~ p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0x_2E0,V1y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27a))))) ).

tff(thm_2Eset__relation_2Etc__empty__eqn,axiom,
    ! [A_27a: $tType] : ( c_2Eset__relation_2Etc_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27a))) = c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)) ) ).

tff(thm_2Eset__relation_2Etc__domain__range,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2y_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)))
     => ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V0r_2E0)))
        & p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V0r_2E0))) ) ) ).

tff(thm_2Eset__relation_2Errestrict__tc,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2e_2E0: A_27a,V3e_27_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2e_2E0,V3e_27_2E0),c_2Eset__relation_2Etc_2E1(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0x_2E0))))
     => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2e_2E0,V3e_27_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V1r_2E0))) ) ).

tff(thm_2Eset__relation_2Etc__SWAP,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Etc_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2ESWAP_2E0(A_27a,A_27a),V0r_2E0)) = c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2ESWAP_2E0(A_27a,A_27a),c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0)) ) ).

tff(thm_2Eset__relation_2Eacyclic__subset,axiom,
    ! [A_27a: $tType,V0r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V0r1_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V1r2_2E0,V0r1_2E0)) )
     => p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V1r2_2E0)) ) ).

tff(thm_2Eset__relation_2Eacyclic__union,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V0r_2E0),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V0r_2E0)),c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V1r_27_2E0),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V1r_27_2E0))))
        & p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V0r_2E0))
        & p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V1r_27_2E0)) )
     => p(c_2Eset__relation_2Eacyclic_2E1(A_27a,c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0r_2E0,V1r_27_2E0))) ) ).

tff(thm_2Eset__relation_2Etransitive__tc,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Etransitive_2E1(A_27a,V0r_2E0))
     => ( c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0) = V0r_2E0 ) ) ).

tff(thm_2Eset__relation_2Etc__transitive,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : p(c_2Eset__relation_2Etransitive_2E1(A_27a,c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0))) ).

tff(thm_2Eset__relation_2Eantisym__subset,axiom,
    ! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Eantisym_2E1(A_27a,V0t_2E0))
     => ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V1s_2E0,V0t_2E0))
       => p(c_2Eset__relation_2Eantisym_2E1(A_27a,V1s_2E0)) ) ) ).

tff(thm_2Eset__relation_2Epartial__order__dom__rng,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27a] :
      ( ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V0r_2E0))
        & p(c_2Eset__relation_2Epartial__order_2E2(A_27a,V0r_2E0,V1s_2E0)) )
     => ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0)) ) ) ).

tff(thm_2Eset__relation_2Epartial__order__subset,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Eset__relation_2Epartial__order_2E2(A_27a,V0r_2E0,V1s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2s_27_2E0,V1s_2E0)) )
     => p(c_2Eset__relation_2Epartial__order_2E2(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V0r_2E0,V2s_27_2E0),V2s_27_2E0)) ) ).

tff(thm_2Eset__relation_2Estrict__partial__order,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Epartial__order_2E2(A_27a,V0r_2E0,V1s_2E0))
     => ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,c_2Eset__relation_2Estrict_2E1(A_27a,V0r_2E0)),V1s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Erange_2E1(A_27a,A_27a,c_2Eset__relation_2Estrict_2E1(A_27a,V0r_2E0)),V1s_2E0))
        & p(c_2Eset__relation_2Etransitive_2E1(A_27a,c_2Eset__relation_2Estrict_2E1(A_27a,V0r_2E0)))
        & p(c_2Eset__relation_2Eantisym_2E1(A_27a,c_2Eset__relation_2Estrict_2E1(A_27a,V0r_2E0))) ) ) ).

tff(thm_2Eset__relation_2Estrict__partial__order__acyclic,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Epartial__order_2E2(A_27a,V0r_2E0,V1s_2E0))
     => p(c_2Eset__relation_2Eacyclic_2E1(A_27a,c_2Eset__relation_2Estrict_2E1(A_27a,V0r_2E0))) ) ).

tff(thm_2Eset__relation_2Elinear__order__subset,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0r_2E0,V1s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2s_27_2E0,V1s_2E0)) )
     => p(c_2Eset__relation_2Elinear__order_2E2(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V0r_2E0,V2s_27_2E0),V2s_27_2E0)) ) ).

tff(thm_2Eset__relation_2Epartial__order__linear__order,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0r_2E0,V1s_2E0))
     => p(c_2Eset__relation_2Epartial__order_2E2(A_27a,V0r_2E0,V1s_2E0)) ) ).

tff(thm_2Eset__relation_2Estrict__linear__order__dom__rng,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27a] :
      ( ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V0r_2E0))
        & p(c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,V0r_2E0,V1s_2E0)) )
     => ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0)) ) ) ).

tff(thm_2Eset__relation_2Elinear__order__dom__rng,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27a] :
      ( ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V0r_2E0))
        & p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0r_2E0,V1s_2E0)) )
     => ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0)) ) ) ).

tff(thm_2Eset__relation_2ERREFL__EXP__RSUBSET,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27a,V1R_2E0,c_2Eset__relation_2ERREFL__EXP_2E2(A_27a,V1R_2E0,V0s_2E0))) ).

tff(thm_2Eset__relation_2ERREFL__EXP__UNIV,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Eset__relation_2ERREFL__EXP_2E2(A_27a,V0R_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = V0R_2E0 ) ).

tff(thm_2Eset__relation_2EREL__RESTRICT__UNIV,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,V0R_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = V0R_2E0 ) ).

tff(thm_2Eset__relation_2Ein__rel__to__reln,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0xy_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0xy_2E0,c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,V1R_2E0)) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1R_2E0,c_2Epair_2EFST_2E1(A_27a,A_27b,V0xy_2E0)),c_2Epair_2ESND_2E1(A_27a,A_27b,V0xy_2E0)) ) ).

tff(thm_2Eset__relation_2Ereln__to__rel__app,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a,V2r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ereln__to__rel_2E3(A_27a,A_27b,V2r_2E0,V1x_2E0,V0y_2E0) = c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0),V2r_2E0) ) ).

tff(thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY,axiom,
    ! [A_27a: $tType,A_27b: $tType] : ( c_2Eset__relation_2Erel__to__reln_2E0(A_27a,A_27b) = c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Emin_2Ebool) ) ).

tff(thm_2Eset__relation_2Ereln__to__rel__IS__CURRY,axiom,
    ! [A_27a: $tType,A_27b: $tType] : ( c_2Eset__relation_2Ereln__to__rel_2E0(A_27a,A_27b) = c_2Epair_2ECURRY_2E0(A_27a,A_27b,tyop_2Emin_2Ebool) ) ).

tff(thm_2Eset__relation_2Erel__to__reln__inv,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27b,c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,V0R_2E0)) = V0R_2E0 ) ).

tff(thm_2Eset__relation_2Ereln__to__rel__inv,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27b,V0r_2E0)) = V0r_2E0 ) ).

tff(thm_2Eset__relation_2Ereln__to__rel__11,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
      ( ( c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27b,V1r1_2E0) = c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27b,V0r2_2E0) )
    <=> ( V1r1_2E0 = V0r2_2E0 ) ) ).

tff(thm_2Eset__relation_2Erel__to__reln__11,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( ( c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,V1R1_2E0) = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,V0R2_2E0) )
    <=> ( V1R1_2E0 = V0R2_2E0 ) ) ).

tff(thm_2Eset__relation_2Erel__to__reln__swap,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( ( V0r_2E0 = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,V1R_2E0) )
    <=> ( c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27b,V0r_2E0) = V1R_2E0 ) ) ).

tff(thm_2Eset__relation_2Edomain__to__rel__conv,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Edomain_2E1(A_27a,A_27b,V0r_2E0) = c_2Erelation_2ERDOM_2E1(A_27a,A_27b,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27b,V0r_2E0)) ) ).

tff(thm_2Eset__relation_2Erange__to__rel__conv,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Erange_2E1(A_27a,A_27b,V0r_2E0) = c_2Erelation_2ERRANGE_2E1(A_27b,A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27b,A_27a,V0r_2E0)) ) ).

tff(thm_2Eset__relation_2Estrict__to__rel__conv,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Estrict_2E1(A_27a,V0r_2E0) = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27a,c_2Erelation_2ESTRORD_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V0r_2E0))) ) ).

tff(thm_2Eset__relation_2Errestrict__to__rel__conv,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0s_2E0) = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27a,c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V1r_2E0),V0s_2E0)) ) ).

tff(thm_2Eset__relation_2Ercomp__to__rel__conv,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ercomp_2E2(A_27a,A_27b,A_27c,V1r1_2E0,V0r2_2E0) = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,c_2Erelation_2EO_2E2(A_27a,A_27c,A_27b,c_2Eset__relation_2Ereln__to__rel_2E1(A_27c,A_27b,V0r2_2E0),c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27c,V1r1_2E0))) ) ).

tff(thm_2Eset__relation_2Euniv__reln__to__rel__conv,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Euniv__reln_2E1(A_27a,V0s_2E0) = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27a,c_2Eset__relation_2ERRUNIV_2E1(A_27a,V0s_2E0)) ) ).

tff(thm_2Eset__relation_2Etc__to__rel__conv,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Etc_2E1(A_27a,V0r_2E0) = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27a,c_2Erelation_2ETC_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V0r_2E0))) ) ).

tff(thm_2Eset__relation_2Eacyclic__reln__to__rel__conv,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eacyclic_2E1(A_27a,V0r_2E0) = c_2Erelation_2Eirreflexive_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V0r_2E0))) ) ).

tff(thm_2Eset__relation_2Eirreflexive__reln__to__rel__conv,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eirreflexive_2E2(A_27a,V1r_2E0,V0s_2E0) = c_2Erelation_2Eirreflexive_2E1(A_27a,c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V1r_2E0),V0s_2E0)) ) ).

tff(thm_2Eset__relation_2Eirreflexive__reln__to__rel__conv__UNIV,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eirreflexive_2E2(A_27a,V0r_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Erelation_2Eirreflexive_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V0r_2E0)) ) ).

tff(thm_2Eset__relation_2Ereflexive__reln__to__rel__conv,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ereflexive_2E2(A_27a,V1r_2E0,V0s_2E0) = c_2Erelation_2Ereflexive_2E1(A_27a,c_2Eset__relation_2ERREFL__EXP_2E2(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V1r_2E0),V0s_2E0)) ) ).

tff(thm_2Eset__relation_2Ereflexive__reln__to__rel__conv__UNIV,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Ereflexive_2E2(A_27a,V0r_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Erelation_2Ereflexive_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V0r_2E0)) ) ).

tff(thm_2Eset__relation_2Etransitive__reln__to__rel__conv,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Etransitive_2E1(A_27a,V0r_2E0) = c_2Erelation_2Etransitive_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V0r_2E0)) ) ).

tff(thm_2Eset__relation_2Eantisym__reln__to__rel__conv,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eantisym_2E1(A_27a,V0r_2E0) = c_2Erelation_2Eantisymmetric_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V0r_2E0)) ) ).

tff(thm_2Eset__relation_2Epartial__order__reln__to__rel__conv,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Epartial__order_2E2(A_27a,V1r_2E0,V0s_2E0))
    <=> ( p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V1r_2E0),c_2Eset__relation_2ERRUNIV_2E1(A_27a,V0s_2E0)))
        & p(c_2Erelation_2EWeakOrder_2E1(A_27a,c_2Eset__relation_2ERREFL__EXP_2E2(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V1r_2E0),V0s_2E0))) ) ) ).

tff(thm_2Eset__relation_2Epartial__order__reln__to__rel__conv__UNIV,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Epartial__order_2E2(A_27a,V0r_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Erelation_2EWeakOrder_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V0r_2E0)) ) ).

tff(thm_2Eset__relation_2Elinear__order__reln__to__rel__conv__UNIV,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Elinear__order_2E2(A_27a,V0r_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Erelation_2EWeakLinearOrder_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V0r_2E0)) ) ).

tff(thm_2Eset__relation_2Estrict__linear__order__reln__to__rel__conv__UNIV,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,V0r_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Erelation_2EStrongLinearOrder_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V0r_2E0)) ) ).

tff(thm_2Eset__relation_2Ereln__rel__conv__thms,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y_2E0: A_27b,V1xy_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0: A_27a,V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V5r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V6r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V7r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V8r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V9r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V10r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V11R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V12R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V13R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V14R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1xy_2E0,c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,V13R_2E0)) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13R_2E0,c_2Epair_2EFST_2E1(A_27a,A_27b,V1xy_2E0)),c_2Epair_2ESND_2E1(A_27a,A_27b,V1xy_2E0)) )
      & ( c_2Eset__relation_2Ereln__to__rel_2E3(A_27a,A_27b,V9r_2E0,V2x_2E0,V0y_2E0) = c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V0y_2E0),V9r_2E0) )
      & ( c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27b,c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,V13R_2E0)) = V13R_2E0 )
      & ( c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27b,V9r_2E0)) = V9r_2E0 )
      & ( ( c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27b,V7r1_2E0) = c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27b,V5r2_2E0) )
      <=> ( V7r1_2E0 = V5r2_2E0 ) )
      & ( ( c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,V12R1_2E0) = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,V11R2_2E0) )
      <=> ( V12R1_2E0 = V11R2_2E0 ) )
      & ( c_2Eset__relation_2ERREFL__EXP_2E2(A_27a,V14R_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = V14R_2E0 )
      & ( c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,V14R_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = V14R_2E0 )
      & ( c_2Eset__relation_2Edomain_2E1(A_27a,A_27b,V9r_2E0) = c_2Erelation_2ERDOM_2E1(A_27a,A_27b,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27b,V9r_2E0)) )
      & ( c_2Eset__relation_2Erange_2E1(A_27a,A_27b,V8r_2E0) = c_2Erelation_2ERRANGE_2E1(A_27b,A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27b,A_27a,V8r_2E0)) )
      & ( c_2Eset__relation_2Estrict_2E1(A_27a,V10r_2E0) = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27a,c_2Erelation_2ESTRORD_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V10r_2E0))) )
      & ( c_2Eset__relation_2Errestrict_2E2(A_27a,V10r_2E0,V3s_2E0) = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27a,c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V10r_2E0),V3s_2E0)) )
      & ( c_2Eset__relation_2Ercomp_2E2(A_27a,A_27b,A_27c,V6r1_2E0,V4r2_2E0) = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27b,c_2Erelation_2EO_2E2(A_27a,A_27c,A_27b,c_2Eset__relation_2Ereln__to__rel_2E1(A_27c,A_27b,V4r2_2E0),c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27c,V6r1_2E0))) )
      & ( c_2Eset__relation_2Euniv__reln_2E1(A_27a,V3s_2E0) = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27a,c_2Eset__relation_2ERRUNIV_2E1(A_27a,V3s_2E0)) )
      & ( c_2Eset__relation_2Etc_2E1(A_27a,V10r_2E0) = c_2Eset__relation_2Erel__to__reln_2E1(A_27a,A_27a,c_2Erelation_2ETC_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V10r_2E0))) )
      & ( c_2Eset__relation_2Eacyclic_2E1(A_27a,V10r_2E0) = c_2Erelation_2Eirreflexive_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V10r_2E0))) )
      & ( c_2Eset__relation_2Eirreflexive_2E2(A_27a,V10r_2E0,V3s_2E0) = c_2Erelation_2Eirreflexive_2E1(A_27a,c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V10r_2E0),V3s_2E0)) )
      & ( c_2Eset__relation_2Ereflexive_2E2(A_27a,V10r_2E0,V3s_2E0) = c_2Erelation_2Ereflexive_2E1(A_27a,c_2Eset__relation_2ERREFL__EXP_2E2(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V10r_2E0),V3s_2E0)) )
      & ( c_2Eset__relation_2Etransitive_2E1(A_27a,V10r_2E0) = c_2Erelation_2Etransitive_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V10r_2E0)) )
      & ( c_2Eset__relation_2Eantisym_2E1(A_27a,V10r_2E0) = c_2Erelation_2Eantisymmetric_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V10r_2E0)) )
      & ( c_2Eset__relation_2Epartial__order_2E2(A_27a,V10r_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Erelation_2EWeakOrder_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V10r_2E0)) )
      & ( c_2Eset__relation_2Elinear__order_2E2(A_27a,V10r_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Erelation_2EWeakLinearOrder_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V10r_2E0)) )
      & ( c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,V10r_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Erelation_2EStrongLinearOrder_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V10r_2E0)) ) ) ).

tff(thm_2Eset__relation_2Eacyclic__WF,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V1r_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V1r_2E0),V0s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V1r_2E0),V0s_2E0)) )
     => p(c_2Erelation_2EWF_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V1r_2E0))) ) ).

tff(thm_2Eset__relation_2Eminimal__elements__subset,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1lo_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0s_2E0,V1lo_2E0),V0s_2E0)) ).

tff(thm_2Eset__relation_2Eminimal__elements__SWAP,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0xs_2E0,c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2ESWAP_2E0(A_27a,A_27a),V1r_2E0)) = c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V0xs_2E0,V1r_2E0) ) ).

tff(thm_2Eset__relation_2Emaximal__union,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V1s_2E0,c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V2r1_2E0,V3r2_2E0))))
     => ( p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V1s_2E0,V2r1_2E0)))
        & p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V1s_2E0,V3r2_2E0))) ) ) ).

tff(thm_2Eset__relation_2Eminimal__union,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V1s_2E0,c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V2r1_2E0,V3r2_2E0))))
     => ( p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V1s_2E0,V2r1_2E0)))
        & p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V1s_2E0,V3r2_2E0))) ) ) ).

tff(thm_2Eset__relation_2Eminimal__elements__mono,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V2r_2E0,V1r_27_2E0))
     => p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0xs_2E0,V1r_27_2E0),c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0xs_2E0,V2r_2E0))) ) ).

tff(thm_2Eset__relation_2Eminimal__elements__rrestrict,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0xs_2E0,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0xs_2E0)) = c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0xs_2E0,V1r_2E0) ) ).

tff(thm_2Eset__relation_2EWF__has__minimal__path,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,c_2Eset__relation_2Ereln__to__rel_2E1(A_27a,A_27a,V2r_2E0)))
     => ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
       => ? [V3y_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V1s_2E0,V2r_2E0)))
            & ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V3y_2E0,V0x_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V2r_2E0)))
              | ( V3y_2E0 = V0x_2E0 ) ) ) ) ) ).

tff(thm_2Eset__relation_2Efinite__acyclic__has__maximal,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) )
       => ! [V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
            ( p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V1r_2E0))
           => ? [V2x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V0s_2E0,V1r_2E0))) ) ) ) ).

tff(thm_2Eset__relation_2Efinite__acyclic__has__minimal,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) )
       => ! [V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
            ( p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V1r_2E0))
           => ? [V2x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0s_2E0,V1r_2E0))) ) ) ) ).

tff(thm_2Eset__relation_2Emaximal__TC,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V1r_2E0),V0s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V1r_2E0),V0s_2E0)) )
     => ( c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V0s_2E0,c_2Eset__relation_2Etc_2E1(A_27a,V1r_2E0)) = c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V0s_2E0,V1r_2E0) ) ) ).

tff(thm_2Eset__relation_2Eminimal__TC,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V1r_2E0),V0s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V1r_2E0),V0s_2E0)) )
     => ( c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0s_2E0,c_2Eset__relation_2Etc_2E1(A_27a,V1r_2E0)) = c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0s_2E0,V1r_2E0) ) ) ).

tff(thm_2Eset__relation_2Efinite__acyclic__has__minimal__path,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V1r_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
        & ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0s_2E0,V1r_2E0))) )
     => ? [V3y_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0s_2E0,V1r_2E0)))
          & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V3y_2E0,V2x_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V1r_2E0))) ) ) ).

tff(thm_2Eset__relation_2Efinite__acyclic__has__maximal__path,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V1r_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
        & ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V0s_2E0,V1r_2E0))) )
     => ? [V3y_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V0s_2E0,V1r_2E0)))
          & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),c_2Eset__relation_2Etc_2E1(A_27a,V1r_2E0))) ) ) ).

tff(thm_2Eset__relation_2Efinite__prefix__po__has__minimal__path,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Eset__relation_2Epartial__order_2E2(A_27a,V0r_2E0,V1s_2E0))
        & p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,V0r_2E0,V1s_2E0))
        & ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V3s_27_2E0,V0r_2E0)))
        & p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V3s_27_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3s_27_2E0,V1s_2E0)) )
     => ? [V4x_27_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_27_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V3s_27_2E0,V0r_2E0)))
          & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V4x_27_2E0,V2x_2E0),V0r_2E0)) ) ) ).

tff(thm_2Eset__relation_2Eempty__strict__linear__order,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,V0r_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))
    <=> ( V0r_2E0 = c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)) ) ) ).

tff(thm_2Eset__relation_2Eempty__linear__order,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0r_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))
    <=> ( V0r_2E0 = c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)) ) ) ).

tff(thm_2Eset__relation_2Elinear__order__restrict,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V1r_2E0,V0s_2E0))
     => p(c_2Eset__relation_2Elinear__order_2E2(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V2s_27_2E0),c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V2s_27_2E0))) ) ).

tff(thm_2Eset__relation_2Estrict__linear__order__restrict,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,V1r_2E0,V0s_2E0))
     => p(c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V2s_27_2E0),c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V2s_27_2E0))) ) ).

tff(thm_2Eset__relation_2Elinear__order__dom__rg,axiom,
    ! [A_27a: $tType,V0lo_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0lo_2E0,V1X_2E0))
     => ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V0lo_2E0),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V0lo_2E0)) = V1X_2E0 ) ) ).

tff(thm_2Eset__relation_2Elinear__order__refl,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1lo_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V1lo_2E0,V2X_2E0))
     => ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2X_2E0))
       => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0x_2E0,V0x_2E0),V1lo_2E0)) ) ) ).

tff(thm_2Eset__relation_2Elinear__order__in__set,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2lo_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V2lo_2E0,V3X_2E0))
     => ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V0y_2E0),V2lo_2E0))
       => ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V3X_2E0))
          & p(c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,V3X_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2EIN__MIN__LO,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2lo_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V3X_2E0))
     => ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V2lo_2E0,V3X_2E0))
       => ( p(c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V3X_2E0,V2lo_2E0)))
         => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0y_2E0,V1x_2E0),V2lo_2E0)) ) ) ) ).

tff(thm_2Eset__relation_2Eextend__linear__order,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))] :
      ( ! [V2x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0,V2x_2E0),V1s_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27a,V3y_2E0,V2x_2E0),c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))))) )
     => ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
          ( ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
            & p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0r_2E0,V1s_2E0)) )
         => p(c_2Eset__relation_2Elinear__order_2E2(A_27a,c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0r_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0,V2x_2E0),V1s_2E0))),c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))))) ) ) ).

tff(thm_2Eset__relation_2Estrict__linear__order__acyclic,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,V0r_2E0,V1s_2E0))
     => p(c_2Eset__relation_2Eacyclic_2E1(A_27a,V0r_2E0)) ) ).

tff(thm_2Eset__relation_2Estrict__linear__order__union__acyclic,axiom,
    ! [A_27a: $tType,V0r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,V0r1_2E0,V2s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V1r2_2E0),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V1r2_2E0)),V2s_2E0)) )
     => ( c_2Eset__relation_2Eacyclic_2E1(A_27a,c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0r1_2E0,V1r2_2E0)) = c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V1r2_2E0,V0r1_2E0) ) ) ).

tff(thm_2Eset__relation_2Estrict__linear__order,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0r_2E0,V1s_2E0))
     => p(c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,c_2Eset__relation_2Estrict_2E1(A_27a,V0r_2E0),V1s_2E0)) ) ).

tff(thm_2Eset__relation_2Elinear__order,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))] :
      ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),F0_2E0,V1s_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V2x_2E0),c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0)) )
     => ! [V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,V0r_2E0,V1s_2E0))
         => p(c_2Eset__relation_2Elinear__order_2E2(A_27a,c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0r_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),F0_2E0,V1s_2E0))),V1s_2E0)) ) ) ).

tff(thm_2Eset__relation_2Efinite__strict__linear__order__has__maximal,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,V1r_2E0,V0s_2E0))
        & ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
     => ? [V2x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V0s_2E0,V1r_2E0))) ) ).

tff(thm_2Eset__relation_2Efinite__strict__linear__order__has__minimal,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Eset__relation_2Estrict__linear__order_2E2(A_27a,V1r_2E0,V0s_2E0))
        & ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
     => ? [V2x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0s_2E0,V1r_2E0))) ) ).

tff(thm_2Eset__relation_2Efinite__linear__order__has__maximal,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V1r_2E0,V0s_2E0))
        & ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
     => ? [V2x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V0s_2E0,V1r_2E0))) ) ).

tff(thm_2Eset__relation_2Efinite__linear__order__has__minimal,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V1r_2E0,V0s_2E0))
        & ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
     => ? [V2x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0s_2E0,V1r_2E0))) ) ).

tff(thm_2Eset__relation_2Emaximal__linear__order,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27a] :
      ( ( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V0s_2E0))
        & p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V1r_2E0,V0s_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V0s_2E0,V1r_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V3y_2E0,V2x_2E0),V1r_2E0)) ) ).

tff(thm_2Eset__relation_2Eminimal__linear__order,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27a] :
      ( ( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V0s_2E0))
        & p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V1r_2E0,V0s_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V0s_2E0,V1r_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0),V1r_2E0)) ) ).

tff(thm_2Eset__relation_2Eminimal__linear__order__unique,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: A_27a,V4y_2E0: A_27a] :
      ( ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0r_2E0,V1s_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V2s_27_2E0,V0r_2E0)))
        & p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V2s_27_2E0,V0r_2E0)))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2s_27_2E0,V1s_2E0)) )
     => ( V3x_2E0 = V4y_2E0 ) ) ).

tff(thm_2Eset__relation_2Efinite__prefix__linear__order__has__unique__minimal,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V1r_2E0,V2s_2E0))
        & p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,V1r_2E0,V2s_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V3s_27_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3s_27_2E0,V2s_2E0)) )
     => p(c_2Epred__set_2ESING_2E1(A_27a,c_2Eset__relation_2Eminimal__elements_2E2(A_27a,V3s_27_2E0,V1r_2E0))) ) ).

tff(thm_2Eset__relation_2Enat__order__iso__thm,axiom,
    ! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V12x_2E0: A_27a,V13y_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F3_2E0,V0f_2E0),V12x_2E0),V13y_2E0))
        <=> ? [V14m_2E0: tyop_2Enum_2Enum,V15n_2E0: tyop_2Enum_2Enum] :
              ( p(c_2Earithmetic_2E_3C_3D_2E2(V14m_2E0,V15n_2E0))
              & ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0f_2E0,V14m_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V12x_2E0) )
              & ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0f_2E0,V15n_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V13y_2E0) ) ) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V12x_2E0: A_27a,V13y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F1_2E0,V0f_2E0),V12x_2E0),V13y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27a,V12x_2E0,V13y_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F3_2E0,V0f_2E0),V12x_2E0),V13y_2E0)) )
       => ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V8x_2E0: A_27a,V9y_2E0: A_27a] :
              ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V0f_2E0),V8x_2E0),V9y_2E0))
            <=> ? [V10m_2E0: tyop_2Enum_2Enum,V11n_2E0: tyop_2Enum_2Enum] :
                  ( p(c_2Earithmetic_2E_3C_3D_2E2(V10m_2E0,V11n_2E0))
                  & ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0f_2E0,V10m_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V8x_2E0) )
                  & ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0f_2E0,V11n_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V9y_2E0) ) ) )
         => ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V8x_2E0: A_27a,V9y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V8x_2E0),V9y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27a,V8x_2E0,V9y_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V0f_2E0),V8x_2E0),V9y_2E0)) )
           => ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                ( ( ! [V2n_2E0: tyop_2Enum_2Enum,V3m_2E0: tyop_2Enum_2Enum] :
                      ( ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0f_2E0,V3m_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0f_2E0,V2n_2E0) )
                        & ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0f_2E0,V3m_2E0) != c_2Eoption_2ENONE_2E0(A_27a) ) )
                     => ( V3m_2E0 = V2n_2E0 ) )
                  & ! [V4x_2E0: A_27a] :
                      ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V1s_2E0))
                     => ? [V5m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0f_2E0,V5m_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V4x_2E0) ) )
                  & ! [V6m_2E0: tyop_2Enum_2Enum,V7x_2E0: A_27a] :
                      ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0f_2E0,V6m_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V7x_2E0) )
                     => p(c_2Ebool_2EIN_2E2(A_27a,V7x_2E0,V1s_2E0)) ) )
               => ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0))),V1s_2E0))
                  & p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F1_2E0,V0f_2E0))),V1s_2E0)) ) ) ) ) ) ) ).

tff(thm_2Eset__relation_2Eupper__bounds__lem,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x1_2E0: A_27a,V3x2_2E0: A_27a] :
      ( ( p(c_2Eset__relation_2Etransitive_2E1(A_27a,V0r_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V2x1_2E0,c_2Eset__relation_2Eupper__bounds_2E2(A_27a,A_27a,V1s_2E0,V0r_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x1_2E0,V3x2_2E0),V0r_2E0)) )
     => p(c_2Ebool_2EIN_2E2(A_27a,V3x2_2E0,c_2Eset__relation_2Eupper__bounds_2E2(A_27a,A_27a,V1s_2E0,V0r_2E0))) ) ).

tff(thm_2Eset__relation_2Ezorns__lemma,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) )
        & p(c_2Eset__relation_2Epartial__order_2E2(A_27a,V0r_2E0,V1s_2E0))
        & ! [V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Eset__relation_2Echain_2E2(A_27a,V2t_2E0,V0r_2E0))
           => ( c_2Eset__relation_2Eupper__bounds_2E2(A_27a,A_27a,V2t_2E0,V0r_2E0) != c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) )
     => ? [V3x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Eset__relation_2Emaximal__elements_2E2(A_27a,V1s_2E0,V0r_2E0))) ) ).

tff(thm_2Eset__relation_2Eper__delete,axiom,
    ! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))] :
      ( ! [V2e_2E0: A_27a,V4es_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V2e_2E0),V4es_2E0) = c_2Epred__set_2EDELETE_2E2(A_27a,V4es_2E0,V2e_2E0) )
     => ( ! [V3es_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2e_2E0: A_27a,V1xss_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V3es_2E0),V2e_2E0),V1xss_2E0))
          <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3es_2E0,c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V2e_2E0),V1xss_2E0)))
              & ( V3es_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) )
       => ( ! [V2e_2E0: A_27a,V1xss_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3es_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V2e_2E0),V1xss_2E0),V3es_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3es_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V3es_2E0),V2e_2E0),V1xss_2E0)) )
         => ! [V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1xss_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2e_2E0: A_27a] :
              ( p(c_2Eset__relation_2Eper_2E2(A_27a,V0xs_2E0,V1xss_2E0))
             => p(c_2Eset__relation_2Eper_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V0xs_2E0,V2e_2E0),c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V2e_2E0),V1xss_2E0)))) ) ) ) ) ).

tff(thm_2Eset__relation_2Eper__restrict__per,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Eset__relation_2Eper_2E2(A_27a,V1s_2E0,V0r_2E0))
     => p(c_2Eset__relation_2Eper_2E2(A_27a,V2s_27_2E0,c_2Eset__relation_2Eper__restrict_2E2(A_27a,V0r_2E0,V2s_27_2E0))) ) ).

tff(thm_2Eset__relation_2Ecountable__per,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1xss_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0xs_2E0))
        & p(c_2Eset__relation_2Eper_2E2(A_27a,V0xs_2E0,V1xss_2E0)) )
     => p(c_2Epred__set_2Ecountable_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1xss_2E0)) ) ).

tff(thm_2Eset__relation_2Eall__choices__thm,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2y_2E0: A_27a] :
      ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0,c_2Eset__relation_2Eall__choices_2E1(A_27a,V1s_2E0)))
        & p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,V0x_2E0)) )
     => ? [V3z_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3z_2E0,V1s_2E0))
          & p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,V3z_2E0)) ) ) ).

tff(thm_2Eset__relation_2Elinear__order__num__order,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EINJ_2E3(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1s_2E0,V2t_2E0))
     => p(c_2Eset__relation_2Elinear__order_2E2(A_27a,c_2Eset__relation_2Enum__order_2E2(A_27a,V0f_2E0,V1s_2E0),V1s_2E0)) ) ).

tff(thm_2Eset__relation_2Enum__order__finite__prefix,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EINJ_2E3(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1s_2E0,V2t_2E0))
     => p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,c_2Eset__relation_2Enum__order_2E2(A_27a,V0f_2E0,V1s_2E0),V1s_2E0)) ) ).

tff(thm_2Eset__relation_2Enth__min__ind,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ( ! [V1r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0,V1r_27_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2s_2E0,V3r_2E0)),c_2Enum_2E0_2E0))
        & ! [V4r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V7n_2E0: tyop_2Enum_2Enum] :
            ( ! [V8min_2E0: tyop_2Eoption_2Eoption(A_27a)] :
                ( ( ( V8min_2E0 = c_2Eset__relation_2Eget__min_2E2(A_27a,V4r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5s_2E0,V6r_2E0)) )
                  & ( V8min_2E0 != c_2Eoption_2ENONE_2E0(A_27a) ) )
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0,V4r_27_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(A_27a,V5s_2E0,c_2Eoption_2ETHE_2E1(A_27a,V8min_2E0)),V6r_2E0)),V7n_2E0)) )
           => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0,V4r_27_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5s_2E0,V6r_2E0)),c_2Enum_2ESUC_2E1(V7n_2E0))) ) )
     => ! [V9v_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10v1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V11v2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V12v3_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0,V9v_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10v1_2E0,V11v2_2E0)),V12v3_2E0)) ) ).

tff(thm_2Eset__relation_2Enth__min__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))))] :
      ( ! [V7min_2E0: tyop_2Eoption_2Eoption(A_27a)] :
          ( p(app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool,F1_2E0,V7min_2E0))
        <=> ( V7min_2E0 = c_2Eoption_2ENONE_2E0(A_27a) ) )
     => ( ! [V4r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V6n_2E0: tyop_2Enum_2Enum,V7min_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))),F0_2E0,V4r_27_2E0),V3s_2E0),V5r_2E0),V6n_2E0),V7min_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool,F1_2E0,V7min_2E0),c_2Eoption_2ENONE_2E0(A_27a),c_2Eset__relation_2Enth__min_2E3(A_27a,V4r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(A_27a,V3s_2E0,c_2Eoption_2ETHE_2E1(A_27a,V7min_2E0)),V5r_2E0),V6n_2E0)) )
       => ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Enth__min_2E3(A_27a,V1r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0,V2r_2E0),c_2Enum_2E0_2E0) = c_2Eset__relation_2Eget__min_2E2(A_27a,V1r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0,V2r_2E0)) )
          & ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V6n_2E0: tyop_2Enum_2Enum] : ( c_2Eset__relation_2Enth__min_2E3(A_27a,V4r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3s_2E0,V5r_2E0),c_2Enum_2ESUC_2E1(V6n_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))),F0_2E0,V4r_27_2E0),V3s_2E0),V5r_2E0),V6n_2E0),c_2Eset__relation_2Eget__min_2E2(A_27a,V4r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3s_2E0,V5r_2E0))) ) ) ) ) ).

tff(thm_2Eset__relation_2Enth__min__def__compute,axiom,
    ! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))))] :
      ( ! [V7min_2E0: tyop_2Eoption_2Eoption(A_27a)] :
          ( p(app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool,F3_2E0,V7min_2E0))
        <=> ( V7min_2E0 = c_2Eoption_2ENONE_2E0(A_27a) ) )
     => ( ! [V4r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V6n_2E0: tyop_2Enum_2Enum,V7min_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))),F0_2E0,V4r_27_2E0),V3s_2E0),V5r_2E0),V6n_2E0),V7min_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool,F3_2E0,V7min_2E0),c_2Eoption_2ENONE_2E0(A_27a),c_2Eset__relation_2Enth__min_2E3(A_27a,V4r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(A_27a,V3s_2E0,c_2Eoption_2ETHE_2E1(A_27a,V7min_2E0)),V5r_2E0),c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V6n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
       => ( ! [V12min_2E0: tyop_2Eoption_2Eoption(A_27a)] :
              ( p(app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool,F2_2E0,V12min_2E0))
            <=> ( V12min_2E0 = c_2Eoption_2ENONE_2E0(A_27a) ) )
         => ( ! [V9r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V8s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V10r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V11n_2E0: tyop_2Enum_2Enum,V12min_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))),F1_2E0,V9r_27_2E0),V8s_2E0),V10r_2E0),V11n_2E0),V12min_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool,F2_2E0,V12min_2E0),c_2Eoption_2ENONE_2E0(A_27a),c_2Eset__relation_2Enth__min_2E3(A_27a,V9r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(A_27a,V8s_2E0,c_2Eoption_2ETHE_2E1(A_27a,V12min_2E0)),V10r_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V11n_2E0)))) )
           => ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Enth__min_2E3(A_27a,V1r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0,V2r_2E0),c_2Enum_2E0_2E0) = c_2Eset__relation_2Eget__min_2E2(A_27a,V1r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0,V2r_2E0)) )
              & ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V6n_2E0: tyop_2Enum_2Enum] : ( c_2Eset__relation_2Enth__min_2E3(A_27a,V4r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3s_2E0,V5r_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V6n_2E0))) = c_2Ebool_2ELET_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))),F0_2E0,V4r_27_2E0),V3s_2E0),V5r_2E0),V6n_2E0),c_2Eset__relation_2Eget__min_2E2(A_27a,V4r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3s_2E0,V5r_2E0))) )
              & ! [V8s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V9r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V11n_2E0: tyop_2Enum_2Enum] : ( c_2Eset__relation_2Enth__min_2E3(A_27a,V9r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V8s_2E0,V10r_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V11n_2E0))) = c_2Ebool_2ELET_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))),F1_2E0,V9r_27_2E0),V8s_2E0),V10r_2E0),V11n_2E0),c_2Eset__relation_2Eget__min_2E2(A_27a,V9r_27_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V8s_2E0,V10r_2E0))) ) ) ) ) ) ) ).

tff(thm_2Eset__relation_2Elinear__order__of__countable__po,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V1s_2E0))
        & p(c_2Eset__relation_2Epartial__order_2E2(A_27a,V0r_2E0,V1s_2E0))
        & p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,V0r_2E0,V1s_2E0)) )
     => ? [V2r_27_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
          ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V2r_27_2E0,V1s_2E0))
          & p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,V2r_27_2E0,V1s_2E0))
          & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0r_2E0,V2r_27_2E0)) ) ) ).

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