%------------------------------------------------------------------------------
% File     : ITP057_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    : wellorder.ax [Gau19]
%          : HL4057_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  418 ( 165 unt; 142 typ;   0 def)
%            Number of atoms       :  608 ( 272 equ)
%            Maximal formula atoms :   13 (   1 avg)
%            Number of connectives :  353 (  21   ~;  16   |; 109   &)
%                                         (  51 <=>; 156  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  111 (  69   >;  42   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  139 ( 139 usr;  11 con; 0-6 aty)
%            Number of variables   : 1265 (1069   !;  34   ?;1265   :)
%                                         ( 162  !>;   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(tyop_2Esum_2Esum,type,
    tyop_2Esum_2Esum: ( $tType * $tType ) > $tType ).

tff(tyop_2Ewellorder_2Ewellorder,type,
    tyop_2Ewellorder_2Ewellorder: $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_23_23_2E0,type,
    c_2Epair_2E_23_23_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d)))) ).

tff(c_2Epair_2E_23_23_2E2,type,
    c_2Epair_2E_23_23_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27c) * tyop_2Emin_2Efun(A_27b,A_27d) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d)) ) ).

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_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

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

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).

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

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

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

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

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

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

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

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

tff(c_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_2Ewellorder_2EADD1_2E0,type,
    c_2Ewellorder_2EADD1_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a))) ).

tff(c_2Ewellorder_2EADD1_2E2,type,
    c_2Ewellorder_2EADD1_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Ewellorder_2Ewellorder(A_27a) ) > tyop_2Ewellorder_2Ewellorder(A_27a) ) ).

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_2Epred__set_2EBIJ_2E0,type,
    c_2Epred__set_2EBIJ_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_2EBIJ_2E3,type,
    c_2Epred__set_2EBIJ_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_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_2Epair_2ECURRY_2E1,type,
    c_2Epair_2ECURRY_2E1: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( 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_2Ewellorder_2EChain_2E0,type,
    c_2Ewellorder_2EChain_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_2Ewellorder_2EChain_2E2,type,
    c_2Ewellorder_2EChain_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_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_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_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_2Esum_2EINL_2E0,type,
    c_2Esum_2EINL_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)) ).

tff(c_2Esum_2EINL_2E1,type,
    c_2Esum_2EINL_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Esum_2Esum(A_27a,A_27b) ) ).

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_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_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_2Epred__set_2ESUBSET_2E0,type,
    c_2Epred__set_2ESUBSET_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

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

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

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

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

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

tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
    c_2Ebool_2ETYPE__DEFINITION_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
    c_2Ebool_2ETYPE__DEFINITION_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).

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

tff(c_2Epred__set_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_2EWFREC_2E0,type,
    c_2Erelation_2EWFREC_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))) ).

tff(c_2Erelation_2EWFREC_2E2,type,
    c_2Erelation_2EWFREC_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).

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_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_2Epred__set_2Ecount_2E0,type,
    c_2Epred__set_2Ecount_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

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

tff(c_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_2Ewellorder_2EelsOf_2E0,type,
    c_2Ewellorder_2EelsOf_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Ewellorder_2EelsOf_2E1,type,
    c_2Ewellorder_2EelsOf_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ewellorder_2Ewellorder(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Ewellorder_2Efinite_2E0,type,
    c_2Ewellorder_2Efinite_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool) ).

tff(c_2Ewellorder_2Efinite_2E1,type,
    c_2Ewellorder_2Efinite_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ewellorder_2Ewellorder(A_27a) > tyop_2Emin_2Ebool ) ).

tff(c_2Ewellorder_2Efl_2E0,type,
    c_2Ewellorder_2Efl_2E0: 
      !>[A_27a: $tType] : 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_2Ewellorder_2Efl_2E1,type,
    c_2Ewellorder_2Efl_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Ewellorder_2Efl_2E2,type,
    c_2Ewellorder_2Efl_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ewellorder_2EfromNatWO_2E0,type,
    c_2Ewellorder_2EfromNatWO_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))) ).

tff(c_2Ewellorder_2EfromNatWO_2E1,type,
    c_2Ewellorder_2EfromNatWO_2E1: 
      !>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)) ) ).

tff(c_2Ewellorder_2Eiseg_2E0,type,
    c_2Ewellorder_2Eiseg_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Ewellorder_2Eiseg_2E2,type,
    c_2Ewellorder_2Eiseg_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Ewellorder_2Ewellorder(A_27a) * A_27a ) > tyop_2Emin_2Efun(A_27a,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_2Ewellorder_2Eorderiso_2E0,type,
    c_2Ewellorder_2Eorderiso_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool)) ).

tff(c_2Ewellorder_2Eorderiso_2E2,type,
    c_2Ewellorder_2Eorderiso_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Ewellorder_2Ewellorder(A_27a) * tyop_2Ewellorder_2Ewellorder(A_27b) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ewellorder_2Eorderlt_2E0,type,
    c_2Ewellorder_2Eorderlt_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool)) ).

tff(c_2Ewellorder_2Eorderlt_2E2,type,
    c_2Ewellorder_2Eorderlt_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Ewellorder_2Ewellorder(A_27a) * tyop_2Ewellorder_2Ewellorder(A_27b) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ewellorder_2Eposet_2E0,type,
    c_2Ewellorder_2Eposet_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_2Ewellorder_2Eposet_2E1,type,
    c_2Ewellorder_2Eposet_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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_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_2Ewellorder_2Eremove_2E0,type,
    c_2Ewellorder_2Eremove_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a))) ).

tff(c_2Ewellorder_2Eremove_2E2,type,
    c_2Ewellorder_2Eremove_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Ewellorder_2Ewellorder(A_27a) ) > tyop_2Ewellorder_2Ewellorder(A_27a) ) ).

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_2Eoption_2Esome_2E0,type,
    c_2Eoption_2Esome_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)) ).

tff(c_2Eoption_2Esome_2E1,type,
    c_2Eoption_2Esome_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Eoption_2Eoption(A_27a) ) ).

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_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_2Ewellorder_2EwZERO_2E0,type,
    c_2Ewellorder_2EwZERO_2E0: 
      !>[A_27a: $tType] : tyop_2Ewellorder_2Ewellorder(A_27a) ).

tff(c_2Ewellorder_2Ewellfounded_2E0,type,
    c_2Ewellorder_2Ewellfounded_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_2Ewellorder_2Ewellfounded_2E1,type,
    c_2Ewellorder_2Ewellfounded_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Ewellorder_2Ewellorder_2E0,type,
    c_2Ewellorder_2Ewellorder_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_2Ewellorder_2Ewellorder_2E1,type,
    c_2Ewellorder_2Ewellorder_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Ewellorder_2Ewellorder__ABS_2E0,type,
    c_2Ewellorder_2Ewellorder__ABS_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(A_27a)) ).

tff(c_2Ewellorder_2Ewellorder__ABS_2E1,type,
    c_2Ewellorder_2Ewellorder__ABS_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Ewellorder_2Ewellorder(A_27a) ) ).

tff(c_2Ewellorder_2Ewellorder__REP_2E0,type,
    c_2Ewellorder_2Ewellorder__REP_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Ewellorder_2Ewellorder__REP_2E1,type,
    c_2Ewellorder_2Ewellorder__REP_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ewellorder_2Ewellorder(A_27a) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) ).

tff(c_2Ewellorder_2Ewleast_2E0,type,
    c_2Ewellorder_2Ewleast_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))) ).

tff(c_2Ewellorder_2Ewleast_2E2,type,
    c_2Ewellorder_2Ewleast_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Ewellorder_2Ewellorder(A_27a) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Ewellorder_2Ewo2wo_2E0,type,
    c_2Ewellorder_2Ewo2wo_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))) ).

tff(c_2Ewellorder_2Ewo2wo_2E2,type,
    c_2Ewellorder_2Ewo2wo_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Ewellorder_2Ewellorder(A_27a) * tyop_2Ewellorder_2Ewellorder(A_27b) ) > tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)) ) ).

tff(c_2Ewellorder_2Ewo2wo_2E3,type,
    c_2Ewellorder_2Ewo2wo_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Ewellorder_2Ewellorder(A_27a) * tyop_2Ewellorder_2Ewellorder(A_27b) * A_27a ) > tyop_2Eoption_2Eoption(A_27b) ) ).

tff(c_2Ewellorder_2Ewobound_2E0,type,
    c_2Ewellorder_2Ewobound_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a))) ).

tff(c_2Ewellorder_2Ewobound_2E2,type,
    c_2Ewellorder_2Ewobound_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Ewellorder_2Ewellorder(A_27a) ) > tyop_2Ewellorder_2Ewellorder(A_27a) ) ).

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_23_23_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b_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,A_27b)] : ( c_2Epair_2E_23_23_2E2(A_27a,A_27a,A_27b,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27b,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27b,A_27b))),c_2Epair_2E_23_23_2E0(A_27a,A_27a,A_27b,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_23_23_2E2_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] : ( c_2Epair_2E_23_23_2E2(A_27c,A_27d,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_23_23_2E0(A_27c,A_27d,A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_23_23_2E2_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27a)] : ( c_2Epair_2E_23_23_2E2(A_27c,A_27d,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epair_2E_23_23_2E0(A_27c,A_27d,A_27b,A_27a),X0_2E0),X1_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_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_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_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_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_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)] : ( c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))),c_2Epair_2E_2C_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).

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

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

tff(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(arityeq2_2Ec_2Ewellorder_2EADD1_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2EADD1_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a)),c_2Ewellorder_2EADD1_2E0(A_27a),X0_2E0),X1_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(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_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),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(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)),c_2Epred__set_2EBIJ_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27b),X2_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ewellorder_2Ewellorder_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X2_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ebool_2ECOND_2E3(tyop_2Ewellorder_2Ewellorder(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Ewellorder_2Ewellorder(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epair_2ECURRY_2E1(A_27a,A_27a,tyop_2Emin_2Ebool,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_2Epair_2ECURRY_2E0(A_27a,A_27a,tyop_2Emin_2Ebool),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2EChain_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_2Ewellorder_2EChain_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_2Ewellorder_2EChain_2E0(A_27a),X0_2E0),X1_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_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Epred__set_2EDELETE_2E2(tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EDELETE_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Epred__set_2EDELETE_2E2(tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EDELETE_2E0(tyop_2Eoption_2Eoption(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_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_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_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),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_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27d_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27d,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27d,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Eoption_2Eoption(A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Eoption_2Eoption(A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Eoption_2Eoption(A_27b),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Eoption_2Eoption(A_27b),A_27b),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_27b_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27b,A_27b)),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_27b,A_27b),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_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27b,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27d_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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_27c,A_27d),tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27d_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27b,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_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_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_27b_2CA_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27b,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_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),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(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)),c_2Epred__set_2EINJ_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Esum_2EINL_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_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_2Epred__set_2EINSERT_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_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_2EINSERT_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),c_2Ebool_2ELET_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28A_27b_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),c_2Ebool_2ELET_2E0(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_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_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b] : ( c_2Eoption_2ESOME_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E0(A_27b),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(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ewellorder_2Ewellorder_28A_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),X1_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,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_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(A_27a)),X0_2E0),X1_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_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0) = app_2E2(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)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),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_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(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_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Ewellorder_2Ewellorder_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Ewellorder_2Ewellorder(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Ewellorder_2Ewellorder(A_27a)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))] : ( c_2Erelation_2EWFREC_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Erelation_2EWFREC_2E0(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0) ) ).

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

tff(arityeq1_2Ec_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_2Eset__relation_2Eantisym_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eantisym_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E0(A_27b),X0_2E0) ) ).

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

tff(arityeq1_2Ec_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_2Edomain_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Edomain_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E0(A_27c,A_27d),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2EelsOf_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2EelsOf_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ewellorder_2EelsOf_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2EelsOf_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] : ( c_2Ewellorder_2EelsOf_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ewellorder_2EelsOf_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2EelsOf_2E1_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))] : ( c_2Ewellorder_2EelsOf_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),c_2Ewellorder_2EelsOf_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Efinite_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Efinite_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool,c_2Ewellorder_2Efinite_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Efinite_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] : ( c_2Ewellorder_2Efinite_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool,c_2Ewellorder_2Efinite_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Efl_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: A_27a] : ( c_2Ewellorder_2Efl_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(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_2Ebool),c_2Ewellorder_2Efl_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Efl_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Efl_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_2Ewellorder_2Efl_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2EfromNatWO_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Ewellorder_2EfromNatWO_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),c_2Ewellorder_2EfromNatWO_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eiseg_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: A_27a] : ( c_2Ewellorder_2Eiseg_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ewellorder_2Eiseg_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eiseg_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),X1_2E0: A_27b] : ( c_2Ewellorder_2Eiseg_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ewellorder_2Eiseg_2E0(A_27b),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_2Elinear__order_2E2_2Emono_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_2Elinear__order_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(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_2Elinear__order_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderiso_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] : ( c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderiso_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27c)] : ( c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27c),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderiso_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Eorderiso_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderiso_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27c)] : ( c_2Ewellorder_2Eorderiso_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27c),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderiso_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27c),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27d)] : ( c_2Ewellorder_2Eorderiso_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27d),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27c),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27d),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderiso_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eorderlt_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Eorderlt_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderlt_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eorderlt_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] : ( c_2Ewellorder_2Eorderlt_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderlt_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eorderlt_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27c)] : ( c_2Ewellorder_2Eorderlt_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27c),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderlt_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eorderlt_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Eorderlt_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderlt_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eorderlt_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27c)] : ( c_2Ewellorder_2Eorderlt_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27c),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderlt_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Eorderlt_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27d)] : ( c_2Ewellorder_2Eorderlt_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27d),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27d),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderlt_2E0(A_27b,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Eposet_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Eposet_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewellorder_2Eposet_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Eposet_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Eposet_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewellorder_2Eposet_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_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_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(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27d_20mono_2EA_27c,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Erange_2E1(A_27d,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E0(A_27d,A_27c),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(arityeq2_2Ec_2Ewellorder_2Eremove_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Eremove_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a)),c_2Ewellorder_2Eremove_2E0(A_27a),X0_2E0),X1_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_2Eoption_2Esome_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eoption_2Esome_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E0(A_27a),X0_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(arityeq1_2Ec_2Eset__relation_2Estrict_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Estrict_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E0(A_27b),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_2Etransitive_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Etransitive_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Ewellfounded_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewellfounded_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewellorder_2Ewellfounded_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Ewellorder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewellorder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewellorder_2Ewellorder_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Ewellorder_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewellorder_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewellorder_2Ewellorder_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Ewellorder_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewellorder_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewellorder_2Ewellorder_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Ewellorder_2E1_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewellorder_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewellorder_2Ewellorder_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Ewellorder__ABS_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(A_27a),c_2Ewellorder_2Ewellorder__ABS_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Ewellorder__ABS_2E1_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewellorder__ABS_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),c_2Ewellorder_2Ewellorder__ABS_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Ewellorder__REP_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Ewellorder_2Ewellorder__REP_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewellorder_2Ewellorder__REP_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] : ( c_2Ewellorder_2Ewellorder__REP_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Ewellorder_2Ewellorder__REP_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Ewleast_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewleast_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Ewellorder_2Ewleast_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Ewleast_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewleast_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),c_2Ewellorder_2Ewleast_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Ewo2wo_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] : ( c_2Ewellorder_2Ewo2wo_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Ewellorder_2Ewo2wo_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ewellorder_2Ewo2wo_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),X2_2E0: A_27a] : ( c_2Ewellorder_2Ewo2wo_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Ewellorder_2Ewo2wo_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Ewo2wo_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Ewo2wo_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2Ewellorder_2Ewo2wo_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ewellorder_2Ewo2wo_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X2_2E0: A_27b] : ( c_2Ewellorder_2Ewo2wo_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2Ewellorder_2Ewo2wo_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Ewobound_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Ewobound_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a)),c_2Ewellorder_2Ewobound_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ewellorder_2Ewobound_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] : ( c_2Ewellorder_2Ewobound_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Ewellorder_2Ewellorder(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Ewellorder_2Ewellorder(A_27b)),c_2Ewellorder_2Ewobound_2E0(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_2Ewellorder_2Ewellfounded__def,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Ewellorder_2Ewellfounded_2E1(A_27a,V0R_2E0))
    <=> ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ? [V2w_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V2w_2E0,V1s_2E0))
         => ? [V3min_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(A_27a,V3min_2E0,V1s_2E0))
              & ! [V4w_2E0: A_27a] :
                  ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V4w_2E0,V3min_2E0),V0R_2E0))
                 => ~ p(c_2Ebool_2EIN_2E2(A_27a,V4w_2E0,V1s_2E0)) ) ) ) ) ).

tff(thm_2Ewellorder_2Ewellorder__def,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Ewellorder_2Ewellorder_2E1(A_27a,V0R_2E0))
    <=> ( p(c_2Ewellorder_2Ewellfounded_2E1(A_27a,c_2Eset__relation_2Estrict_2E1(A_27a,V0R_2E0)))
        & p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0R_2E0,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))))
        & p(c_2Eset__relation_2Ereflexive_2E2(A_27a,V0R_2E0,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)))) ) ) ).

tff(thm_2Ewellorder_2Ewellorder__TY__DEF,axiom,
    ! [A_27a: $tType] :
    ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(A_27a),c_2Ewellorder_2Ewellorder_2E0(A_27a),V0rep_2E0)) ).

tff(thm_2Ewellorder_2Ewellorder__ABSREP,axiom,
    ! [A_27a: $tType] :
      ( ! [V0a_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0a_2E0)) = V0a_2E0 )
      & ! [V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
          ( p(c_2Ewellorder_2Ewellorder_2E1(A_27a,V1r_2E0))
        <=> ( c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,V1r_2E0)) = V1r_2E0 ) ) ) ).

tff(thm_2Ewellorder_2EelsOf__def,axiom,
    ! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0)),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0))) ) ).

tff(thm_2Ewellorder_2Eiseg__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V1x_2E0: A_27a,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1x_2E0),V0w_2E0),V2y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2y_2E0,c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2y_2E0,V1x_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0)))) )
     => ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1x_2E0: A_27a] : ( c_2Ewellorder_2Eiseg_2E2(A_27a,V0w_2E0,V1x_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1x_2E0),V0w_2E0)) ) ) ).

tff(thm_2Ewellorder_2Ewobound__def,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Ewobound_2E2(A_27a,V0x_2E0,V1w_2E0) = c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w_2E0),c_2Ewellorder_2Eiseg_2E2(A_27a,V1w_2E0,V0x_2E0))) ) ).

tff(thm_2Ewellorder_2EfromNatWO__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))))] :
      ( ! [V1i_2E0: tyop_2Enum_2Enum,V2j_2E0: tyop_2Enum_2Enum,V0n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1i_2E0),V2j_2E0),V0n_2E0))
        <=> ( p(c_2Earithmetic_2E_3C_3D_2E2(V1i_2E0,V2j_2E0))
            & p(c_2Eprim__rec_2E_3C_2E2(V2j_2E0,V0n_2E0)) ) )
     => ( ! [V0n_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum,V2j_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))),F0_2E0,V0n_2E0),V1i_2E0),V2j_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,A_27a,V1i_2E0),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,A_27a,V2j_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1i_2E0),V2j_2E0),V0n_2E0)) )
       => ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Ewellorder_2EfromNatWO_2E1(A_27a,V0n_2E0) = c_2Ewellorder_2Ewellorder__ABS_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))),F0_2E0,V0n_2E0)))) ) ) ) ).

tff(thm_2Ewellorder_2Eorderiso__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] :
      ( p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27b,V0w1_2E0,V1w2_2E0))
    <=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
          ( ! [V3x_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w1_2E0)))
             => p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0),c_2Ewellorder_2EelsOf_2E1(A_27b,V1w2_2E0))) )
          & ! [V4x1_2E0: A_27a,V5x2_2E0: A_27a] :
              ( ( p(c_2Ebool_2EIN_2E2(A_27a,V4x1_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w1_2E0)))
                & p(c_2Ebool_2EIN_2E2(A_27a,V5x2_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w1_2E0))) )
             => ( ( app_2E2(A_27a,A_27b,V2f_2E0,V4x1_2E0) = app_2E2(A_27a,A_27b,V2f_2E0,V5x2_2E0) )
              <=> ( V4x1_2E0 = V5x2_2E0 ) ) )
          & ! [V6y_2E0: A_27b] :
              ( p(c_2Ebool_2EIN_2E2(A_27b,V6y_2E0,c_2Ewellorder_2EelsOf_2E1(A_27b,V1w2_2E0)))
             => ? [V7x_2E0: A_27a] :
                  ( p(c_2Ebool_2EIN_2E2(A_27a,V7x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w1_2E0)))
                  & ( app_2E2(A_27a,A_27b,V2f_2E0,V7x_2E0) = V6y_2E0 ) ) )
          & ! [V8x_2E0: A_27a,V9y_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V8x_2E0,V9y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w1_2E0))))
             => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(A_27b,A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V8x_2E0),app_2E2(A_27a,A_27b,V2f_2E0,V9y_2E0)),c_2Eset__relation_2Estrict_2E1(A_27b,c_2Ewellorder_2Ewellorder__REP_2E1(A_27b,V1w2_2E0)))) ) ) ) ).

tff(thm_2Ewellorder_2Eorderlt__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] :
      ( p(c_2Ewellorder_2Eorderlt_2E2(A_27a,A_27b,V0w1_2E0,V1w2_2E0))
    <=> ? [V2x_2E0: A_27b] :
          ( p(c_2Ebool_2EIN_2E2(A_27b,V2x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27b,V1w2_2E0)))
          & p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27b,V0w1_2E0,c_2Ewellorder_2Ewobound_2E2(A_27b,V2x_2E0,V1w2_2E0))) ) ) ).

tff(thm_2Ewellorder_2Ewleast__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_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(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0w_2E0),V1s_2E0),V2x_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0)))
            & ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
            & ! [V3y_2E0: A_27a] :
                ( ( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0)))
                  & ~ p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0))
                  & ( V2x_2E0 != V3y_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_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0)))) ) ) )
     => ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewleast_2E2(A_27a,V0w_2E0,V1s_2E0) = c_2Eoption_2Esome_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0w_2E0),V1s_2E0)) ) ) ).

tff(thm_2Ewellorder_2Ewo2wo__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F4_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool)),F3_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b))),F2_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b))),F1_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V7s1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] :
          ( p(app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool),F4_2E0,V7s1_2E0),V1w2_2E0))
        <=> ( V7s1_2E0 = c_2Ewellorder_2EelsOf_2E1(A_27b,V1w2_2E0) ) )
     => ( ! [V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V7s1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),F3_2E0,V1w2_2E0),V7s1_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool),F4_2E0,V7s1_2E0),V1w2_2E0),c_2Eoption_2ENONE_2E0(A_27b),c_2Ewellorder_2Ewleast_2E2(A_27b,V1w2_2E0,V7s1_2E0)) )
       => ( ! [V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V6s0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),F2_2E0,V1w2_2E0),V6s0_2E0) = c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),F3_2E0,V1w2_2E0),c_2Epred__set_2EIMAGE_2E2(tyop_2Eoption_2Eoption(A_27b),A_27b,c_2Eoption_2ETHE_2E0(A_27b),c_2Epred__set_2EDELETE_2E2(tyop_2Eoption_2Eoption(A_27b),V6s0_2E0,c_2Eoption_2ENONE_2E0(A_27b)))) )
         => ( ! [V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V0w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V4f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),F1_2E0,V1w2_2E0),V0w1_2E0),V4f_2E0),V5x_2E0) = c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),F2_2E0,V1w2_2E0),c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),V4f_2E0,c_2Ewellorder_2Eiseg_2E2(A_27a,V0w1_2E0,V5x_2E0))) )
           => ( ! [V0w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2x_2E0: A_27a,V3y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0w1_2E0),V2x_2E0),V3y_2E0) = 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_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w1_2E0))) )
             => ! [V0w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] : ( c_2Ewellorder_2Ewo2wo_2E2(A_27a,A_27b,V0w1_2E0,V1w2_2E0) = c_2Erelation_2EWFREC_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0w1_2E0),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),F1_2E0,V1w2_2E0),V0w1_2E0)) ) ) ) ) ) ) ).

tff(thm_2Ewellorder_2EwZERO__def,axiom,
    ! [A_27a: $tType] : ( c_2Ewellorder_2EwZERO_2E0(A_27a) = c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27a))) ) ).

tff(thm_2Ewellorder_2Efinite__def,axiom,
    ! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Efinite_2E1(A_27a,V0w_2E0) = c_2Epred__set_2EFINITE_2E1(A_27a,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0)) ) ).

tff(thm_2Ewellorder_2Eremove__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(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)))))] :
      ( ! [V2x_2E0: A_27a,V0e_2E0: A_27a,V3y_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
          ( p(app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V0e_2E0),V3y_2E0),V1w_2E0))
        <=> ( ( V2x_2E0 != V0e_2E0 )
            & ( V3y_2E0 != V0e_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_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w_2E0))) ) )
     => ( ! [V0e_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),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_2Ewellorder_2Ewellorder(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))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(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,V0e_2E0),V1w_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_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V0e_2E0),V3y_2E0),V1w_2E0)) )
       => ! [V0e_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Eremove_2E2(A_27a,V0e_2E0,V1w_2E0) = c_2Ewellorder_2Ewellorder__ABS_2E1(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_2Ewellorder_2Ewellorder(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))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(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,V0e_2E0),V1w_2E0)))) ) ) ) ).

tff(thm_2Ewellorder_2EADD1__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))] :
      ( ! [V0e_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),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_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0,V0e_2E0),V1w_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,V0e_2E0),c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w_2E0))) )
     => ! [V0e_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2EADD1_2E2(A_27a,V0e_2E0,V1w_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Ewellorder_2Ewellorder(A_27a),c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w_2E0)),V1w_2E0,c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w_2E0),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),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_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0,V0e_2E0),V1w_2E0))),c_2Epred__set_2EINSERT_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0e_2E0,V0e_2E0),c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)))))) ) ) ).

tff(thm_2Ewellorder_2Efl,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1x_2E0: A_27a] :
      ( p(c_2Ewellorder_2Efl_2E2(A_27a,V0l_2E0,V1x_2E0))
    <=> ? [V2y_2E0: A_27a] :
          ( p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0)))
          | p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V2y_2E0,V1x_2E0))) ) ) ).

tff(thm_2Ewellorder_2Eposet,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Ewellorder_2Eposet_2E1(A_27a,V0l_2E0))
    <=> ( ! [V1x_2E0: A_27a] :
            ( p(c_2Ewellorder_2Efl_2E2(A_27a,V0l_2E0,V1x_2E0))
           => p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V1x_2E0))) )
        & ! [V2x_2E0: A_27a,V3y_2E0: A_27a,V4z_2E0: A_27a] :
            ( ( p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0)))
              & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V3y_2E0,V4z_2E0))) )
           => p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V4z_2E0))) )
        & ! [V5x_2E0: A_27a,V6y_2E0: A_27a] :
            ( ( p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V5x_2E0,V6y_2E0)))
              & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V6y_2E0,V5x_2E0))) )
           => ( V5x_2E0 = V6y_2E0 ) ) ) ) ).

tff(thm_2Ewellorder_2Echain,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ewellorder_2EChain_2E2(A_27a,V0l_2E0,V1P_2E0))
    <=> ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
          ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0))
            & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3y_2E0)) )
         => ( p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V3y_2E0)))
            | p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V3y_2E0,V2x_2E0))) ) ) ) ).

tff(thm_2Ewellorder_2Ewellfounded__WF,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewellfounded_2E1(A_27a,V0R_2E0) = c_2Erelation_2EWF_2E1(A_27a,c_2Epair_2ECURRY_2E1(A_27a,A_27a,tyop_2Emin_2Ebool,V0R_2E0)) ) ).

tff(thm_2Ewellorder_2Ewellorder__EMPTY,axiom,
    ! [A_27a: $tType] : p(c_2Ewellorder_2Ewellorder_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)))) ).

tff(thm_2Ewellorder_2Ewellorder__SING,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
      ( p(c_2Ewellorder_2Ewellorder_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0x_2E0,V1y_2E0),c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)))))
    <=> ( V0x_2E0 = V1y_2E0 ) ) ).

tff(thm_2Ewellorder_2Errestrict__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)] : p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Eset__relation_2Errestrict_2E2(A_27a,V0r_2E0,V1s_2E0),V0r_2E0)) ).

tff(thm_2Ewellorder_2Ewellfounded__subset,axiom,
    ! [A_27a: $tType,V0r0_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_2Ewellorder_2Ewellfounded_2E1(A_27a,V1r_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0r0_2E0,V1r_2E0)) )
     => p(c_2Ewellorder_2Ewellfounded_2E1(A_27a,V0r0_2E0)) ) ).

tff(thm_2Ewellorder_2EmkWO__destWO,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0a_2E0)) = V0a_2E0 ) ).

tff(thm_2Ewellorder_2EdestWO__mkWO,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Ewellorder_2Ewellorder_2E1(A_27a,V0r_2E0))
     => ( c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,V0r_2E0)) = V0r_2E0 ) ) ).

tff(thm_2Ewellorder_2EWIN__elsOf,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(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,V0y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0))))
     => ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w_2E0)))
        & p(c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w_2E0))) ) ) ).

tff(thm_2Ewellorder_2EWLE__elsOf,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(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,V0y_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0)))
     => ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w_2E0)))
        & p(c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w_2E0))) ) ) ).

tff(thm_2Ewellorder_2EWIN__trichotomy,axiom,
    ! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a] :
      ( ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0)))
        & p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_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_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0))))
        | ( V1x_2E0 = V2y_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),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0)))) ) ) ).

tff(thm_2Ewellorder_2EWIN__REFL,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0x_2E0,V0x_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w_2E0))) = c_2Ebool_2EF_2E0 ) ).

tff(thm_2Ewellorder_2EWLE__TRANS,axiom,
    ! [A_27a: $tType,V0z_2E0: A_27a,V1y_2E0: A_27a,V2x_2E0: A_27a,V3w_2E0: tyop_2Ewellorder_2Ewellorder(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,V1y_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0)))
        & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1y_2E0,V0z_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V0z_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0))) ) ).

tff(thm_2Ewellorder_2EWLE__ANTISYM,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(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,V0y_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_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),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0))) )
     => ( V1x_2E0 = V0y_2E0 ) ) ).

tff(thm_2Ewellorder_2EWIN__WLE,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(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,V0y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_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),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0))) ) ).

tff(thm_2Ewellorder_2EelsOf__WLE,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w_2E0)) = c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0x_2E0,V0x_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w_2E0)) ) ).

tff(thm_2Ewellorder_2Etransitive__strict,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))
        & p(c_2Eset__relation_2Eantisym_2E1(A_27a,V0r_2E0)) )
     => p(c_2Eset__relation_2Etransitive_2E1(A_27a,c_2Eset__relation_2Estrict_2E1(A_27a,V0r_2E0))) ) ).

tff(thm_2Ewellorder_2EWIN__TRANS,axiom,
    ! [A_27a: $tType,V0z_2E0: A_27a,V1y_2E0: A_27a,V2x_2E0: A_27a,V3w_2E0: tyop_2Ewellorder_2Ewellorder(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,V1y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0))))
        & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1y_2E0,V0z_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0)))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V0z_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0)))) ) ).

tff(thm_2Ewellorder_2EWIN__WF,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))] :
      ( ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1p_2E0: tyop_2Epair_2Eprod(A_27a,A_27a)] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),F0_2E0,V0w_2E0),V1p_2E0) = c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V1p_2E0,c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0))) )
     => ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : p(c_2Ewellorder_2Ewellfounded_2E1(A_27a,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),F0_2E0,V0w_2E0))) ) ).

tff(thm_2Ewellorder_2EWIN__WF2,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0w_2E0),V1x_2E0),V2y_2E0) = 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_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0))) )
     => ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : p(c_2Erelation_2EWF_2E1(A_27a,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0w_2E0))) ) ).

tff(thm_2Ewellorder_2Estrict__subset,axiom,
    ! [A_27a: $tType,V0r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r1_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),V1r1_2E0,V0r2_2E0))
     => p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Eset__relation_2Estrict_2E1(A_27a,V1r1_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,V0r2_2E0))) ) ).

tff(thm_2Ewellorder_2Etransitive__rrestrict,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_2Etransitive_2E1(A_27a,V1r_2E0))
     => p(c_2Eset__relation_2Etransitive_2E1(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0s_2E0))) ) ).

tff(thm_2Ewellorder_2Eantisym__rrestrict,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_2Eantisym_2E1(A_27a,V1r_2E0))
     => p(c_2Eset__relation_2Eantisym_2E1(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0s_2E0))) ) ).

tff(thm_2Ewellorder_2Elinear__order__rrestrict,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_2Elinear__order_2E2(A_27a,V1r_2E0,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))))
     => p(c_2Eset__relation_2Elinear__order_2E2(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0s_2E0),c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0s_2E0)),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0s_2E0))))) ) ).

tff(thm_2Ewellorder_2Ereflexive__rrestrict,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_2Ereflexive_2E2(A_27a,V1r_2E0,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))))
     => p(c_2Eset__relation_2Ereflexive_2E2(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0s_2E0),c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0s_2E0)),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V1r_2E0,V0s_2E0))))) ) ).

tff(thm_2Ewellorder_2Ewellorder__rrestrict,axiom,
    ! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ewellorder_2Ewellorder_2E1(A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0),V1s_2E0))) ).

tff(thm_2Ewellorder_2EWIN__wobound,axiom,
    ! [A_27a: $tType,V0z_2E0: A_27a,V1y_2E0: A_27a,V2x_2E0: A_27a,V3w_2E0: tyop_2Ewellorder_2Ewellorder(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,V1y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,c_2Ewellorder_2Ewobound_2E2(A_27a,V0z_2E0,V3w_2E0)))))
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V0z_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0))))
        & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1y_2E0,V0z_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0))))
        & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V1y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0)))) ) ) ).

tff(thm_2Ewellorder_2EWLE__wobound,axiom,
    ! [A_27a: $tType,V0z_2E0: A_27a,V1y_2E0: A_27a,V2x_2E0: A_27a,V3w_2E0: tyop_2Ewellorder_2Ewellorder(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,V1y_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,c_2Ewellorder_2Ewobound_2E2(A_27a,V0z_2E0,V3w_2E0))))
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V0z_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0))))
        & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1y_2E0,V0z_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0))))
        & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V1y_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0))) ) ) ).

tff(thm_2Ewellorder_2Ewellorder__cases,axiom,
    ! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
    ? [V1s_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( p(c_2Ewellorder_2Ewellorder_2E1(A_27a,V1s_2E0))
      & ( V0w_2E0 = c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,V1s_2E0) ) ) ).

tff(thm_2Ewellorder_2EWEXTENSION,axiom,
    ! [A_27a: $tType,V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
      ( ( V1w1_2E0 = V0w2_2E0 )
    <=> ! [V2a_2E0: A_27a,V3b_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2a_2E0,V3b_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w1_2E0)) = c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2a_2E0,V3b_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w2_2E0)) ) ) ).

tff(thm_2Ewellorder_2Ewobound2,axiom,
    ! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1b_2E0: A_27a,V2a_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2a_2E0,V1b_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0))))
     => ( c_2Ewellorder_2Ewobound_2E2(A_27a,V2a_2E0,c_2Ewellorder_2Ewobound_2E2(A_27a,V1b_2E0,V0w_2E0)) = c_2Ewellorder_2Ewobound_2E2(A_27a,V2a_2E0,V0w_2E0) ) ) ).

tff(thm_2Ewellorder_2Ewellorder__fromNat,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))))] :
      ( ! [V1i_2E0: tyop_2Enum_2Enum,V2j_2E0: tyop_2Enum_2Enum,V0n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1i_2E0),V2j_2E0),V0n_2E0))
        <=> ( p(c_2Earithmetic_2E_3C_3D_2E2(V1i_2E0,V2j_2E0))
            & p(c_2Eprim__rec_2E_3C_2E2(V2j_2E0,V0n_2E0)) ) )
     => ( ! [V0n_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum,V2j_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),F0_2E0,V0n_2E0),V1i_2E0),V2j_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1i_2E0,V2j_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1i_2E0),V2j_2E0),V0n_2E0)) )
       => ! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Ewellorder_2Ewellorder_2E1(tyop_2Enum_2Enum,c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),F0_2E0,V0n_2E0))))) ) ) ).

tff(thm_2Ewellorder_2EINJ__preserves__transitive,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Eset__relation_2Etransitive_2E1(A_27a,V1r_2E0))
        & p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,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)),V0t_2E0)) )
     => p(c_2Eset__relation_2Etransitive_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_23_23_2E2(A_27a,A_27a,A_27b,A_27b,V2f_2E0,V2f_2E0),V1r_2E0))) ) ).

tff(thm_2Ewellorder_2EINJ__preserves__antisym,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Eset__relation_2Eantisym_2E1(A_27a,V1r_2E0))
        & p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,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)),V0t_2E0)) )
     => p(c_2Eset__relation_2Eantisym_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_23_23_2E2(A_27a,A_27a,A_27b,A_27b,V2f_2E0,V2f_2E0),V1r_2E0))) ) ).

tff(thm_2Ewellorder_2EINJ__preserves__linear__order,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V1r_2E0,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))))
        & p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,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)),V0t_2E0)) )
     => p(c_2Eset__relation_2Elinear__order_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_23_23_2E2(A_27a,A_27a,A_27b,A_27b,V2f_2E0,V2f_2E0),V1r_2E0),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,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))))) ) ).

tff(thm_2Ewellorder_2Edomain__IMAGE__ff,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Ebool),V1g_2E0: tyop_2Emin_2Efun(A_27d,A_27b),V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Eset__relation_2Edomain_2E1(A_27a,A_27b,c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_23_23_2E2(A_27c,A_27d,A_27a,A_27b,V2f_2E0,V1g_2E0),V0r_2E0)) = c_2Epred__set_2EIMAGE_2E2(A_27c,A_27a,V2f_2E0,c_2Eset__relation_2Edomain_2E1(A_27c,A_27d,V0r_2E0)) ) ).

tff(thm_2Ewellorder_2Erange__IMAGE__ff,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Ebool),V1g_2E0: tyop_2Emin_2Efun(A_27d,A_27a),V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2Eset__relation_2Erange_2E1(A_27a,A_27b,c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_23_23_2E2(A_27c,A_27d,A_27b,A_27a,V2f_2E0,V1g_2E0),V0r_2E0)) = c_2Epred__set_2EIMAGE_2E2(A_27d,A_27a,V1g_2E0,c_2Eset__relation_2Erange_2E1(A_27d,A_27c,V0r_2E0)) ) ).

tff(thm_2Ewellorder_2EINJ__preserves__wellorder,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Ewellorder_2Ewellorder_2E1(A_27a,V1r_2E0))
        & p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,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)),V0t_2E0)) )
     => p(c_2Ewellorder_2Ewellorder_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_23_23_2E2(A_27a,A_27a,A_27b,A_27b,V2f_2E0,V2f_2E0),V1r_2E0))) ) ).

tff(thm_2Ewellorder_2Ewellorder__fromNat__SUM,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))))] :
      ( ! [V1i_2E0: tyop_2Enum_2Enum,V2j_2E0: tyop_2Enum_2Enum,V0n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1i_2E0),V2j_2E0),V0n_2E0))
        <=> ( p(c_2Earithmetic_2E_3C_3D_2E2(V1i_2E0,V2j_2E0))
            & p(c_2Eprim__rec_2E_3C_2E2(V2j_2E0,V0n_2E0)) ) )
     => ( ! [V0n_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum,V2j_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))),F0_2E0,V0n_2E0),V1i_2E0),V2j_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,A_27a,V1i_2E0),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,A_27a,V2j_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1i_2E0),V2j_2E0),V0n_2E0)) )
       => ! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Ewellorder_2Ewellorder_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))),F0_2E0,V0n_2E0))))) ) ) ).

tff(thm_2Ewellorder_2EfromNatWO__11,axiom,
    ! [A_27a: $tType,V0j_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum] :
      ( ( c_2Ewellorder_2EfromNatWO_2E1(A_27a,V1i_2E0) = c_2Ewellorder_2EfromNatWO_2E1(A_27a,V0j_2E0) )
    <=> ( V1i_2E0 = V0j_2E0 ) ) ).

tff(thm_2Ewellorder_2EelsOf__fromNatWO,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] : ( c_2Ewellorder_2EelsOf_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Ewellorder_2EfromNatWO_2E1(A_27a,V0n_2E0)) = c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Esum_2EINL_2E0(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2Ecount_2E1(V0n_2E0)) ) ).

tff(thm_2Ewellorder_2EWLE__WIN,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(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,V0y_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0)))
     => ( ( V1x_2E0 = V0y_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),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0)))) ) ) ).

tff(thm_2Ewellorder_2EelsOf__wobound,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0x_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0x_2E0),V1w_2E0),V2y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2y_2E0,c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2y_2E0,V0x_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w_2E0)))) )
     => ! [V0x_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2EelsOf_2E1(A_27a,c_2Ewellorder_2Ewobound_2E2(A_27a,V0x_2E0,V1w_2E0)) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0x_2E0),V1w_2E0)) ) ) ).

tff(thm_2Ewellorder_2Eorderiso__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V1w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
      ( p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27b,V1w1_2E0,V0w2_2E0))
    <=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
          ( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V2f_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w1_2E0),c_2Ewellorder_2EelsOf_2E1(A_27b,V0w2_2E0)))
          & ! [V3x_2E0: A_27a,V4y_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,V4y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w1_2E0))))
             => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(A_27b,A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0),app_2E2(A_27a,A_27b,V2f_2E0,V4y_2E0)),c_2Eset__relation_2Estrict_2E1(A_27b,c_2Ewellorder_2Ewellorder__REP_2E1(A_27b,V0w2_2E0)))) ) ) ) ).

tff(thm_2Ewellorder_2Eorderiso__REFL,axiom,
    ! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27a,V0w_2E0,V0w_2E0)) ).

tff(thm_2Ewellorder_2Eorderiso__SYM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] :
      ( p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27b,V0w1_2E0,V1w2_2E0))
     => p(c_2Ewellorder_2Eorderiso_2E2(A_27b,A_27a,V1w2_2E0,V0w1_2E0)) ) ).

tff(thm_2Ewellorder_2Eorderiso__TRANS,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V2w3_2E0: tyop_2Ewellorder_2Ewellorder(A_27c)] :
      ( ( p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27b,V0w1_2E0,V1w2_2E0))
        & p(c_2Ewellorder_2Eorderiso_2E2(A_27b,A_27c,V1w2_2E0,V2w3_2E0)) )
     => p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27c,V0w1_2E0,V2w3_2E0)) ) ).

tff(thm_2Ewellorder_2Eorderlt__REFL,axiom,
    ! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Eorderlt_2E2(A_27a,A_27a,V0w_2E0,V0w_2E0) = c_2Ebool_2EF_2E0 ) ).

tff(thm_2Ewellorder_2Ewobounds__preserve__bijections,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V2w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V3f_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w1_2E0),c_2Ewellorder_2EelsOf_2E1(A_27b,V1w2_2E0)))
        & p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w1_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_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w1_2E0))))
           => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(A_27b,A_27b,app_2E2(A_27a,A_27b,V3f_2E0,V4x_2E0),app_2E2(A_27a,A_27b,V3f_2E0,V5y_2E0)),c_2Eset__relation_2Estrict_2E1(A_27b,c_2Ewellorder_2Ewellorder__REP_2E1(A_27b,V1w2_2E0)))) ) )
     => p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V3f_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,c_2Ewellorder_2Ewobound_2E2(A_27a,V0x_2E0,V2w1_2E0)),c_2Ewellorder_2EelsOf_2E1(A_27b,c_2Ewellorder_2Ewobound_2E2(A_27b,app_2E2(A_27a,A_27b,V3f_2E0,V0x_2E0),V1w2_2E0)))) ) ).

tff(thm_2Ewellorder_2Eorderlt__TRANS,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V2w3_2E0: tyop_2Ewellorder_2Ewellorder(A_27c)] :
      ( ( p(c_2Ewellorder_2Eorderlt_2E2(A_27a,A_27b,V0w1_2E0,V1w2_2E0))
        & p(c_2Ewellorder_2Eorderlt_2E2(A_27b,A_27c,V1w2_2E0,V2w3_2E0)) )
     => p(c_2Ewellorder_2Eorderlt_2E2(A_27a,A_27c,V0w1_2E0,V2w3_2E0)) ) ).

tff(thm_2Ewellorder_2Ewo2wo__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b))),F0_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)))] :
      ( ! [V4s1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] :
          ( p(app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool),F2_2E0,V4s1_2E0),V0w2_2E0))
        <=> ( V4s1_2E0 = c_2Ewellorder_2EelsOf_2E1(A_27b,V0w2_2E0) ) )
     => ( ! [V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V4s1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),F1_2E0,V0w2_2E0),V4s1_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool),F2_2E0,V4s1_2E0),V0w2_2E0),c_2Eoption_2ENONE_2E0(A_27b),c_2Ewellorder_2Ewleast_2E2(A_27b,V0w2_2E0,V4s1_2E0)) )
       => ( ! [V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V3s0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),F0_2E0,V0w2_2E0),V3s0_2E0) = c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),F1_2E0,V0w2_2E0),c_2Epred__set_2EIMAGE_2E2(tyop_2Eoption_2Eoption(A_27b),A_27b,c_2Eoption_2ETHE_2E0(A_27b),c_2Epred__set_2EDELETE_2E2(tyop_2Eoption_2Eoption(A_27b),V3s0_2E0,c_2Eoption_2ENONE_2E0(A_27b)))) )
         => ! [V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2x_2E0: A_27a] : ( c_2Ewellorder_2Ewo2wo_2E3(A_27a,A_27b,V1w_2E0,V0w2_2E0,V2x_2E0) = c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),F0_2E0,V0w2_2E0),c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),c_2Ewellorder_2Ewo2wo_2E2(A_27a,A_27b,V1w_2E0,V0w2_2E0),c_2Ewellorder_2Eiseg_2E2(A_27a,V1w_2E0,V2x_2E0))) ) ) ) ) ).

tff(thm_2Ewellorder_2Ewleast__IN__wo,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( c_2Ewellorder_2Ewleast_2E2(A_27a,V1w_2E0,V2s_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V0x_2E0) )
     => ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w_2E0)))
        & ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2s_2E0))
        & ! [V3y_2E0: A_27a] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w_2E0)))
              & ~ p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V2s_2E0))
              & ( V0x_2E0 != V3y_2E0 ) )
           => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0x_2E0,V3y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w_2E0)))) ) ) ) ).

tff(thm_2Ewellorder_2Ewleast__EQ__NONE,axiom,
    ! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( c_2Ewellorder_2Ewleast_2E2(A_27a,V0w_2E0,V1s_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
     => p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0),V1s_2E0)) ) ).

tff(thm_2Ewellorder_2Ewo2wo__IN__w2,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V1w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2x_2E0: A_27a,V3y_2E0: A_27b] :
      ( ( c_2Ewellorder_2Ewo2wo_2E3(A_27a,A_27b,V1w1_2E0,V0w2_2E0,V2x_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V3y_2E0) )
     => p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,c_2Ewellorder_2EelsOf_2E1(A_27b,V0w2_2E0))) ) ).

tff(thm_2Ewellorder_2EIMAGE__wo2wo__SUBSET,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eoption_2Eoption(A_27a),A_27a,c_2Eoption_2ETHE_2E0(A_27a),c_2Epred__set_2EDELETE_2E2(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2EIMAGE_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),c_2Ewellorder_2Ewo2wo_2E2(A_27b,A_27a,V2w1_2E0,V1w2_2E0),c_2Ewellorder_2Eiseg_2E2(A_27b,V2w1_2E0,V0x_2E0)),c_2Eoption_2ENONE_2E0(A_27a))),c_2Ewellorder_2EelsOf_2E1(A_27a,V1w2_2E0))) ).

tff(thm_2Ewellorder_2Ewo2wo__EQ__NONE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V1w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2x_2E0: A_27a] :
      ( ( c_2Ewellorder_2Ewo2wo_2E3(A_27a,A_27b,V1w1_2E0,V0w2_2E0,V2x_2E0) = c_2Eoption_2ENONE_2E0(A_27b) )
     => ! [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),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w1_2E0))))
         => ( c_2Ewellorder_2Ewo2wo_2E3(A_27a,A_27b,V1w1_2E0,V0w2_2E0,V3y_2E0) = c_2Eoption_2ENONE_2E0(A_27b) ) ) ) ).

tff(thm_2Ewellorder_2Ewo2wo__EQ__SOME__downwards,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V1w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2x_2E0: A_27a,V3y_2E0: A_27b] :
      ( ( c_2Ewellorder_2Ewo2wo_2E3(A_27a,A_27b,V1w1_2E0,V0w2_2E0,V2x_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V3y_2E0) )
     => ! [V4x0_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V4x0_2E0,V2x_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w1_2E0))))
         => ? [V5y0_2E0: A_27b] : ( c_2Ewellorder_2Ewo2wo_2E3(A_27a,A_27b,V1w1_2E0,V0w2_2E0,V4x0_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V5y0_2E0) ) ) ) ).

tff(thm_2Ewellorder_2Emono__woseg,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x2_2E0: A_27a,V1x1_2E0: A_27a,V2w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V3w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x1_2E0,V0x2_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w1_2E0))))
     => p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(tyop_2Eoption_2Eoption(A_27b),A_27b,c_2Eoption_2ETHE_2E0(A_27b),c_2Epred__set_2EDELETE_2E2(tyop_2Eoption_2Eoption(A_27b),c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),c_2Ewellorder_2Ewo2wo_2E2(A_27a,A_27b,V3w1_2E0,V2w2_2E0),c_2Ewellorder_2Eiseg_2E2(A_27a,V3w1_2E0,V1x1_2E0)),c_2Eoption_2ENONE_2E0(A_27b))),c_2Epred__set_2EIMAGE_2E2(tyop_2Eoption_2Eoption(A_27b),A_27b,c_2Eoption_2ETHE_2E0(A_27b),c_2Epred__set_2EDELETE_2E2(tyop_2Eoption_2Eoption(A_27b),c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),c_2Ewellorder_2Ewo2wo_2E2(A_27a,A_27b,V3w1_2E0,V2w2_2E0),c_2Ewellorder_2Eiseg_2E2(A_27a,V3w1_2E0,V0x2_2E0)),c_2Eoption_2ENONE_2E0(A_27b))))) ) ).

tff(thm_2Ewellorder_2Ewo2wo__11,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x2_2E0: A_27a,V2x1_2E0: A_27a,V3w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V4w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
      ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x1_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V4w1_2E0)))
        & p(c_2Ebool_2EIN_2E2(A_27a,V1x2_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V4w1_2E0)))
        & ( c_2Ewellorder_2Ewo2wo_2E3(A_27a,A_27b,V4w1_2E0,V3w2_2E0,V2x1_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V0y_2E0) )
        & ( c_2Ewellorder_2Ewo2wo_2E3(A_27a,A_27b,V4w1_2E0,V3w2_2E0,V1x2_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V0y_2E0) ) )
     => ( V2x1_2E0 = V1x2_2E0 ) ) ).

tff(thm_2Ewellorder_2Ewleast__SUBSET,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V3s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( ( c_2Ewellorder_2Ewleast_2E2(A_27a,V2w_2E0,V4s1_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V1x_2E0) )
        & ( c_2Ewellorder_2Ewleast_2E2(A_27a,V2w_2E0,V3s2_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V0y_2E0) )
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V4s1_2E0,V3s2_2E0)) )
     => ( ( V1x_2E0 = V0y_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),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0)))) ) ) ).

tff(thm_2Ewellorder_2Ewo2wo__mono,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0y0_2E0: A_27a,V1y_2E0: A_27a,V2x0_2E0: A_27b,V3x_2E0: A_27b,V4w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V5w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] :
      ( ( ( c_2Ewellorder_2Ewo2wo_2E3(A_27b,A_27a,V5w1_2E0,V4w2_2E0,V2x0_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V0y0_2E0) )
        & ( c_2Ewellorder_2Ewo2wo_2E3(A_27b,A_27a,V5w1_2E0,V4w2_2E0,V3x_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V1y_2E0) )
        & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(A_27b,A_27b,V2x0_2E0,V3x_2E0),c_2Eset__relation_2Estrict_2E1(A_27b,c_2Ewellorder_2Ewellorder__REP_2E1(A_27b,V5w1_2E0)))) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0y0_2E0,V1y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V4w2_2E0)))) ) ).

tff(thm_2Ewellorder_2Ewo2wo__ONTO,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0y0_2E0: A_27b,V1y_2E0: A_27b,V2x_2E0: A_27a,V3w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V4w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
      ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V4w1_2E0)))
        & ( c_2Ewellorder_2Ewo2wo_2E3(A_27a,A_27b,V4w1_2E0,V3w2_2E0,V2x_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V1y_2E0) )
        & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(A_27b,A_27b,V0y0_2E0,V1y_2E0),c_2Eset__relation_2Estrict_2E1(A_27b,c_2Ewellorder_2Ewellorder__REP_2E1(A_27b,V3w2_2E0)))) )
     => ? [V5x0_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V5x0_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V4w1_2E0)))
          & ( c_2Ewellorder_2Ewo2wo_2E3(A_27a,A_27b,V4w1_2E0,V3w2_2E0,V5x0_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V0y0_2E0) ) ) ) ).

tff(thm_2Ewellorder_2Ewo2wo__EQ__NONE__woseg,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] :
      ( ( c_2Ewellorder_2Ewo2wo_2E3(A_27b,A_27a,V2w1_2E0,V1w2_2E0,V0x_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
     => ( c_2Ewellorder_2EelsOf_2E1(A_27a,V1w2_2E0) = c_2Epred__set_2EIMAGE_2E2(tyop_2Eoption_2Eoption(A_27a),A_27a,c_2Eoption_2ETHE_2E0(A_27a),c_2Epred__set_2EDELETE_2E2(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2EIMAGE_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),c_2Ewellorder_2Ewo2wo_2E2(A_27b,A_27a,V2w1_2E0,V1w2_2E0),c_2Ewellorder_2Eiseg_2E2(A_27b,V2w1_2E0,V0x_2E0)),c_2Eoption_2ENONE_2E0(A_27a))) ) ) ).

tff(thm_2Ewellorder_2Eorderlt__trichotomy,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V1w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
      ( p(c_2Ewellorder_2Eorderlt_2E2(A_27a,A_27b,V1w1_2E0,V0w2_2E0))
      | p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27b,V1w1_2E0,V0w2_2E0))
      | p(c_2Ewellorder_2Eorderlt_2E2(A_27b,A_27a,V0w2_2E0,V1w1_2E0)) ) ).

tff(thm_2Ewellorder_2EelsOf__wZERO,axiom,
    ! [A_27a: $tType] : ( c_2Ewellorder_2EelsOf_2E1(A_27a,c_2Ewellorder_2EwZERO_2E0(A_27a)) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).

tff(thm_2Ewellorder_2EWIN__wZERO,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V0y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,c_2Ewellorder_2EwZERO_2E0(A_27a)))) = c_2Ebool_2EF_2E0 ) ).

tff(thm_2Ewellorder_2EWLE__wZERO,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V0y_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,c_2Ewellorder_2EwZERO_2E0(A_27a))) = c_2Ebool_2EF_2E0 ) ).

tff(thm_2Ewellorder_2Eorderiso__wZERO,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] :
      ( p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27b,c_2Ewellorder_2EwZERO_2E0(A_27a),V0w_2E0))
    <=> ( V0w_2E0 = c_2Ewellorder_2EwZERO_2E0(A_27b) ) ) ).

tff(thm_2Ewellorder_2EelsOf__EQ__EMPTY,axiom,
    ! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
      ( ( c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
    <=> ( V0w_2E0 = c_2Ewellorder_2EwZERO_2E0(A_27a) ) ) ).

tff(thm_2Ewellorder_2ELT__wZERO,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Eorderlt_2E2(A_27a,A_27b,V0w_2E0,c_2Ewellorder_2EwZERO_2E0(A_27b)) = c_2Ebool_2EF_2E0 ) ).

tff(thm_2Ewellorder_2Eorderlt__WF,axiom,
    ! [A_27a: $tType] : p(c_2Erelation_2EWF_2E1(tyop_2Ewellorder_2Ewellorder(A_27a),c_2Ewellorder_2Eorderlt_2E0(A_27a,A_27a))) ).

tff(thm_2Ewellorder_2Eorderlt__orderiso,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0y0_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V1x0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2b0_2E0: tyop_2Ewellorder_2Ewellorder(A_27d),V3a0_2E0: tyop_2Ewellorder_2Ewellorder(A_27c)] :
      ( ( p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27b,V1x0_2E0,V0y0_2E0))
        & p(c_2Ewellorder_2Eorderiso_2E2(A_27c,A_27d,V3a0_2E0,V2b0_2E0)) )
     => ( c_2Ewellorder_2Eorderlt_2E2(A_27a,A_27c,V1x0_2E0,V3a0_2E0) = c_2Ewellorder_2Eorderlt_2E2(A_27b,A_27d,V0y0_2E0,V2b0_2E0) ) ) ).

tff(thm_2Ewellorder_2Efinite__iso,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V1w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
      ( p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27b,V1w1_2E0,V0w2_2E0))
     => ( c_2Ewellorder_2Efinite_2E1(A_27a,V1w1_2E0) = c_2Ewellorder_2Efinite_2E1(A_27b,V0w2_2E0) ) ) ).

tff(thm_2Ewellorder_2Efinite__wZERO,axiom,
    ! [A_27a: $tType] : p(c_2Ewellorder_2Efinite_2E1(A_27a,c_2Ewellorder_2EwZERO_2E0(A_27a))) ).

tff(thm_2Ewellorder_2Eorderiso__unique,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V1w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2f2_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V3f1_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w1_2E0),c_2Ewellorder_2EelsOf_2E1(A_27b,V0w2_2E0)))
        & p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V2f2_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w1_2E0),c_2Ewellorder_2EelsOf_2E1(A_27b,V0w2_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_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w1_2E0))))
           => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(A_27b,A_27b,app_2E2(A_27a,A_27b,V3f1_2E0,V4x_2E0),app_2E2(A_27a,A_27b,V3f1_2E0,V5y_2E0)),c_2Eset__relation_2Estrict_2E1(A_27b,c_2Ewellorder_2Ewellorder__REP_2E1(A_27b,V0w2_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_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w1_2E0))))
           => p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(A_27b,A_27b,app_2E2(A_27a,A_27b,V2f2_2E0,V6x_2E0),app_2E2(A_27a,A_27b,V2f2_2E0,V7y_2E0)),c_2Eset__relation_2Estrict_2E1(A_27b,c_2Ewellorder_2Ewellorder__REP_2E1(A_27b,V0w2_2E0)))) ) )
     => ! [V8x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V8x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w1_2E0)))
         => ( app_2E2(A_27a,A_27b,V3f1_2E0,V8x_2E0) = app_2E2(A_27a,A_27b,V2f2_2E0,V8x_2E0) ) ) ) ).

tff(thm_2Ewellorder_2Eseteq__wlog,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( ( ! [V2a_2E0: A_27a,V3b_2E0: A_27a] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,V2a_2E0),V3b_2E0))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,V3b_2E0),V2a_2E0)) )
        & ! [V4x_2E0: A_27b,V5a_2E0: A_27a,V6b_2E0: A_27a] :
            ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,V5a_2E0),V6b_2E0))
              & p(c_2Ebool_2EIN_2E2(A_27b,V4x_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1f_2E0,V5a_2E0))) )
           => p(c_2Ebool_2EIN_2E2(A_27b,V4x_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1f_2E0,V6b_2E0))) ) )
     => ! [V7a_2E0: A_27a,V8b_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,V7a_2E0),V8b_2E0))
         => ( app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1f_2E0,V7a_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1f_2E0,V8b_2E0) ) ) ) ).

tff(thm_2Ewellorder_2Ewo__INDUCTION,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
      ( ! [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,V3y_2E0,V2x_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w_2E0))))
             => ( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w_2E0)))
               => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3y_2E0)) ) )
         => ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w_2E0)))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) ) )
     => ! [V4x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w_2E0)))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0)) ) ) ).

tff(thm_2Ewellorder_2EFORALL__NUM,axiom,
    ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V1n_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V1n_2E0))
    <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Enum_2E0_2E0))
        & ! [V2n_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Enum_2ESUC_2E1(V2n_2E0))) ) ) ).

tff(thm_2Ewellorder_2Estrict__UNION,axiom,
    ! [A_27a: $tType,V0r2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Estrict_2E1(A_27a,c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V1r1_2E0,V0r2_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Eset__relation_2Estrict_2E1(A_27a,V1r1_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,V0r2_2E0)) ) ).

tff(thm_2Ewellorder_2EWLE__WIN__EQ,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(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,V0y_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0)))
    <=> ( ( ( V1x_2E0 = V0y_2E0 )
          & p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w_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),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0)))) ) ) ).

tff(thm_2Ewellorder_2Ewellorder__remove,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(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)))))] :
      ( ! [V2x_2E0: A_27a,V1e_2E0: A_27a,V3y_2E0: A_27a,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
          ( p(app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V1e_2E0),V3y_2E0),V0w_2E0))
        <=> ( ( V2x_2E0 != V1e_2E0 )
            & ( V3y_2E0 != V1e_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_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0))) ) )
     => ( ! [V1e_2E0: A_27a,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),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_2Ewellorder_2Ewellorder(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))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(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,V1e_2E0),V0w_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_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V1e_2E0),V3y_2E0),V0w_2E0)) )
       => ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1e_2E0: A_27a] : p(c_2Ewellorder_2Ewellorder_2E1(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_2Ewellorder_2Ewellorder(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))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(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,V1e_2E0),V0w_2E0))))) ) ) ).

tff(thm_2Ewellorder_2EelsOf__remove,axiom,
    ! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1e_2E0: A_27a] : ( c_2Ewellorder_2EelsOf_2E1(A_27a,c_2Ewellorder_2Eremove_2E2(A_27a,V1e_2E0,V0w_2E0)) = c_2Epred__set_2EDELETE_2E2(A_27a,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0),V1e_2E0) ) ).

tff(thm_2Ewellorder_2EWIN__remove,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V3e_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,V0y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,c_2Ewellorder_2Eremove_2E2(A_27a,V3e_2E0,V2w_2E0)))))
    <=> ( ( V1x_2E0 != V3e_2E0 )
        & ( V0y_2E0 != V3e_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),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0)))) ) ) ).

tff(thm_2Ewellorder_2Ewellorder__ADD1,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))] :
      ( ! [V1e_2E0: A_27a,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),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_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0,V1e_2E0),V0w_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,V1e_2E0),c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0))) )
     => ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1e_2E0: A_27a] :
          ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V1e_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0)))
         => p(c_2Ewellorder_2Ewellorder_2E1(A_27a,c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),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_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0,V1e_2E0),V0w_2E0))),c_2Epred__set_2EINSERT_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1e_2E0,V1e_2E0),c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)))))) ) ) ).

tff(thm_2Ewellorder_2EelsOf__ADD1,axiom,
    ! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1e_2E0: A_27a] : ( c_2Ewellorder_2EelsOf_2E1(A_27a,c_2Ewellorder_2EADD1_2E2(A_27a,V1e_2E0,V0w_2E0)) = c_2Epred__set_2EINSERT_2E2(A_27a,V1e_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0)) ) ).

tff(thm_2Ewellorder_2EWIN__ADD1,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V3e_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,V0y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,c_2Ewellorder_2EADD1_2E2(A_27a,V3e_2E0,V2w_2E0)))))
    <=> ( ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V3e_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w_2E0)))
          & p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w_2E0)))
          & ( V0y_2E0 = V3e_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),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0)))) ) ) ).

tff(thm_2Ewellorder_2EelsOf__cardeq__iso,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0wo_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
      ( p(c_2Epred__set_2EINJ_2E3(A_27b,A_27a,V1f_2E0,c_2Ewellorder_2EelsOf_2E1(A_27b,V0wo_2E0),c_2Epred__set_2EUNIV_2E0(A_27a)))
     => ? [V2wo_27_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : p(c_2Ewellorder_2Eorderiso_2E2(A_27b,A_27a,V0wo_2E0,V2wo_27_2E0)) ) ).

tff(thm_2Ewellorder_2Eallsets__wellorderable,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
    ? [V1wo_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2EelsOf_2E1(A_27a,V1wo_2E0) = V0s_2E0 ) ).

tff(thm_2Ewellorder_2EWF,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
    <=> ! [V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ? [V2w_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1B_2E0,V2w_2E0))
         => ? [V3min_2E0: A_27a] :
              ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1B_2E0,V3min_2E0))
              & ! [V4b_2E0: A_27a] :
                  ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4b_2E0),V3min_2E0))
                 => ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1B_2E0,V4b_2E0)) ) ) ) ) ).

tff(thm_2Ewellorder_2EWF__EQ,axiom,
    ! [A_27a: $tType,V0_3C_3C_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,V0_3C_3C_2E0))
    <=> ! [V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0))
        <=> ? [V3x_2E0: A_27a] :
              ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3x_2E0))
              & ! [V4y_2E0: A_27a] :
                  ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0_3C_3C_2E0,V4y_2E0),V3x_2E0))
                 => ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V4y_2E0)) ) ) ) ) ).

tff(thm_2Ewellorder_2EWF__IND,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
    <=> ! [V1P_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),V0R_2E0,V3y_2E0),V2x_2E0))
                 => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3y_2E0)) )
             => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0)) )
         => ! [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V4x_2E0)) ) ) ).

tff(thm_2Ewellorder_2EWF__DCHAIN,axiom,
    ! [A_27a: $tType,V0_3C_3C_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,V0_3C_3C_2E0))
    <=> ~ ? [V1s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
          ! [V2n_2E0: tyop_2Enum_2Enum] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0_3C_3C_2E0,app_2E2(tyop_2Enum_2Enum,A_27a,V1s_2E0,c_2Enum_2ESUC_2E1(V2n_2E0))),app_2E2(tyop_2Enum_2Enum,A_27a,V1s_2E0,V2n_2E0))) ) ).

tff(thm_2Ewellorder_2EWF__UREC,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0_3C_3C_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,V0_3C_3C_2E0))
     => ! [V1H_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] :
          ( ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4x_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),V0_3C_3C_2E0,V5z_2E0),V4x_2E0))
                 => ( app_2E2(A_27a,A_27b,V2f_2E0,V5z_2E0) = app_2E2(A_27a,A_27b,V3g_2E0,V5z_2E0) ) )
             => ( app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1H_2E0,V2f_2E0),V4x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1H_2E0,V3g_2E0),V4x_2E0) ) )
         => ! [V6f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
              ( ( ! [V8x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V6f_2E0,V8x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1H_2E0,V6f_2E0),V8x_2E0) )
                & ! [V9x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V7g_2E0,V9x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1H_2E0,V7g_2E0),V9x_2E0) ) )
             => ( V6f_2E0 = V7g_2E0 ) ) ) ) ).

tff(thm_2Ewellorder_2EWF__UREC__WF,axiom,
    ! [A_27a: $tType,V0_3C_3C_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V1H_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
          ( ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4x_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),V0_3C_3C_2E0,V5z_2E0),V4x_2E0))
                 => ( app_2E2(A_27a,tyop_2Emin_2Ebool,V2f_2E0,V5z_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V3g_2E0,V5z_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),V1H_2E0,V2f_2E0),V4x_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),V1H_2E0,V3g_2E0),V4x_2E0) ) )
         => ! [V6f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V7g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( ( ! [V8x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,V6f_2E0,V8x_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),V1H_2E0,V6f_2E0),V8x_2E0) )
                & ! [V9x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,V7g_2E0,V9x_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),V1H_2E0,V7g_2E0),V9x_2E0) ) )
             => ( V6f_2E0 = V7g_2E0 ) ) )
     => p(c_2Erelation_2EWF_2E1(A_27a,V0_3C_3C_2E0)) ) ).

tff(thm_2Ewellorder_2EWF__REC__INVARIANT,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0_3C_3C_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,V0_3C_3C_2E0))
     => ! [V1H_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2S_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
          ( ! [V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V5x_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),V0_3C_3C_2E0,V6z_2E0),V5x_2E0))
                 => ( ( app_2E2(A_27a,A_27b,V3f_2E0,V6z_2E0) = app_2E2(A_27a,A_27b,V4g_2E0,V6z_2E0) )
                    & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2S_2E0,V6z_2E0),app_2E2(A_27a,A_27b,V3f_2E0,V6z_2E0))) ) )
             => ( ( app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1H_2E0,V3f_2E0),V5x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1H_2E0,V4g_2E0),V5x_2E0) )
                & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2S_2E0,V5x_2E0),app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1H_2E0,V3f_2E0),V5x_2E0))) ) )
         => ? [V7f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
            ! [V8x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V7f_2E0,V8x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1H_2E0,V7f_2E0),V8x_2E0) ) ) ) ).

tff(thm_2Ewellorder_2EWF__REC,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0_3C_3C_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,V0_3C_3C_2E0))
     => ! [V1H_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] :
          ( ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4x_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),V0_3C_3C_2E0,V5z_2E0),V4x_2E0))
                 => ( app_2E2(A_27a,A_27b,V2f_2E0,V5z_2E0) = app_2E2(A_27a,A_27b,V3g_2E0,V5z_2E0) ) )
             => ( app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1H_2E0,V2f_2E0),V4x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1H_2E0,V3g_2E0),V4x_2E0) ) )
         => ? [V6f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
            ! [V7x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V6f_2E0,V7x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1H_2E0,V6f_2E0),V7x_2E0) ) ) ) ).

tff(thm_2Ewellorder_2EWF__num,axiom,
    p(c_2Erelation_2EWF_2E1(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E0)) ).

tff(thm_2Ewellorder_2EWF__REC__num,axiom,
    ! [A_27a: $tType,V0H_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3n_2E0: tyop_2Enum_2Enum] :
          ( ! [V4m_2E0: tyop_2Enum_2Enum] :
              ( p(c_2Eprim__rec_2E_3C_2E2(V4m_2E0,V3n_2E0))
             => ( app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V4m_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V2g_2E0,V4m_2E0) ) )
         => ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0H_2E0,V1f_2E0),V3n_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0H_2E0,V2g_2E0),V3n_2E0) ) )
     => ? [V5f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
        ! [V6n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,V5f_2E0,V6n_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0H_2E0,V5f_2E0),V6n_2E0) ) ) ).

tff(thm_2Ewellorder_2EZL,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ewellorder_2Eposet_2E1(A_27a,V0l_2E0))
        & ? [V1x_2E0: A_27a] : p(c_2Ewellorder_2Efl_2E2(A_27a,V0l_2E0,V1x_2E0))
        & ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ewellorder_2EChain_2E2(A_27a,V0l_2E0,V2P_2E0))
           => ? [V3y_2E0: A_27a] :
                ( p(c_2Ewellorder_2Efl_2E2(A_27a,V0l_2E0,V3y_2E0))
                & ! [V4x_2E0: A_27a] :
                    ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V4x_2E0))
                   => p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V4x_2E0,V3y_2E0))) ) ) ) )
     => ? [V5y_2E0: A_27a] :
          ( p(c_2Ewellorder_2Efl_2E2(A_27a,V0l_2E0,V5y_2E0))
          & ! [V6x_2E0: A_27a] :
              ( p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,V0l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V5y_2E0,V6x_2E0)))
             => ( V5y_2E0 = V6x_2E0 ) ) ) ) ).

tff(thm_2Ewellorder_2EPOSET__RESTRICTED__SUBSET,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_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(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)),F0_2E0,V0P_2E0),V1x_2E0),V2y_2E0))
        <=> ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0))
            & p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V2y_2E0))
            & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1x_2E0,V2y_2E0)) ) )
     => ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : p(c_2Ewellorder_2Eposet_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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)),F0_2E0,V0P_2E0)))) ) ).

tff(thm_2Ewellorder_2EFL__RESTRICTED__SUBSET,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_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(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)),F0_2E0,V0P_2E0),V1x_2E0),V2y_2E0))
        <=> ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0))
            & p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V2y_2E0))
            & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1x_2E0,V2y_2E0)) ) )
     => ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Efl_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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)),F0_2E0,V0P_2E0))) = V0P_2E0 ) ) ).

tff(thm_2Ewellorder_2EZL__SUBSETS,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ! [V1c_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
          ( ( ! [V2x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0,V1c_2E0))
               => p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
            & ! [V3x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0,V1c_2E0))
                  & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4y_2E0,V1c_2E0)) )
               => ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3x_2E0,V4y_2E0))
                  | p(c_2Epred__set_2ESUBSET_2E2(A_27a,V4y_2E0,V3x_2E0)) ) ) )
         => ? [V5z_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V5z_2E0))
              & ! [V6x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                  ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6x_2E0,V1c_2E0))
                 => p(c_2Epred__set_2ESUBSET_2E2(A_27a,V6x_2E0,V5z_2E0)) ) ) )
     => ? [V7a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V7a_2E0))
          & ! [V8x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V8x_2E0))
                & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V7a_2E0,V8x_2E0)) )
             => ( V7a_2E0 = V8x_2E0 ) ) ) ) ).

tff(thm_2Ewellorder_2EZL__SUBSETS__BIGUNION,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ! [V1c_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
          ( ( ! [V2x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0,V1c_2E0))
               => p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
            & ! [V3x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0,V1c_2E0))
                  & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4y_2E0,V1c_2E0)) )
               => ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3x_2E0,V4y_2E0))
                  | p(c_2Epred__set_2ESUBSET_2E2(A_27a,V4y_2E0,V3x_2E0)) ) ) )
         => p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,V1c_2E0))) )
     => ? [V5a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V5a_2E0))
          & ! [V6x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V6x_2E0))
                & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V5a_2E0,V6x_2E0)) )
             => ( V5a_2E0 = V6x_2E0 ) ) ) ) ).

tff(thm_2Ewellorder_2EZL__SUBSETS__BIGUNION__NONEMPTY,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( ? [V1x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0))
        & ! [V2c_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
            ( ( ? [V3x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0,V2c_2E0))
              & ! [V4x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                  ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4x_2E0,V2c_2E0))
                 => p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0)) )
              & ! [V5x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                  ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5x_2E0,V2c_2E0))
                    & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6y_2E0,V2c_2E0)) )
                 => ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V5x_2E0,V6y_2E0))
                    | p(c_2Epred__set_2ESUBSET_2E2(A_27a,V6y_2E0,V5x_2E0)) ) ) )
           => p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,V2c_2E0))) ) )
     => ? [V7a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V7a_2E0))
          & ! [V8x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V8x_2E0))
                & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V7a_2E0,V8x_2E0)) )
             => ( V7a_2E0 = V8x_2E0 ) ) ) ) ).

tff(thm_2Ewellorder_2EFLATTEN__LEMMA,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V3x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
         => ( app_2E2(A_27b,A_27a,V0g_2E0,app_2E2(A_27a,A_27b,V1f_2E0,V3x_2E0)) = V3x_2E0 ) )
    <=> ! [V4y_2E0: A_27b,V5x_2E0: A_27a] :
          ( ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V2s_2E0))
            & ( V4y_2E0 = app_2E2(A_27a,A_27b,V1f_2E0,V5x_2E0) ) )
         => ( app_2E2(A_27b,A_27a,V0g_2E0,V4y_2E0) = V5x_2E0 ) ) ) ).

tff(thm_2Ewellorder_2ETARSKI__SET,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2t_2E0))
         => p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,V1s_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,V2t_2E0))) )
     => ? [V3s_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),V0f_2E0,V3s_2E0) = V3s_2E0 ) ) ).

tff(thm_2Ewellorder_2EINJECTIVE__LEFT__INVERSE__NONEMPTY,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ? [V3x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
     => ( ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V1s_2E0))
              & p(c_2Ebool_2EIN_2E2(A_27a,V5y_2E0,V1s_2E0))
              & ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V5y_2E0) ) )
           => ( V4x_2E0 = V5y_2E0 ) )
      <=> ? [V6g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
            ( ! [V7y_2E0: A_27b] :
                ( p(c_2Ebool_2EIN_2E2(A_27b,V7y_2E0,V2t_2E0))
               => p(c_2Ebool_2EIN_2E2(A_27a,app_2E2(A_27b,A_27a,V6g_2E0,V7y_2E0),V1s_2E0)) )
            & ! [V8x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V8x_2E0,V1s_2E0))
               => ( app_2E2(A_27b,A_27a,V6g_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V8x_2E0)) = V8x_2E0 ) ) ) ) ) ).

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