ITP001 Axioms: ITP008_7.ax


%------------------------------------------------------------------------------
% File     : ITP008_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    : combin.ax [Gau19]
%          : HL4008_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  197 (  93 unt;  65 typ;   0 def)
%            Number of atoms       :  188 ( 140 equ)
%            Maximal formula atoms :    6 (   0 avg)
%            Number of connectives :   64 (   8   ~;   4   |;  11   &)
%                                         (  25 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   65 (  33   >;  32   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   63 (  63 usr;   7 con; 0-6 aty)
%            Number of variables   :  670 ( 570   !;   1   ?; 670   :)
%                                         (  99  !>;   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(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_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_2Ecombin_2E_3A_3E_2E0,type,
    c_2Ecombin_2E_3A_3E_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)) ).

tff(c_2Ecombin_2E_3A_3E_2E2,type,
    c_2Ecombin_2E_3A_3E_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27b * tyop_2Emin_2Efun(A_27b,A_27a) ) > A_27a ) ).

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_2Ecombin_2EASSOC_2E0,type,
    c_2Ecombin_2EASSOC_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool) ).

tff(c_2Ecombin_2EASSOC_2E1,type,
    c_2Ecombin_2EASSOC_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)) > tyop_2Emin_2Ebool ) ).

tff(c_2Emarker_2EAbbrev_2E0,type,
    c_2Emarker_2EAbbrev_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).

tff(c_2Ecombin_2EC_2E0,type,
    c_2Ecombin_2EC_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(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))) ).

tff(c_2Ecombin_2EC_2E2,type,
    c_2Ecombin_2EC_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) * A_27b ) > tyop_2Emin_2Efun(A_27a,A_27c) ) ).

tff(c_2Ecombin_2EC_2E3,type,
    c_2Ecombin_2EC_2E3: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) * A_27b * A_27a ) > A_27c ) ).

tff(c_2Ecombin_2ECOMM_2E0,type,
    c_2Ecombin_2ECOMM_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool) ).

tff(c_2Ecombin_2ECOMM_2E1,type,
    c_2Ecombin_2ECOMM_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)) > 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_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2Ecombin_2EFAIL_2E0,type,
    c_2Ecombin_2EFAIL_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).

tff(c_2Ecombin_2EFAIL_2E2,type,
    c_2Ecombin_2EFAIL_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > A_27a ) ).

tff(c_2Ecombin_2EFCOMM_2E0,type,
    c_2Ecombin_2EFCOMM_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool)) ).

tff(c_2Ecombin_2EFCOMM_2E2,type,
    c_2Ecombin_2EFCOMM_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) * tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)) ) > tyop_2Emin_2Ebool ) ).

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

tff(c_2Ecombin_2EI_2E1,type,
    c_2Ecombin_2EI_2E1: 
      !>[A_27a: $tType] : ( A_27a > A_27a ) ).

tff(c_2Ecombin_2EK_2E0,type,
    c_2Ecombin_2EK_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).

tff(c_2Ecombin_2EK_2E1,type,
    c_2Ecombin_2EK_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27b,A_27a) ) ).

tff(c_2Ecombin_2EK_2E2,type,
    c_2Ecombin_2EK_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > A_27a ) ).

tff(c_2Ecombin_2ELEFT__ID_2E0,type,
    c_2Ecombin_2ELEFT__ID_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Ecombin_2ELEFT__ID_2E2,type,
    c_2Ecombin_2ELEFT__ID_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * 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_2Ecombin_2EMONOID_2E0,type,
    c_2Ecombin_2EMONOID_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Ecombin_2EMONOID_2E2,type,
    c_2Ecombin_2EMONOID_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)) * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ecombin_2ERIGHT__ID_2E0,type,
    c_2Ecombin_2ERIGHT__ID_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ).

tff(c_2Ecombin_2ERIGHT__ID_2E2,type,
    c_2Ecombin_2ERIGHT__ID_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) * A_27b ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ecombin_2ES_2E0,type,
    c_2Ecombin_2ES_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_2Ecombin_2ES_2E2,type,
    c_2Ecombin_2ES_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Efun(A_27a,A_27c) ) ).

tff(c_2Ecombin_2ES_2E3,type,
    c_2Ecombin_2ES_2E3: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) * tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27c ) ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(c_2Ecombin_2EUPDATE_2E0,type,
    c_2Ecombin_2EUPDATE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))) ).

tff(c_2Ecombin_2EUPDATE_2E3,type,
    c_2Ecombin_2EUPDATE_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).

tff(c_2Ecombin_2EUPDATE_2E4,type,
    c_2Ecombin_2EUPDATE_2E4: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(c_2Ecombin_2EW_2E0,type,
    c_2Ecombin_2EW_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)) ).

tff(c_2Ecombin_2EW_2E2,type,
    c_2Ecombin_2EW_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)) * 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_2Ebool_2Eliteral__case_2E0,type,
    c_2Ebool_2Eliteral__case_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_2Eliteral__case_2E2,type,
    c_2Ebool_2Eliteral__case_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

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

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

tff(c_2Ecombin_2Eo_2E3,type,
    c_2Ecombin_2Eo_2E3: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) * A_27a ) > A_27b ) ).

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_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_2Ecombin_2E_3A_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Ecombin_2E_3A_3E_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),c_2Ecombin_2E_3A_3E_2E0(A_27a,A_27b),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_2Ecombin_2EASSOC_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2EASSOC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] : ( c_2Ecombin_2EASSOC_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a] : ( c_2Ecombin_2EC_2E2(A_27a,A_27a,tyop_2Emin_2Ebool,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EC_2E0(A_27a,A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0: A_27b,X2_2E0: A_27a] : ( c_2Ecombin_2EC_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27c,app_2E2(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(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ecombin_2EC_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X1_2E0: A_27c,X2_2E0: A_27a] : ( c_2Ecombin_2EC_2E3(A_27a,A_27c,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27b,app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EC_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: A_27c] : ( c_2Ecombin_2EC_2E2(A_27b,A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2EC_2E0(A_27b,A_27c,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2Ecombin_2ECOMM_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27b,X2_2E0: A_27b] : ( c_2Ebool_2ECOND_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ebool_2ECOND_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2EFAIL_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2Ecombin_2EFAIL_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EFAIL_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2EFCOMM_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2EFCOMM_2E2(A_27a,A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EFCOMM_2E0(A_27a,A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2EFCOMM_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2EFCOMM_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EFCOMM_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Ecombin_2EI_2E1(A_27a,X0_2E0) = app_2E2(A_27a,A_27a,c_2Ecombin_2EI_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2EK_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2Ecombin_2EK_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EK_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: A_27c] : ( c_2Ecombin_2EK_2E1(A_27c,A_27a,X0_2E0) = app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2EK_2E0(A_27c,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: A_27c] : ( c_2Ecombin_2EK_2E1(A_27c,A_27b,X0_2E0) = app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2EK_2E0(A_27c,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27d_20mono_2EA_27f,axiom,
    ! [A_27d: $tType,A_27f: $tType,X0_2E0: A_27d] : ( c_2Ecombin_2EK_2E1(A_27d,A_27f,X0_2E0) = app_2E2(A_27d,tyop_2Emin_2Efun(A_27f,A_27d),c_2Ecombin_2EK_2E0(A_27d,A_27f),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27e_20mono_2EA_27f,axiom,
    ! [A_27e: $tType,A_27f: $tType,X0_2E0: A_27e] : ( c_2Ecombin_2EK_2E1(A_27e,A_27f,X0_2E0) = app_2E2(A_27e,tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2EK_2E0(A_27e,A_27f),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2ELEFT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a] : ( c_2Ecombin_2ELEFT__ID_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ELEFT__ID_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2ELEFT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0: A_27a] : ( c_2Ecombin_2ELEFT__ID_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ELEFT__ID_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Ebool_2ELET_2E2(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_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),c_2Ebool_2ELET_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: A_27b] : ( c_2Ebool_2ELET_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27b,A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27a),c_2Ebool_2ELET_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: A_27b] : ( c_2Ebool_2ELET_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ebool_2ELET_2E0(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_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: A_27c] : ( c_2Ebool_2ELET_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27c,A_27a,app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2ELET_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: A_27c] : ( c_2Ebool_2ELET_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27b),c_2Ebool_2ELET_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a] : ( c_2Ecombin_2EMONOID_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EMONOID_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Ecombin_2EMONOID_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EMONOID_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2ERIGHT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a] : ( c_2Ecombin_2ERIGHT__ID_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ERIGHT__ID_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2ERIGHT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: A_27b] : ( c_2Ecombin_2ERIGHT__ID_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ecombin_2ERIGHT__ID_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0: A_27a] : ( c_2Ecombin_2ES_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = 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)),c_2Ecombin_2ES_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0: A_27a] : ( c_2Ecombin_2ES_2E3(A_27a,A_27c,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2ES_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2ES_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,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_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2ES_2E0(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2ES_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2ES_2E0(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EUPDATE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0: A_27a] : ( c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EUPDATE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: A_27c,X1_2E0: A_27d,X2_2E0: tyop_2Emin_2Efun(A_27c,A_27d)] : ( c_2Ecombin_2EUPDATE_2E3(A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),c_2Ecombin_2EUPDATE_2E0(A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: A_27c,X1_2E0: A_27d,X2_2E0: tyop_2Emin_2Efun(A_27c,A_27d),X3_2E0: A_27c] : ( c_2Ecombin_2EUPDATE_2E4(A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27c,A_27d,app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),c_2Ecombin_2EUPDATE_2E0(A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: A_27a] : ( c_2Ecombin_2EW_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EW_2E0(A_27a,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(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Ebool_2Eliteral__case_2E2(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_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),c_2Ebool_2Eliteral__case_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: A_27b] : ( c_2Ebool_2Eliteral__case_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27b,A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27a),c_2Ebool_2Eliteral__case_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: A_27b] : ( c_2Ebool_2Eliteral__case_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ebool_2Eliteral__case_2E0(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2Eliteral__case_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: A_27c] : ( c_2Ebool_2Eliteral__case_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27c,A_27a,app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2Eliteral__case_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: A_27c] : ( c_2Ebool_2Eliteral__case_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27b),c_2Ebool_2Eliteral__case_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E0(A_27a,A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E0(A_27c,A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X2_2E0: A_27c] : ( c_2Ecombin_2Eo_2E3(A_27c,A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E0(A_27c,A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27d,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(A_27d,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(A_27d,A_27b)),c_2Ecombin_2Eo_2E0(A_27d,A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0: A_27b] : ( c_2Ecombin_2Eo_2E3(A_27b,A_27c,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27c,app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2Eo_2E0(A_27b,A_27c,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27c,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ecombin_2Eo_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27b,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E0(A_27a,A_27b,A_27b),X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27c)] : ( c_2Ecombin_2Eo_2E2(A_27d,A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27a),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27a)),c_2Ecombin_2Eo_2E0(A_27d,A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0: A_27a] : ( c_2Ecombin_2Eo_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [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_27c)] : ( c_2Ecombin_2Eo_2E2(A_27d,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27b)),c_2Ecombin_2Eo_2E0(A_27d,A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27f_20mono_2EA_27e_20mono_2EA_27d,axiom,
    ! [A_27d: $tType,A_27e: $tType,A_27f: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,A_27e),X1_2E0: tyop_2Emin_2Efun(A_27f,A_27d)] : ( c_2Ecombin_2Eo_2E2(A_27f,A_27e,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(A_27f,A_27e),app_2E2(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(A_27f,A_27e)),c_2Ecombin_2Eo_2E0(A_27f,A_27e,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,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(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),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_2Ecombin_2EK__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1x_27_2E0: A_27b] : ( c_2Ecombin_2EK_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0) = V0x_2E0 ) ).

tff(thm_2Ecombin_2ES__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1x_27_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_27_27_2E0: A_27a] : ( c_2Ecombin_2ES_2E3(A_27a,A_27b,A_27c,V0x_2E0,V1x_27_2E0,V2x_27_27_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0x_2E0,V2x_27_27_2E0),app_2E2(A_27a,A_27b,V1x_27_2E0,V2x_27_27_2E0)) ) ).

tff(thm_2Ecombin_2EI__DEF,axiom,
    ! [A_27a: $tType] : ( c_2Ecombin_2EI_2E0(A_27a) = c_2Ecombin_2ES_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),A_27a,c_2Ecombin_2EK_2E0(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E0(A_27a,A_27a)) ) ).

tff(thm_2Ecombin_2EC__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1x_27_2E0: A_27b,V2x_27_27_2E0: A_27a] : ( c_2Ecombin_2EC_2E3(A_27a,A_27b,A_27c,V0x_2E0,V1x_27_2E0,V2x_27_27_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0x_2E0,V2x_27_27_2E0),V1x_27_2E0) ) ).

tff(thm_2Ecombin_2EW__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V1x_27_2E0: A_27a] : ( c_2Ecombin_2EW_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0) = app_2E2(A_27a,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0,V1x_27_2E0),V1x_27_2E0) ) ).

tff(thm_2Ecombin_2Eo__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2x_2E0: A_27a] : ( c_2Ecombin_2Eo_2E3(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0) = app_2E2(A_27c,A_27b,V0f_2E0,app_2E2(A_27a,A_27c,V1g_2E0,V2x_2E0)) ) ).

tff(thm_2Ecombin_2EAPP__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Ecombin_2E_3A_3E_2E2(A_27a,A_27b,V0x_2E0,V1f_2E0) = app_2E2(A_27b,A_27a,V1f_2E0,V0x_2E0) ) ).

tff(thm_2Ecombin_2EUPDATE__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V0a_2E0: A_27a,V3x_27_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0a_2E0),V3x_27_2E0))
        <=> ( V0a_2E0 = V3x_27_2E0 ) )
     => ! [V0a_2E0: A_27a,V1b_2E0: A_27b,V2x_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3x_27_2E0: A_27a] : ( c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,V0a_2E0,V1b_2E0,V2x_2E0,V3x_27_2E0) = c_2Ebool_2ECOND_2E3(A_27b,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0a_2E0),V3x_27_2E0),V1b_2E0,app_2E2(A_27a,A_27b,V2x_2E0,V3x_27_2E0)) ) ) ).

tff(thm_2Ecombin_2EASSOC__DEF,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
      ( p(c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0))
    <=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] : ( app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V1x_2E0),app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V2y_2E0),V3z_2E0)) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V1x_2E0),V2y_2E0)),V3z_2E0) ) ) ).

tff(thm_2Ecombin_2ECOMM__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))] :
      ( p(c_2Ecombin_2ECOMM_2E1(A_27a,A_27b,V0f_2E0))
    <=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,V1x_2E0),V2y_2E0) = app_2E2(A_27a,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,V2y_2E0),V1x_2E0) ) ) ).

tff(thm_2Ecombin_2EFCOMM__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1g_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a))] :
      ( p(c_2Ecombin_2EFCOMM_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0))
    <=> ! [V2x_2E0: A_27c,V3y_2E0: A_27a,V4z_2E0: A_27b] : ( app_2E2(A_27a,A_27a,app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0,V2x_2E0),app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0,V3y_2E0),V4z_2E0)) = app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0,app_2E2(A_27a,A_27a,app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0,V2x_2E0),V3y_2E0)),V4z_2E0) ) ) ).

tff(thm_2Ecombin_2ERIGHT__ID__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1e_2E0: A_27b] :
      ( p(c_2Ecombin_2ERIGHT__ID_2E2(A_27a,A_27b,V0f_2E0,V1e_2E0))
    <=> ! [V2x_2E0: A_27a] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0,V2x_2E0),V1e_2E0) = V2x_2E0 ) ) ).

tff(thm_2Ecombin_2ELEFT__ID__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27a] :
      ( p(c_2Ecombin_2ELEFT__ID_2E2(A_27a,A_27b,V0f_2E0,V1e_2E0))
    <=> ! [V2x_2E0: A_27b] : ( app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V1e_2E0),V2x_2E0) = V2x_2E0 ) ) ).

tff(thm_2Ecombin_2EMONOID__DEF,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V1e_2E0: A_27a] :
      ( p(c_2Ecombin_2EMONOID_2E2(A_27a,V0f_2E0,V1e_2E0))
    <=> ( p(c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0))
        & p(c_2Ecombin_2ERIGHT__ID_2E2(A_27a,A_27a,V0f_2E0,V1e_2E0))
        & p(c_2Ecombin_2ELEFT__ID_2E2(A_27a,A_27a,V0f_2E0,V1e_2E0)) ) ) ).

tff(thm_2Ecombin_2EFAIL__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1x_27_2E0: A_27b] : ( c_2Ecombin_2EFAIL_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0) = V0x_2E0 ) ).

tff(thm_2Ecombin_2Eo__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V2x_2E0: A_27c] : ( c_2Ecombin_2Eo_2E3(A_27c,A_27b,A_27a,V0f_2E0,V1g_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,app_2E2(A_27c,A_27a,V1g_2E0,V2x_2E0)) ) ).

tff(thm_2Ecombin_2Eo__ASSOC,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V2h_2E0: tyop_2Emin_2Efun(A_27d,A_27c)] : ( c_2Ecombin_2Eo_2E2(A_27d,A_27b,A_27a,V0f_2E0,c_2Ecombin_2Eo_2E2(A_27d,A_27a,A_27c,V1g_2E0,V2h_2E0)) = c_2Ecombin_2Eo_2E2(A_27d,A_27b,A_27c,c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,V0f_2E0,V1g_2E0),V2h_2E0) ) ).

tff(thm_2Ecombin_2Eo__ABS__L,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V3x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),F0_2E0,V1f_2E0),V3x_2E0) = app_2E2(A_27a,A_27c,V1f_2E0,V3x_2E0) )
     => ! [V0g_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2x_2E0: A_27b] : ( c_2Ecombin_2Eo_2E3(A_27b,A_27c,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),F0_2E0,V1f_2E0),V0g_2E0,V2x_2E0) = app_2E2(A_27a,A_27c,V1f_2E0,app_2E2(A_27b,A_27a,V0g_2E0,V2x_2E0)) ) ) ).

tff(thm_2Ecombin_2Eo__ABS__R,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c))] :
      ( ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V3x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),F0_2E0,V0g_2E0),V3x_2E0) = app_2E2(A_27a,A_27c,V0g_2E0,V3x_2E0) )
     => ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V2x_2E0: A_27a] : ( c_2Ecombin_2Eo_2E3(A_27a,A_27b,A_27c,V1f_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),F0_2E0,V0g_2E0),V2x_2E0) = app_2E2(A_27c,A_27b,V1f_2E0,app_2E2(A_27a,A_27c,V0g_2E0,V2x_2E0)) ) ) ).

tff(thm_2Ecombin_2EK__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( c_2Ecombin_2EK_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0) = V0x_2E0 ) ).

tff(thm_2Ecombin_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] : ( c_2Ecombin_2ES_2E3(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(thm_2Ecombin_2ES__ABS__L,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),F0_2E0,V1f_2E0),V3x_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0,V3x_2E0) )
     => ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V2x_2E0: A_27a] : ( c_2Ecombin_2ES_2E3(A_27a,A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),F0_2E0,V1f_2E0),V0g_2E0,V2x_2E0) = app_2E2(A_27c,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0,V2x_2E0),app_2E2(A_27a,A_27c,V0g_2E0,V2x_2E0)) ) ) ).

tff(thm_2Ecombin_2ES__ABS__R,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c))] :
      ( ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V3x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),F0_2E0,V0g_2E0),V3x_2E0) = app_2E2(A_27a,A_27c,V0g_2E0,V3x_2E0) )
     => ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V2x_2E0: A_27a] : ( c_2Ecombin_2ES_2E3(A_27a,A_27c,A_27b,V1f_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),F0_2E0,V0g_2E0),V2x_2E0) = app_2E2(A_27c,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0,V2x_2E0),app_2E2(A_27a,A_27c,V0g_2E0,V2x_2E0)) ) ) ).

tff(thm_2Ecombin_2EC__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)),V1x_2E0: A_27b,V2y_2E0: A_27a] : ( c_2Ecombin_2EC_2E3(A_27a,A_27b,A_27c,V0f_2E0,V1x_2E0,V2y_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2y_2E0),V1x_2E0) ) ).

tff(thm_2Ecombin_2EC__ABS__L,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),F0_2E0,V1f_2E0),V3x_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0,V3x_2E0) )
     => ! [V0y_2E0: A_27c,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V2x_2E0: A_27a] : ( c_2Ecombin_2EC_2E3(A_27a,A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),F0_2E0,V1f_2E0),V0y_2E0,V2x_2E0) = app_2E2(A_27c,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0,V2x_2E0),V0y_2E0) ) ) ).

tff(thm_2Ecombin_2EW__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V1x_2E0: A_27a] : ( c_2Ecombin_2EW_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,V1x_2E0),V1x_2E0) ) ).

tff(thm_2Ecombin_2EI__THM,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Ecombin_2EI_2E1(A_27a,V0x_2E0) = V0x_2E0 ) ).

tff(thm_2Ecombin_2EI__o__ID,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( c_2Ecombin_2Eo_2E2(A_27a,A_27b,A_27b,c_2Ecombin_2EI_2E0(A_27b),V0f_2E0) = V0f_2E0 )
      & ( c_2Ecombin_2Eo_2E2(A_27a,A_27b,A_27a,V0f_2E0,c_2Ecombin_2EI_2E0(A_27a)) = V0f_2E0 ) ) ).

tff(thm_2Ecombin_2EK__o__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1v_2E0: A_27c] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,c_2Ecombin_2EK_2E1(A_27c,A_27b,V1v_2E0),V0f_2E0) = c_2Ecombin_2EK_2E1(A_27c,A_27a,V1v_2E0) )
      & ! [V2f_2E0: tyop_2Emin_2Efun(A_27d,A_27e),V3v_2E0: A_27d] : ( c_2Ecombin_2Eo_2E2(A_27f,A_27e,A_27d,V2f_2E0,c_2Ecombin_2EK_2E1(A_27d,A_27f,V3v_2E0)) = c_2Ecombin_2EK_2E1(A_27e,A_27f,app_2E2(A_27d,A_27e,V2f_2E0,V3v_2E0)) ) ) ).

tff(thm_2Ecombin_2EUPDATE__APPLY,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
      ( ! [V0a_2E0: A_27a,V1x_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,V0a_2E0,V1x_2E0,V2f_2E0,V0a_2E0) = V1x_2E0 )
      & ! [V3a_2E0: A_27c,V4b_2E0: A_27c,V5x_2E0: A_27d,V6f_2E0: tyop_2Emin_2Efun(A_27c,A_27d)] :
          ( ( V3a_2E0 != V4b_2E0 )
         => ( c_2Ecombin_2EUPDATE_2E4(A_27c,A_27d,V3a_2E0,V5x_2E0,V6f_2E0,V4b_2E0) = app_2E2(A_27c,A_27d,V6f_2E0,V4b_2E0) ) ) ) ).

tff(thm_2Ecombin_2EAPPLY__UPDATE__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V1a_2E0: A_27a,V3c_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V3c_2E0))
        <=> ( V1a_2E0 = V3c_2E0 ) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b,V3c_2E0: A_27a] : ( c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,V1a_2E0,V2b_2E0,V0f_2E0,V3c_2E0) = c_2Ebool_2ECOND_2E3(A_27b,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V3c_2E0),V2b_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V3c_2E0)) ) ) ).

tff(thm_2Ecombin_2EUPDATE__COMMUTES,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27a,V3c_2E0: A_27b,V4d_2E0: A_27b] :
      ( ( V1a_2E0 != V2b_2E0 )
     => ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2b_2E0,V4d_2E0,V0f_2E0)) = c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2b_2E0,V4d_2E0,c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,V0f_2E0)) ) ) ).

tff(thm_2Ecombin_2EUPDATE__EQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b,V3c_2E0: A_27b] : ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V2b_2E0,V0f_2E0)) = c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,V0f_2E0) ) ).

tff(thm_2Ecombin_2EUPDATE__APPLY__ID,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b] :
      ( ( app_2E2(A_27a,A_27b,V0f_2E0,V1a_2E0) = V2b_2E0 )
    <=> ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V2b_2E0,V0f_2E0) = V0f_2E0 ) ) ).

tff(thm_2Ecombin_2EUPDATE__APPLY__IMP__ID,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1b_2E0: A_27b,V2a_2E0: A_27a] :
      ( ( app_2E2(A_27a,A_27b,V0f_2E0,V2a_2E0) = V1b_2E0 )
     => ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2a_2E0,V1b_2E0,V0f_2E0) = V0f_2E0 ) ) ).

tff(thm_2Ecombin_2EAPPLY__UPDATE__ID,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a] : ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V1a_2E0),V0f_2E0) = V0f_2E0 ) ).

tff(thm_2Ecombin_2EUPD11__SAME__BASE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27a,V3c_2E0: A_27b,V4d_2E0: A_27b] :
      ( ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,V0f_2E0) = c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2b_2E0,V4d_2E0,V0f_2E0) )
    <=> ( ( ( V1a_2E0 = V2b_2E0 )
          & ( V3c_2E0 = V4d_2E0 ) )
        | ( ( V1a_2E0 != V2b_2E0 )
          & ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,V0f_2E0) = V0f_2E0 )
          & ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2b_2E0,V4d_2E0,V0f_2E0) = V0f_2E0 ) ) ) ) ).

tff(thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27c,A_27d),V1f1_2E0: A_27a,V2f2_2E0: A_27b,V3a_2E0: A_27c,V4b_2E0: A_27d,V5c_2E0: A_27d] :
      ( ( V4b_2E0 != V5c_2E0 )
     => ( c_2Ecombin_2EUPDATE_2E3(A_27c,A_27d,V3a_2E0,V4b_2E0,V0f_2E0) != c_2Ecombin_2EUPDATE_2E3(A_27c,A_27d,V3a_2E0,V5c_2E0,V0f_2E0) ) ) ).

tff(thm_2Ecombin_2EUPD11__SAME__KEY__AND__BASE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b,V3c_2E0: A_27b] :
      ( ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V2b_2E0,V0f_2E0) = c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,V0f_2E0) )
    <=> ( V2b_2E0 = V3c_2E0 ) ) ).

tff(thm_2Ecombin_2EUPD__SAME__KEY__UNWIND,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2a_2E0: A_27a,V3b_2E0: A_27b,V4c_2E0: A_27b] :
      ( ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2a_2E0,V3b_2E0,V0f1_2E0) = c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2a_2E0,V4c_2E0,V1f2_2E0) )
     => ( ( V3b_2E0 = V4c_2E0 )
        & ! [V5v_2E0: A_27b] : ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2a_2E0,V5v_2E0,V0f1_2E0) = c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2a_2E0,V5v_2E0,V1f2_2E0) ) ) ) ).

tff(thm_2Ecombin_2EGEN__LET__RAND,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0v_2E0: A_27c,V1f_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V2P_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( app_2E2(A_27b,A_27a,V2P_2E0,c_2Ebool_2ELET_2E2(A_27c,A_27b,V1f_2E0,V0v_2E0)) = c_2Ebool_2ELET_2E2(A_27c,A_27a,c_2Ecombin_2Eo_2E2(A_27c,A_27a,A_27b,V2P_2E0,V1f_2E0),V0v_2E0) ) ).

tff(thm_2Ecombin_2EGEN__LET__RATOR,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: A_27c,V1v_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))] : ( app_2E2(A_27c,A_27a,c_2Ebool_2ELET_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),V2f_2E0,V1v_2E0),V0x_2E0) = c_2Ebool_2ELET_2E2(A_27b,A_27a,c_2Ecombin_2EC_2E2(A_27b,A_27c,A_27a,V2f_2E0,V0x_2E0),V1v_2E0) ) ).

tff(thm_2Ecombin_2ELET__FORALL__ELIM,axiom,
    ! [A_27a: $tType,V0v_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ELET_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V0v_2E0) = c_2Ebool_2E_21_2E1(A_27a,c_2Ecombin_2ES_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E0,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Emarker_2EAbbrev_2E0,c_2Ecombin_2EC_2E2(A_27a,A_27a,tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E0(A_27a),V0v_2E0))),V1f_2E0)) ) ).

tff(thm_2Ecombin_2EGEN__literal__case__RAND,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0v_2E0: A_27c,V1f_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V2P_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( app_2E2(A_27b,A_27a,V2P_2E0,c_2Ebool_2Eliteral__case_2E2(A_27c,A_27b,V1f_2E0,V0v_2E0)) = c_2Ebool_2Eliteral__case_2E2(A_27c,A_27a,c_2Ecombin_2Eo_2E2(A_27c,A_27a,A_27b,V2P_2E0,V1f_2E0),V0v_2E0) ) ).

tff(thm_2Ecombin_2EGEN__literal__case__RATOR,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: A_27c,V1v_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))] : ( app_2E2(A_27c,A_27a,c_2Ebool_2Eliteral__case_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),V2f_2E0,V1v_2E0),V0x_2E0) = c_2Ebool_2Eliteral__case_2E2(A_27b,A_27a,c_2Ecombin_2EC_2E2(A_27b,A_27c,A_27a,V2f_2E0,V0x_2E0),V1v_2E0) ) ).

tff(thm_2Ecombin_2Eliteral__case__FORALL__ELIM,axiom,
    ! [A_27a: $tType,V0v_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2Eliteral__case_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V0v_2E0) = c_2Ebool_2E_21_2E1(A_27a,c_2Ecombin_2ES_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E0,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Emarker_2EAbbrev_2E0,c_2Ecombin_2EC_2E2(A_27a,A_27a,tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E0(A_27a),V0v_2E0))),V1f_2E0)) ) ).

tff(thm_2Ecombin_2EASSOC__CONJ,axiom,
    p(c_2Ecombin_2EASSOC_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E0)) ).

tff(thm_2Ecombin_2EASSOC__SYM,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
      ( p(c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0))
    <=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] : ( app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V1x_2E0),V2y_2E0)),V3z_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V1x_2E0),app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V2y_2E0),V3z_2E0)) ) ) ).

tff(thm_2Ecombin_2EASSOC__DISJ,axiom,
    p(c_2Ecombin_2EASSOC_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E0)) ).

tff(thm_2Ecombin_2EFCOMM__ASSOC,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2EFCOMM_2E2(A_27a,A_27a,A_27a,V0f_2E0,V0f_2E0) = c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0) ) ).

tff(thm_2Ecombin_2EMONOID__CONJ__T,axiom,
    p(c_2Ecombin_2EMONOID_2E2(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E0,c_2Ebool_2ET_2E0)) ).

tff(thm_2Ecombin_2EMONOID__DISJ__F,axiom,
    p(c_2Ecombin_2EMONOID_2E2(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E0,c_2Ebool_2EF_2E0)) ).

tff(thm_2Ecombin_2EFAIL__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a] : ( c_2Ecombin_2EFAIL_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0) = V1x_2E0 ) ).

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