ITP001 Axioms: ITP058_7.ax


%------------------------------------------------------------------------------
% File     : ITP058_7 : TPTP v9.0.0. 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    : wot.ax [Gau19]
%          : HL4058_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  136 (  38 unt;  74 typ;   0 def)
%            Number of atoms       :  105 (  46 equ)
%            Maximal formula atoms :    6 (   0 avg)
%            Number of connectives :   47 (   4   ~;   4   |;   9   &)
%                                         (  20 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   48 (  35   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   72 (  72 usr;   6 con; 0-4 aty)
%            Number of variables   :  218 ( 147   !;   3   ?; 218   :)
%                                         (  68  !>;   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_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).

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

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

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

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

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

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

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

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

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

tff(c_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_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

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

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

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

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

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

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

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

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

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

tff(c_2Epred__set_2ECOMPL_2E0,type,
    c_2Epred__set_2ECOMPL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2ECOMPL_2E1,type,
    c_2Epred__set_2ECOMPL_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > 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_2EGSPEC_2E0,type,
    c_2Epred__set_2EGSPEC_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

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

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

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

tff(c_2Epred__set_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_2Erelation_2ESTRORD_2E0,type,
    c_2Erelation_2ESTRORD_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

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

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

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

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

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

tff(c_2Ewot_2EStrongWellOrder_2E0,type,
    c_2Ewot_2EStrongWellOrder_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_2Ewot_2EStrongWellOrder_2E1,type,
    c_2Ewot_2EStrongWellOrder_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(c_2Erelation_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_2EWeakOrder_2E0,type,
    c_2Erelation_2EWeakOrder_2E0: 
      !>[A_27g: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

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

tff(c_2Ewot_2EWeakWellOrder_2E0,type,
    c_2Ewot_2EWeakWellOrder_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_2Ewot_2EWeakWellOrder_2E1,type,
    c_2Ewot_2EWeakWellOrder_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

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_2Ewot_2Echain_2E0,type,
    c_2Ewot_2Echain_2E0: 
      !>[A_27x: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ewot_2Echain_2E1,type,
    c_2Ewot_2Echain_2E1: 
      !>[A_27x: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Ewot_2Ecpl_2E0,type,
    c_2Ewot_2Ecpl_2E0: 
      !>[A_27x: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Ewot_2Ecpl_2E2,type,
    c_2Ewot_2Ecpl_2E2: 
      !>[A_27x: $tType] : ( ( tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ewot_2Emex_2E0,type,
    c_2Ewot_2Emex_2E0: 
      !>[A_27x: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),A_27x) ).

tff(c_2Ewot_2Emex_2E1,type,
    c_2Ewot_2Emex_2E1: 
      !>[A_27x: $tType] : ( tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool) > A_27x ) ).

tff(c_2Ewot_2Emex__less_2E0,type,
    c_2Ewot_2Emex__less_2E0: 
      !>[A_27x: $tType] : tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)) ).

tff(c_2Ewot_2Emex__less__eq_2E0,type,
    c_2Ewot_2Emex__less__eq_2E0: 
      !>[A_27x: $tType] : tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)) ).

tff(c_2Ewot_2Emex__less__eq_2E2,type,
    c_2Ewot_2Emex__less__eq_2E2: 
      !>[A_27x: $tType] : ( ( A_27x * A_27x ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ewot_2Epreds_2E0,type,
    c_2Ewot_2Epreds_2E0: 
      !>[A_27x: $tType] : tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)) ).

tff(c_2Ewot_2Epreds_2E1,type,
    c_2Ewot_2Epreds_2E1: 
      !>[A_27x: $tType] : ( A_27x > tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool) ) ).

tff(c_2Ewot_2Epreds__image_2E0,type,
    c_2Ewot_2Epreds__image_2E0: 
      !>[A_27x: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Ewot_2Epreds__image_2E1,type,
    c_2Ewot_2Epreds__image_2E1: 
      !>[A_27x: $tType] : ( tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) ).

tff(c_2Ewot_2Esetsuc_2E0,type,
    c_2Ewot_2Esetsuc_2E0: 
      !>[A_27x: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)) ).

tff(c_2Ewot_2Esetsuc_2E1,type,
    c_2Ewot_2Esetsuc_2E1: 
      !>[A_27x: $tType] : ( tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool) ) ).

tff(c_2Ewot_2Esuccl_2E0,type,
    c_2Ewot_2Esuccl_2E0: 
      !>[A_27x: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ewot_2Esuccl_2E1,type,
    c_2Ewot_2Esuccl_2E1: 
      !>[A_27x: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Ewot_2Etower_2E0,type,
    c_2Ewot_2Etower_2E0: 
      !>[A_27x: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ewot_2Etower_2E1,type,
    c_2Ewot_2Etower_2E1: 
      !>[A_27x: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Ewot_2Euncl_2E0,type,
    c_2Ewot_2Euncl_2E0: 
      !>[A_27x: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ewot_2Euncl_2E1,type,
    c_2Ewot_2Euncl_2E1: 
      !>[A_27x: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

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

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

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

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

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27x,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27x),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECHOICE_2E1(A_27x,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),A_27x,c_2Epred__set_2ECHOICE_2E0(A_27x),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECOMPL_2E1(A_27x,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E0(A_27x),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),A_27x,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),A_27x),X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: A_27x,X1_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27x,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27x,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27x),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: A_27x,X1_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27x,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),app_2E2(A_27x,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27x),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2ESTRORD_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ESTRORD_2E1(A_27x,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E0(A_27x),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27x,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27x),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EStrongLinearOrder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EStrongLinearOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewot_2EStrongWellOrder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Ewot_2EStrongWellOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Ewot_2EStrongWellOrder_2E0(A_27a),X0_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_2EWeakOrder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWeakOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewot_2EWeakWellOrder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Ewot_2EWeakWellOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Ewot_2EWeakWellOrder_2E0(A_27a),X0_2E0) ) ).

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

tff(arityeq1_2Ec_2Ewot_2Echain_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ewot_2Echain_2E1(A_27x,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewot_2Echain_2E0(A_27x),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ewot_2Ecpl_2E2_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] : ( c_2Ewot_2Ecpl_2E2(A_27x,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ewot_2Ecpl_2E0(A_27x),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ewot_2Emex_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] : ( c_2Ewot_2Emex_2E1(A_27x,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),A_27x,c_2Ewot_2Emex_2E0(A_27x),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ewot_2Emex__less__eq_2E2_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: A_27x,X1_2E0: A_27x] : ( c_2Ewot_2Emex__less__eq_2E2(A_27x,X0_2E0,X1_2E0) = app_2E2(A_27x,tyop_2Emin_2Ebool,app_2E2(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Ewot_2Emex__less__eq_2E0(A_27x),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ewot_2Epreds_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: A_27x] : ( c_2Ewot_2Epreds_2E1(A_27x,X0_2E0) = app_2E2(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Ewot_2Epreds_2E0(A_27x),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewot_2Epreds__image_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] : ( c_2Ewot_2Epreds__image_2E1(A_27x,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ewot_2Epreds__image_2E0(A_27x),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewot_2Esetsuc_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] : ( c_2Ewot_2Esetsuc_2E1(A_27x,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Ewot_2Esetsuc_2E0(A_27x),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewot_2Esuccl_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ewot_2Esuccl_2E1(A_27x,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewot_2Esuccl_2E0(A_27x),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewot_2Etower_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ewot_2Etower_2E1(A_27x,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewot_2Etower_2E0(A_27x),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewot_2Euncl_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ewot_2Euncl_2E1(A_27x,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewot_2Euncl_2E0(A_27x),X0_2E0) ) ).

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

tff(thm_2Ewot_2Ecpl__def,axiom,
    ! [A_27x: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V1B_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] :
      ( p(c_2Ewot_2Ecpl_2E2(A_27x,V0A_2E0,V1B_2E0))
    <=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27x,V0A_2E0,V1B_2E0))
        | p(c_2Epred__set_2ESUBSET_2E2(A_27x,V1B_2E0,V0A_2E0)) ) ) ).

tff(thm_2Ewot_2Echain__def,axiom,
    ! [A_27x: $tType,V0C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( p(c_2Ewot_2Echain_2E1(A_27x,V0C_2E0))
    <=> ! [V1a_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V2b_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] :
          ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V1a_2E0,V0C_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V2b_2E0,V0C_2E0)) )
         => p(c_2Ewot_2Ecpl_2E2(A_27x,V1a_2E0,V2b_2E0)) ) ) ).

tff(thm_2Ewot_2Emex__def,axiom,
    ! [A_27x: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] : ( c_2Ewot_2Emex_2E1(A_27x,V0s_2E0) = c_2Epred__set_2ECHOICE_2E1(A_27x,c_2Epred__set_2ECOMPL_2E1(A_27x,V0s_2E0)) ) ).

tff(thm_2Ewot_2Esetsuc__def,axiom,
    ! [A_27x: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] : ( c_2Ewot_2Esetsuc_2E1(A_27x,V0s_2E0) = c_2Epred__set_2EINSERT_2E2(A_27x,c_2Ewot_2Emex_2E1(A_27x,V0s_2E0),V0s_2E0) ) ).

tff(thm_2Ewot_2Esuccl__def,axiom,
    ! [A_27x: $tType,V0c_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( p(c_2Ewot_2Esuccl_2E1(A_27x,V0c_2E0))
    <=> ! [V1s_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V1s_2E0,V0c_2E0))
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Ewot_2Esetsuc_2E1(A_27x,V1s_2E0),V0c_2E0)) ) ) ).

tff(thm_2Ewot_2Euncl__def,axiom,
    ! [A_27x: $tType,V0c_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( p(c_2Ewot_2Euncl_2E1(A_27x,V0c_2E0))
    <=> ! [V1w_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
          ( ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V1w_2E0,V0c_2E0))
            & p(c_2Ewot_2Echain_2E1(A_27x,V1w_2E0)) )
         => p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27x,V1w_2E0),V0c_2E0)) ) ) ).

tff(thm_2Ewot_2Etower__def,axiom,
    ! [A_27x: $tType,V0A_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( p(c_2Ewot_2Etower_2E1(A_27x,V0A_2E0))
    <=> ( p(c_2Ewot_2Esuccl_2E1(A_27x,V0A_2E0))
        & p(c_2Ewot_2Euncl_2E1(A_27x,V0A_2E0)) ) ) ).

tff(thm_2Ewot_2Emex__less__eq__def,axiom,
    ! [A_27x: $tType,V0a_2E0: A_27x,V1b_2E0: A_27x] : ( c_2Ewot_2Emex__less__eq_2E2(A_27x,V0a_2E0,V1b_2E0) = c_2Epred__set_2ESUBSET_2E2(A_27x,c_2Ewot_2Epreds_2E1(A_27x,V0a_2E0),c_2Ewot_2Epreds_2E1(A_27x,V1b_2E0)) ) ).

tff(thm_2Ewot_2Emex__less__def,axiom,
    ! [A_27x: $tType] : ( c_2Ewot_2Emex__less_2E0(A_27x) = c_2Erelation_2ESTRORD_2E1(A_27x,c_2Ewot_2Emex__less__eq_2E0(A_27x)) ) ).

tff(thm_2Ewot_2EWeakWellOrder__def,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Ewot_2EWeakWellOrder_2E1(A_27a,V0R_2E0))
    <=> ( p(c_2Erelation_2EWeakOrder_2E1(A_27a,V0R_2E0))
        & ! [V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( ( V1B_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) )
           => ? [V2m_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V2m_2E0,V1B_2E0))
                & ! [V3b_2E0: A_27a] :
                    ( p(c_2Ebool_2EIN_2E2(A_27a,V3b_2E0,V1B_2E0))
                   => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2m_2E0),V3b_2E0)) ) ) ) ) ) ).

tff(thm_2Ewot_2Epreds__image__def,axiom,
    ! [A_27x: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
      ( ! [V0X_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V1x_2E0: A_27x] : ( app_2E2(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewot_2Epreds_2E1(A_27x,V1x_2E0),c_2Ebool_2EIN_2E2(A_27x,V1x_2E0,V0X_2E0)) )
     => ! [V0X_2E0: tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)] : ( c_2Ewot_2Epreds__image_2E1(A_27x,V0X_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),A_27x,app_2E2(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0)) ) ) ).

tff(thm_2Ewot_2EStrongWellOrder__def,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Ewot_2EStrongWellOrder_2E1(A_27a,V0R_2E0))
    <=> ( p(c_2Erelation_2EStrongLinearOrder_2E1(A_27a,V0R_2E0))
        & p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0)) ) ) ).

tff(thm_2Ewot_2EStrongWellOrderExists,axiom,
    ! [A_27a: $tType] :
    ? [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EStrongLinearOrder_2E1(A_27a,V0R_2E0))
      & p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0)) ) ).

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