%------------------------------------------------------------------------------
% File     : ITP045_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : bag.ax [Gau19]
%          : HL4045_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  566 ( 190 unt; 170 typ;   0 def)
%            Number of atoms       :  900 ( 368 equ)
%            Maximal formula atoms :   66 (   1 avg)
%            Number of connectives :  549 (  45   ~;  21   |; 179   &)
%                                         (  95 <=>; 209  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   32 (   6 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  165 (  87   >;  78   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  167 ( 167 usr;  21 con; 0-5 aty)
%            Number of variables   : 1632 (1446   !;  32   ?;1632   :)
%                                         ( 154  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: $tType ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: $tType ).

tff(tyop_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_2Earithmetic_2E_2A_2E0,type,
    c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

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

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

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

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

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

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

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

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

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

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).

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

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

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

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

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

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

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

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

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

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

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

tff(c_2Earithmetic_2E_3E_3D_2E2,type,
    c_2Earithmetic_2E_3E_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

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

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

tff(c_2Ebag_2EBAG__ALL__DISTINCT_2E0,type,
    c_2Ebag_2EBAG__ALL__DISTINCT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool) ).

tff(c_2Ebag_2EBAG__ALL__DISTINCT_2E1,type,
    c_2Ebag_2EBAG__ALL__DISTINCT_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebag_2EBAG__CARD_2E0,type,
    c_2Ebag_2EBAG__CARD_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum) ).

tff(c_2Ebag_2EBAG__CARD_2E1,type,
    c_2Ebag_2EBAG__CARD_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) > tyop_2Enum_2Enum ) ).

tff(c_2Ebag_2EBAG__CARD__RELn_2E0,type,
    c_2Ebag_2EBAG__CARD__RELn_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Ebag_2EBAG__CARD__RELn_2E2,type,
    c_2Ebag_2EBAG__CARD__RELn_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebag_2EBAG__CHOICE_2E0,type,
    c_2Ebag_2EBAG__CHOICE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),A_27a) ).

tff(c_2Ebag_2EBAG__CHOICE_2E1,type,
    c_2Ebag_2EBAG__CHOICE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) > A_27a ) ).

tff(c_2Ebag_2EBAG__DELETE_2E0,type,
    c_2Ebag_2EBAG__DELETE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))) ).

tff(c_2Ebag_2EBAG__DELETE_2E3,type,
    c_2Ebag_2EBAG__DELETE_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebag_2EBAG__DIFF_2E0,type,
    c_2Ebag_2EBAG__DIFF_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))) ).

tff(c_2Ebag_2EBAG__DIFF_2E2,type,
    c_2Ebag_2EBAG__DIFF_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) ).

tff(c_2Ebag_2EBAG__DIFF_2E3,type,
    c_2Ebag_2EBAG__DIFF_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * A_27a ) > tyop_2Enum_2Enum ) ).

tff(c_2Ebag_2EBAG__DISJOINT_2E0,type,
    c_2Ebag_2EBAG__DISJOINT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)) ).

tff(c_2Ebag_2EBAG__DISJOINT_2E2,type,
    c_2Ebag_2EBAG__DISJOINT_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebag_2EBAG__EVERY_2E0,type,
    c_2Ebag_2EBAG__EVERY_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)) ).

tff(c_2Ebag_2EBAG__EVERY_2E2,type,
    c_2Ebag_2EBAG__EVERY_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebag_2EBAG__FILTER_2E0,type,
    c_2Ebag_2EBAG__FILTER_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))) ).

tff(c_2Ebag_2EBAG__FILTER_2E2,type,
    c_2Ebag_2EBAG__FILTER_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) ).

tff(c_2Ebag_2EBAG__FILTER_2E3,type,
    c_2Ebag_2EBAG__FILTER_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * A_27a ) > tyop_2Enum_2Enum ) ).

tff(c_2Ebag_2EBAG__GEN__PROD_2E0,type,
    c_2Ebag_2EBAG__GEN__PROD_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Ebag_2EBAG__GEN__PROD_2E2,type,
    c_2Ebag_2EBAG__GEN__PROD_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Ebag_2EBAG__GEN__SUM_2E0,type,
    c_2Ebag_2EBAG__GEN__SUM_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Ebag_2EBAG__GEN__SUM_2E2,type,
    c_2Ebag_2EBAG__GEN__SUM_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Ebag_2EBAG__IMAGE_2E0,type,
    c_2Ebag_2EBAG__IMAGE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))) ).

tff(c_2Ebag_2EBAG__IMAGE_2E2,type,
    c_2Ebag_2EBAG__IMAGE_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,A_27a) * tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum) ) > tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) ).

tff(c_2Ebag_2EBAG__IMAGE_2E3,type,
    c_2Ebag_2EBAG__IMAGE_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,A_27a) * tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum) * A_27a ) > tyop_2Enum_2Enum ) ).

tff(c_2Ebag_2EBAG__IN_2E0,type,
    c_2Ebag_2EBAG__IN_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)) ).

tff(c_2Ebag_2EBAG__IN_2E2,type,
    c_2Ebag_2EBAG__IN_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebag_2EBAG__INN_2E0,type,
    c_2Ebag_2EBAG__INN_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))) ).

tff(c_2Ebag_2EBAG__INN_2E3,type,
    c_2Ebag_2EBAG__INN_2E3: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Enum_2Enum * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebag_2EBAG__INSERT_2E0,type,
    c_2Ebag_2EBAG__INSERT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))) ).

tff(c_2Ebag_2EBAG__INSERT_2E2,type,
    c_2Ebag_2EBAG__INSERT_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) ).

tff(c_2Ebag_2EBAG__INSERT_2E3,type,
    c_2Ebag_2EBAG__INSERT_2E3: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * A_27a ) > tyop_2Enum_2Enum ) ).

tff(c_2Ebag_2EBAG__INTER_2E0,type,
    c_2Ebag_2EBAG__INTER_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))) ).

tff(c_2Ebag_2EBAG__INTER_2E2,type,
    c_2Ebag_2EBAG__INTER_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) ).

tff(c_2Ebag_2EBAG__INTER_2E3,type,
    c_2Ebag_2EBAG__INTER_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * A_27a ) > tyop_2Enum_2Enum ) ).

tff(c_2Ebag_2EBAG__MERGE_2E0,type,
    c_2Ebag_2EBAG__MERGE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))) ).

tff(c_2Ebag_2EBAG__MERGE_2E2,type,
    c_2Ebag_2EBAG__MERGE_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) ).

tff(c_2Ebag_2EBAG__MERGE_2E3,type,
    c_2Ebag_2EBAG__MERGE_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * A_27a ) > tyop_2Enum_2Enum ) ).

tff(c_2Ebag_2EBAG__OF__SET_2E0,type,
    c_2Ebag_2EBAG__OF__SET_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)) ).

tff(c_2Ebag_2EBAG__OF__SET_2E1,type,
    c_2Ebag_2EBAG__OF__SET_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) ).

tff(c_2Ebag_2EBAG__OF__SET_2E2,type,
    c_2Ebag_2EBAG__OF__SET_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Enum_2Enum ) ).

tff(c_2Ebag_2EBAG__REST_2E0,type,
    c_2Ebag_2EBAG__REST_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)) ).

tff(c_2Ebag_2EBAG__REST_2E1,type,
    c_2Ebag_2EBAG__REST_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) > tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) ).

tff(c_2Ebag_2EBAG__UNION_2E0,type,
    c_2Ebag_2EBAG__UNION_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))) ).

tff(c_2Ebag_2EBAG__UNION_2E2,type,
    c_2Ebag_2EBAG__UNION_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) ).

tff(c_2Ebag_2EBAG__UNION_2E3,type,
    c_2Ebag_2EBAG__UNION_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * A_27a ) > tyop_2Enum_2Enum ) ).

tff(c_2Ebag_2EBIG__BAG__UNION_2E0,type,
    c_2Ebag_2EBIG__BAG__UNION_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)) ).

tff(c_2Ebag_2EBIG__BAG__UNION_2E1,type,
    c_2Ebag_2EBIG__BAG__UNION_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) ).

tff(c_2Ebag_2EBIG__BAG__UNION_2E2,type,
    c_2Ebag_2EBIG__BAG__UNION_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool) * A_27a ) > tyop_2Enum_2Enum ) ).

tff(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_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_2Epred__set_2EDELETE_2E0,type,
    c_2Epred__set_2EDELETE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

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

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

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

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

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

tff(c_2Ebag_2EEL__BAG_2E0,type,
    c_2Ebag_2EEL__BAG_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)) ).

tff(c_2Ebag_2EEL__BAG_2E1,type,
    c_2Ebag_2EEL__BAG_2E1: 
      !>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) ).

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_2Ebag_2EEMPTY__BAG_2E0,type,
    c_2Ebag_2EEMPTY__BAG_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ).

tff(c_2Ebag_2EEMPTY__BAG_2E1,type,
    c_2Ebag_2EEMPTY__BAG_2E1: 
      !>[A_27a: $tType] : ( A_27a > tyop_2Enum_2Enum ) ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

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

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

tff(c_2Ebag_2EFINITE__BAG_2E0,type,
    c_2Ebag_2EFINITE__BAG_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool) ).

tff(c_2Ebag_2EFINITE__BAG_2E1,type,
    c_2Ebag_2EFINITE__BAG_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) > 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_2Ecombin_2EI_2E0,type,
    c_2Ecombin_2EI_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).

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

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

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

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

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

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

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

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

tff(c_2Ebag_2EITBAG_2E0,type,
    c_2Ebag_2EITBAG_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(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,A_27b))) ).

tff(c_2Ebag_2EITBAG_2E3,type,
    c_2Ebag_2EITBAG_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * A_27b ) > A_27b ) ).

tff(c_2Epred__set_2EITSET_2E0,type,
    c_2Epred__set_2EITSET_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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b))) ).

tff(c_2Epred__set_2EITSET_2E3,type,
    c_2Epred__set_2EITSET_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27b ) > A_27b ) ).

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_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_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Ebag_2EPSUB__BAG_2E0,type,
    c_2Ebag_2EPSUB__BAG_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)) ).

tff(c_2Ebag_2EPSUB__BAG_2E2,type,
    c_2Ebag_2EPSUB__BAG_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebag_2ESET__OF__BAG_2E0,type,
    c_2Ebag_2ESET__OF__BAG_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Ebag_2ESET__OF__BAG_2E1,type,
    c_2Ebag_2ESET__OF__BAG_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Ebag_2ESET__OF__BAG_2E2,type,
    c_2Ebag_2ESET__OF__BAG_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebag_2ESING__BAG_2E0,type,
    c_2Ebag_2ESING__BAG_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool) ).

tff(c_2Ebag_2ESING__BAG_2E1,type,
    c_2Ebag_2ESING__BAG_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) > 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_2Ebag_2ESUB__BAG_2E0,type,
    c_2Ebag_2ESUB__BAG_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)) ).

tff(c_2Ebag_2ESUB__BAG_2E2,type,
    c_2Ebag_2ESUB__BAG_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Ebool ) ).

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

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

tff(c_2Epred__set_2ESUM__IMAGE_2E0,type,
    c_2Epred__set_2ESUM__IMAGE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)) ).

tff(c_2Epred__set_2ESUM__IMAGE_2E2,type,
    c_2Epred__set_2ESUM__IMAGE_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Enum_2Enum ) ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

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

tff(c_2Erelation_2ETC_2E3,type,
    c_2Erelation_2ETC_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).

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

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

tff(c_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_2EWFP_2E0,type,
    c_2Erelation_2EWFP_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_2Ebool)) ).

tff(c_2Erelation_2EWFP_2E2,type,
    c_2Erelation_2EWFP_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Ebag_2Ebag__size_2E0,type,
    c_2Ebag_2Ebag__size_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum)) ).

tff(c_2Ebag_2Ebag__size_2E2,type,
    c_2Ebag_2Ebag__size_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Enum_2Enum ) ).

tff(c_2Edivides_2Edivides_2E0,type,
    c_2Edivides_2Edivides_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Edivides_2Edivides_2E2,type,
    c_2Edivides_2Edivides_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Ebag_2Edominates_2E0,type,
    c_2Ebag_2Edominates_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).

tff(c_2Ebag_2Edominates_2E3,type,
    c_2Ebag_2Edominates_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebag_2Emlt1_2E0,type,
    c_2Ebag_2Emlt1_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))) ).

tff(c_2Ebag_2Emlt1_2E1,type,
    c_2Ebag_2Emlt1_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)) ) ).

tff(c_2Ebag_2Emlt1_2E3,type,
    c_2Ebag_2Emlt1_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ) > tyop_2Emin_2Ebool ) ).

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_2Erelation_2Etransitive_2E0,type,
    c_2Erelation_2Etransitive_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).

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

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

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

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

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

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

tff(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_3D_2E0,X0_2E0),X1_2E0) ) ).

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

tff(arityeq1_2Ec_2Ebag_2EBAG__ALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2EBAG__ALL__DISTINCT_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2EBAG__CARD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__CARD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2EBAG__CARD_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__CARD_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__CARD__RELn_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EBAG__CARD__RELn_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebag_2EBAG__CARD__RELn_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2EBAG__CHOICE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__CHOICE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),A_27a,c_2Ebag_2EBAG__CHOICE_2E0(A_27a),X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2EBAG__DELETE_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DELETE_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2EBAG__DELETE_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__DIFF_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__DIFF_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2EBAG__DIFF_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0: A_27a] : ( c_2Ebag_2EBAG__DIFF_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__DIFF_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__DIFF_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DIFF_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__DIFF_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__DIFF_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DIFF_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__DIFF_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__DIFF_2E2_2Emono_2EA_27d,axiom,
    ! [A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DIFF_2E2(A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__DIFF_2E0(A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__DISJOINT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EBAG__DISJOINT_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__DISJOINT_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DISJOINT_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EBAG__DISJOINT_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__EVERY_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__EVERY_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EBAG__EVERY_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__EVERY_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__EVERY_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EBAG__EVERY_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__FILTER_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__FILTER_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__FILTER_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2EBAG__FILTER_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0: A_27a] : ( c_2Ebag_2EBAG__FILTER_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__FILTER_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__FILTER_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__FILTER_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__FILTER_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__GEN__PROD_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EBAG__GEN__PROD_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EBAG__GEN__PROD_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__GEN__SUM_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EBAG__GEN__SUM_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EBAG__GEN__SUM_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__IMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__IMAGE_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__IMAGE_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__IMAGE_2E2_2Emono_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,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__IMAGE_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__IMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__IMAGE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__IMAGE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2EBAG__IMAGE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X2_2E0: A_27a] : ( c_2Ebag_2EBAG__IMAGE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__IMAGE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__IMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__IMAGE_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__IMAGE_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__IMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__IMAGE_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__IN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__IN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EBAG__IN_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__IN_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__IN_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EBAG__IN_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__IN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__IN_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EBAG__IN_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2EBAG__INN_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__INN_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2EBAG__INN_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__INSERT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__INSERT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__INSERT_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2EBAG__INSERT_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0: A_27a] : ( c_2Ebag_2EBAG__INSERT_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__INSERT_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__INSERT_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__INSERT_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__INSERT_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__INSERT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__INSERT_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__INSERT_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__INTER_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__INTER_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__INTER_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2EBAG__INTER_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0: A_27a] : ( c_2Ebag_2EBAG__INTER_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__INTER_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__MERGE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__MERGE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__MERGE_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2EBAG__MERGE_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0: A_27a] : ( c_2Ebag_2EBAG__MERGE_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__MERGE_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2EBAG__OF__SET_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebag_2EBAG__OF__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__OF__SET_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__OF__SET_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Ebag_2EBAG__OF__SET_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__OF__SET_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2EBAG__REST_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__REST_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__REST_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__UNION_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__UNION_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__UNION_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2EBAG__UNION_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0: A_27a] : ( c_2Ebag_2EBAG__UNION_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__UNION_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__UNION_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__UNION_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__UNION_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__UNION_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__UNION_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__UNION_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBAG__UNION_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__UNION_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__UNION_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2EBIG__BAG__UNION_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] : ( c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EBIG__BAG__UNION_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Ebag_2EBIG__BAG__UNION_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).

tff(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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Epred__set_2EDELETE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2EDELETE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0),X1_2E0) ) ).

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

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

tff(arityeq1_2Ec_2Ebag_2EEL__BAG_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Ebag_2EEL__BAG_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEL__BAG_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2EEMPTY__BAG_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Ebag_2EEMPTY__BAG_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,c_2Ebag_2EEMPTY__BAG_2E0(A_27a),X0_2E0) ) ).

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

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2EFINITE__BAG_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EFINITE__BAG_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2EFINITE__BAG_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EFINITE__BAG_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2EFINITE__BAG_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)] : ( c_2Ebag_2EFINITE__BAG_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E0(A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2EFINITE__BAG_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_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: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

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

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

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2EINTER_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2EITBAG_2E3_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: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0: A_27b] : ( c_2Ebag_2EITBAG_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ebag_2EITBAG_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2EITBAG_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EITBAG_2E3(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebag_2EITBAG_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2EITBAG_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EITBAG_2E3(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebag_2EITBAG_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epred__set_2EITSET_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Epred__set_2EITSET_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Epred__set_2EITSET_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Ecombin_2EK_2E1(tyop_2Enum_2Enum,A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ecombin_2EK_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Ebool_2ELET_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2EPSUB__BAG_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EPSUB__BAG_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EPSUB__BAG_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2ESET__OF__BAG_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2ESET__OF__BAG_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2ESET__OF__BAG_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: A_27a] : ( c_2Ebag_2ESET__OF__BAG_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2ESET__OF__BAG_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2ESET__OF__BAG_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2ESING__BAG_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2ESING__BAG_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Ebag_2ESING__BAG_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2ESUB__BAG_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2ESUB__BAG_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2ESUB__BAG_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebag_2ESUB__BAG_2E2_2Emono_2EA_27d,axiom,
    ! [A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum)] : ( c_2Ebag_2ESUB__BAG_2E2(A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2ESUB__BAG_2E0(A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUM__IMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ESUM__IMAGE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),X1_2E0),X2_2E0) ) ).

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

tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0),X1_2E0) ) ).

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

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFP_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Erelation_2EWFP_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Erelation_2EWFP_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),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_2Ebag_2Ebag__size_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2Ebag__size_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Ebag_2Ebag__size_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Edivides_2Edivides_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Edivides_2Edivides_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Edivides_2Edivides_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2Edominates_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebag_2Edominates_2E3(A_27a,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebag_2Edominates_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2Edominates_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ebag_2Edominates_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebag_2Edominates_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2Emlt1_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Ebag_2Emlt1_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E0(A_27a),X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebag_2Emlt1_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2Emlt1_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Ebag_2Emlt1_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Ebag_2Emlt1_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E0(tyop_2Enum_2Enum),X0_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(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(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_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_2Ebag_2EEMPTY__BAG,axiom,
    ! [A_27a: $tType] : ( c_2Ebag_2EEMPTY__BAG_2E0(A_27a) = c_2Ecombin_2EK_2E1(tyop_2Enum_2Enum,A_27a,c_2Enum_2E0_2E0) ) ).

tff(thm_2Ebag_2EBAG__INN,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__INN_2E3(A_27a,V0e_2E0,V1n_2E0,V2b_2E0) = c_2Earithmetic_2E_3E_3D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V2b_2E0,V0e_2E0),V1n_2E0) ) ).

tff(thm_2Ebag_2ESUB__BAG,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
    <=> ! [V2x_2E0: A_27a,V3n_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V2x_2E0,V3n_2E0,V0b1_2E0))
         => p(c_2Ebag_2EBAG__INN_2E3(A_27a,V2x_2E0,V3n_2E0,V1b2_2E0)) ) ) ).

tff(thm_2Ebag_2EPSUB__BAG,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
    <=> ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
        & ( V0b1_2E0 != V1b2_2E0 ) ) ) ).

tff(thm_2Ebag_2EBAG__IN,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V1b_2E0) = c_2Ebag_2EBAG__INN_2E3(A_27a,V0e_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V1b_2E0) ) ).

tff(thm_2Ebag_2EBAG__UNION,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2x_2E0: A_27a] : ( c_2Ebag_2EBAG__UNION_2E3(A_27a,V0b_2E0,V1c_2E0,V2x_2E0) = c_2Earithmetic_2E_2B_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0b_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V1c_2E0,V2x_2E0)) ) ).

tff(thm_2Ebag_2EBAG__DIFF,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2x_2E0: A_27a] : ( c_2Ebag_2EBAG__DIFF_2E3(A_27a,V0b1_2E0,V1b2_2E0,V2x_2E0) = c_2Earithmetic_2E_2D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0b1_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V1b2_2E0,V2x_2E0)) ) ).

tff(thm_2Ebag_2EBAG__INSERT,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V2x_2E0: A_27a,V0e_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,V2x_2E0),V0e_2E0))
        <=> ( V2x_2E0 = V0e_2E0 ) )
     => ! [V0e_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2x_2E0: A_27a] : ( c_2Ebag_2EBAG__INSERT_2E3(A_27a,V0e_2E0,V1b_2E0,V2x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V2x_2E0),V0e_2E0),c_2Earithmetic_2E_2B_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V1b_2E0,V0e_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),app_2E2(A_27a,tyop_2Enum_2Enum,V1b_2E0,V2x_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__INTER,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2x_2E0: A_27a] : ( c_2Ebag_2EBAG__INTER_2E3(A_27a,V0b1_2E0,V1b2_2E0,V2x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0b1_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V1b2_2E0,V2x_2E0)),app_2E2(A_27a,tyop_2Enum_2Enum,V0b1_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V1b2_2E0,V2x_2E0)) ) ).

tff(thm_2Ebag_2EBAG__MERGE,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2x_2E0: A_27a] : ( c_2Ebag_2EBAG__MERGE_2E3(A_27a,V0b1_2E0,V1b2_2E0,V2x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0b1_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V1b2_2E0,V2x_2E0)),app_2E2(A_27a,tyop_2Enum_2Enum,V1b2_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V0b1_2E0,V2x_2E0)) ) ).

tff(thm_2Ebag_2EBAG__DELETE,axiom,
    ! [A_27a: $tType,V0b0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e_2E0: A_27a,V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b0_2E0,V1e_2E0,V2b_2E0))
    <=> ( V0b0_2E0 = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1e_2E0,V2b_2E0) ) ) ).

tff(thm_2Ebag_2ESING__BAG,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESING__BAG_2E1(A_27a,V0b_2E0))
    <=> ? [V1x_2E0: A_27a] : ( V0b_2E0 = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1x_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)) ) ) ).

tff(thm_2Ebag_2EEL__BAG,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a] : ( c_2Ebag_2EEL__BAG_2E1(A_27a,V0e_2E0) = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)) ) ).

tff(thm_2Ebag_2ESET__OF__BAG,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1x_2E0: A_27a] : ( c_2Ebag_2ESET__OF__BAG_2E2(A_27a,V0b_2E0,V1x_2E0) = c_2Ebag_2EBAG__IN_2E2(A_27a,V1x_2E0,V0b_2E0) ) ).

tff(thm_2Ebag_2EBAG__OF__SET,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( c_2Ebag_2EBAG__OF__SET_2E2(A_27a,V0P_2E0,V1x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0P_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2E0_2E0) ) ).

tff(thm_2Ebag_2EBAG__DISJOINT,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,V0b1_2E0,V1b2_2E0) = c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0b1_2E0),c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V1b2_2E0)) ) ).

tff(thm_2Ebag_2EFINITE__BAG,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b_2E0))
    <=> ! [V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] :
          ( ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,V1P_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)))
            & ! [V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
                ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,V1P_2E0,V2b_2E0))
               => ! [V3e_2E0: A_27a] : p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,V1P_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V3e_2E0,V2b_2E0))) ) )
         => p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,V1P_2E0,V0b_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__CARD__RELn,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ebag_2EBAG__CARD__RELn_2E2(A_27a,V0b_2E0,V1n_2E0))
    <=> ! [V2P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
          ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)),c_2Enum_2E0_2E0))
            & ! [V3b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4n_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0,V3b_2E0),V4n_2E0))
               => ! [V5e_2E0: A_27a] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V5e_2E0,V3b_2E0)),c_2Enum_2ESUC_2E1(V4n_2E0))) ) )
         => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0,V0b_2E0),V1n_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__CARD,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b_2E0))
     => p(c_2Ebag_2EBAG__CARD__RELn_2E2(A_27a,V0b_2E0,c_2Ebag_2EBAG__CARD_2E1(A_27a,V0b_2E0))) ) ).

tff(thm_2Ebag_2EBAG__FILTER__DEF,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2x_2E0: A_27a] : ( c_2Ebag_2EBAG__FILTER_2E3(A_27a,V0P_2E0,V1b_2E0,V2x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V1b_2E0,V2x_2E0),c_2Enum_2E0_2E0) ) ).

tff(thm_2Ebag_2EBAG__IMAGE__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] :
      ( ! [V3sb_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum,F0_2E0,V3sb_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Ebag_2EFINITE__BAG_2E1(A_27b,V3sb_2E0),c_2Ebag_2EBAG__CARD_2E1(A_27b,V3sb_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V2x_2E0: A_27a,V4e0_2E0: A_27b] :
            ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V0f_2E0),V2x_2E0),V4e0_2E0))
          <=> ( app_2E2(A_27b,A_27a,V0f_2E0,V4e0_2E0) = V2x_2E0 ) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V1b_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V2x_2E0: A_27a] : ( c_2Ebag_2EBAG__IMAGE_2E3(A_27a,A_27b,V0f_2E0,V1b_2E0,V2x_2E0) = c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum,F0_2E0,c_2Ebag_2EBAG__FILTER_2E2(A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V0f_2E0),V2x_2E0),V1b_2E0)) ) ) ) ).

tff(thm_2Ebag_2EBAG__CHOICE__DEF,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( V0b_2E0 != c_2Ebag_2EEMPTY__BAG_2E0(A_27a) )
     => p(c_2Ebag_2EBAG__IN_2E2(A_27a,c_2Ebag_2EBAG__CHOICE_2E1(A_27a,V0b_2E0),V0b_2E0)) ) ).

tff(thm_2Ebag_2EBAG__REST__DEF,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__REST_2E1(A_27a,V0b_2E0) = c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0b_2E0,c_2Ebag_2EEL__BAG_2E1(A_27a,c_2Ebag_2EBAG__CHOICE_2E1(A_27a,V0b_2E0))) ) ).

tff(thm_2Ebag_2EBAG__GEN__SUM__def,axiom,
    ! [V0bag_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EBAG__GEN__SUM_2E2(V0bag_2E0,V1n_2E0) = c_2Ebag_2EITBAG_2E3(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E0,V0bag_2E0,V1n_2E0) ) ).

tff(thm_2Ebag_2EBAG__GEN__PROD__def,axiom,
    ! [V0bag_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EBAG__GEN__PROD_2E2(V0bag_2E0,V1n_2E0) = c_2Ebag_2EITBAG_2E3(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E0,V0bag_2E0,V1n_2E0) ) ).

tff(thm_2Ebag_2EBAG__EVERY,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__EVERY_2E2(A_27a,V0P_2E0,V1b_2E0))
    <=> ! [V2e_2E0: A_27a] :
          ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e_2E0,V1b_2E0))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2e_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__ALL__DISTINCT,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V0b_2E0))
    <=> ! [V1e_2E0: A_27a] : p(c_2Earithmetic_2E_3C_3D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0b_2E0,V1e_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ).

tff(thm_2Ebag_2EBIG__BAG__UNION__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum))] :
      ( ! [V1x_2E0: A_27a,V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),F0_2E0,V1x_2E0),V2b_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,V2b_2E0,V1x_2E0) )
     => ! [V0sob_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( c_2Ebag_2EBIG__BAG__UNION_2E2(A_27a,V0sob_2E0,V1x_2E0) = c_2Epred__set_2ESUM__IMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),F0_2E0,V1x_2E0),V0sob_2E0) ) ) ).

tff(thm_2Ebag_2Emlt1__def,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2Emlt1_2E3(A_27a,V0r_2E0,V1b1_2E0,V2b2_2E0))
    <=> ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b1_2E0))
        & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V2b2_2E0))
        & ? [V3e_2E0: A_27a,V4rep_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5res_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
            ( ( V1b1_2E0 = c_2Ebag_2EBAG__UNION_2E2(A_27a,V4rep_2E0,V5res_2E0) )
            & ( V2b2_2E0 = c_2Ebag_2EBAG__UNION_2E2(A_27a,V5res_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V3e_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a))) )
            & ! [V6e_27_2E0: A_27a] :
                ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V6e_27_2E0,V4rep_2E0))
               => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0,V6e_27_2E0),V3e_2E0)) ) ) ) ) ).

tff(thm_2Ebag_2Edominates__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebag_2Edominates_2E3(A_27a,A_27b,V0R_2E0,V1s1_2E0,V2s2_2E0))
    <=> ! [V3x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s1_2E0))
         => ? [V4y_2E0: A_27b] :
              ( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V2s2_2E0))
              & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V3x_2E0),V4y_2E0)) ) ) ) ).

tff(thm_2Ebag_2Ebag__size__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))] :
      ( ! [V0eltsize_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e_2E0: A_27a,V3acc_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V0eltsize_2E0),V2e_2E0),V3acc_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),app_2E2(A_27a,tyop_2Enum_2Enum,V0eltsize_2E0,V2e_2E0)),V3acc_2E0) )
     => ! [V0eltsize_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2Ebag__size_2E2(A_27a,V0eltsize_2E0,V1b_2E0) = c_2Ebag_2EITBAG_2E3(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V0eltsize_2E0),V1b_2E0,c_2Enum_2E0_2E0) ) ) ).

tff(thm_2Ebag_2EEMPTY__BAG__alt,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Ebag_2EEMPTY__BAG_2E1(A_27a,V0x_2E0) = c_2Enum_2E0_2E0 ) ).

tff(thm_2Ebag_2EBAG__cases,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( V0b_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) )
      | ? [V1b0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e_2E0: A_27a] : ( V0b_2E0 = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2e_2E0,V1b0_2E0) ) ) ).

tff(thm_2Ebag_2EBAG__MERGE__IDEM,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__MERGE_2E2(A_27a,V0b_2E0,V0b_2E0) = V0b_2E0 ) ).

tff(thm_2Ebag_2EBAG__INN__0,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e_2E0: A_27a] : p(c_2Ebag_2EBAG__INN_2E3(A_27a,V1e_2E0,c_2Enum_2E0_2E0,V0b_2E0)) ).

tff(thm_2Ebag_2EBAG__INN__LESS,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e_2E0: A_27a,V2n_2E0: tyop_2Enum_2Enum,V3m_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V1e_2E0,V2n_2E0,V0b_2E0))
        & p(c_2Eprim__rec_2E_3C_2E2(V3m_2E0,V2n_2E0)) )
     => p(c_2Ebag_2EBAG__INN_2E3(A_27a,V1e_2E0,V3m_2E0,V0b_2E0)) ) ).

tff(thm_2Ebag_2EBAG__IN__BAG__INSERT,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e1_2E0: A_27a,V2e2_2E0: A_27a] :
      ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V1e1_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2e2_2E0,V0b_2E0)))
    <=> ( ( V1e1_2E0 = V2e2_2E0 )
        | p(c_2Ebag_2EBAG__IN_2E2(A_27a,V1e1_2E0,V0b_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__INN__BAG__INSERT,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e1_2E0: A_27a,V3e2_2E0: A_27a] :
      ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V2e1_2E0,V0n_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V3e2_2E0,V1b_2E0)))
    <=> ( ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V2e1_2E0,c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1b_2E0))
          & ( V2e1_2E0 = V3e2_2E0 ) )
        | p(c_2Ebag_2EBAG__INN_2E3(A_27a,V2e1_2E0,V0n_2E0,V1b_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__INN__BAG__INSERT__STRONG,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1n_2E0: tyop_2Enum_2Enum,V2e1_2E0: A_27a,V3e2_2E0: A_27a] :
      ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V2e1_2E0,V1n_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V3e2_2E0,V0b_2E0)))
    <=> ( ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V2e1_2E0,c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0b_2E0))
          & ( V2e1_2E0 = V3e2_2E0 ) )
        | ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V2e1_2E0,V1n_2E0,V0b_2E0))
          & ( V2e1_2E0 != V3e2_2E0 ) ) ) ) ).

tff(thm_2Ebag_2EBAG__UNION__EQ__LCANCEL1,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( V1b_2E0 = c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b_2E0,V0c_2E0) )
    <=> ( V0c_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) ).

tff(thm_2Ebag_2EBAG__UNION__EQ__RCANCEL1,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( V1b_2E0 = c_2Ebag_2EBAG__UNION_2E2(A_27a,V0c_2E0,V1b_2E0) )
    <=> ( V0c_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) ).

tff(thm_2Ebag_2EBAG__IN__BAG__UNION,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e_2E0: A_27a] :
      ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0)))
    <=> ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e_2E0,V0b1_2E0))
        | p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e_2E0,V1b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__INN__BAG__UNION,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1e_2E0: A_27a,V2b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V1e_2E0,V0n_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V2b1_2E0,V3b2_2E0)))
    <=> ? [V4m1_2E0: tyop_2Enum_2Enum,V5m2_2E0: tyop_2Enum_2Enum] :
          ( ( V0n_2E0 = c_2Earithmetic_2E_2B_2E2(V4m1_2E0,V5m2_2E0) )
          & p(c_2Ebag_2EBAG__INN_2E3(A_27a,V1e_2E0,V4m1_2E0,V2b1_2E0))
          & p(c_2Ebag_2EBAG__INN_2E3(A_27a,V1e_2E0,V5m2_2E0,V3b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__INN__BAG__MERGE,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1e_2E0: A_27a,V2b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V1e_2E0,V0n_2E0,c_2Ebag_2EBAG__MERGE_2E2(A_27a,V2b1_2E0,V3b2_2E0)))
    <=> ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V1e_2E0,V0n_2E0,V2b1_2E0))
        | p(c_2Ebag_2EBAG__INN_2E3(A_27a,V1e_2E0,V0n_2E0,V3b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__IN__BAG__MERGE,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,c_2Ebag_2EBAG__MERGE_2E2(A_27a,V1b1_2E0,V2b2_2E0)))
    <=> ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V1b1_2E0))
        | p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V2b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__EXTENSION,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( V0b1_2E0 = V1b2_2E0 )
    <=> ! [V2n_2E0: tyop_2Enum_2Enum,V3e_2E0: A_27a] : ( c_2Ebag_2EBAG__INN_2E3(A_27a,V3e_2E0,V2n_2E0,V0b1_2E0) = c_2Ebag_2EBAG__INN_2E3(A_27a,V3e_2E0,V2n_2E0,V1b2_2E0) ) ) ).

tff(thm_2Ebag_2EBAG__UNION__INSERT,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V1b1_2E0),V2b2_2E0) = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b1_2E0,V2b2_2E0)) )
      & ( c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b1_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V2b2_2E0)) = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b1_2E0,V2b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__INSERT__DIFF,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,V1b_2E0) != V1b_2E0 ) ).

tff(thm_2Ebag_2EBAG__INSERT__NOT__EMPTY,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,V1b_2E0) != c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ).

tff(thm_2Ebag_2EBAG__INSERT__ONE__ONE,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2x_2E0: A_27a] :
      ( ( c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2x_2E0,V0b1_2E0) = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2x_2E0,V1b2_2E0) )
    <=> ( V0b1_2E0 = V1b2_2E0 ) ) ).

tff(thm_2Ebag_2EC__BAG__INSERT__ONE__ONE,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a,V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,V2b_2E0) = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1y_2E0,V2b_2E0) )
    <=> ( V0x_2E0 = V1y_2E0 ) ) ).

tff(thm_2Ebag_2EBAG__INSERT__commutes,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e1_2E0: A_27a,V2e2_2E0: A_27a] : ( c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1e1_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2e2_2E0,V0b_2E0)) = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2e2_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1e1_2E0,V0b_2E0)) ) ).

tff(thm_2Ebag_2EBAG__DECOMPOSE,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V1b_2E0))
     => ? [V2b_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( V1b_2E0 = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V2b_27_2E0) ) ) ).

tff(thm_2Ebag_2EBAG__UNION__LEFT__CANCEL,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b_2E0,V1b1_2E0) = c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b_2E0,V2b2_2E0) )
    <=> ( V1b1_2E0 = V2b2_2E0 ) ) ).

tff(thm_2Ebag_2ECOMM__BAG__UNION,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0) = c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b2_2E0,V0b1_2E0) ) ).

tff(thm_2Ebag_2EBAG__UNION__RIGHT__CANCEL,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b1_2E0,V0b_2E0) = c_2Ebag_2EBAG__UNION_2E2(A_27a,V2b2_2E0,V0b_2E0) )
    <=> ( V1b1_2E0 = V2b2_2E0 ) ) ).

tff(thm_2Ebag_2EASSOC__BAG__UNION,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b2_2E0,V2b3_2E0)) = c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0),V2b3_2E0) ) ).

tff(thm_2Ebag_2EBAG__UNION__EMPTY,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)) = V0b_2E0 )
      & ! [V1b_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__UNION_2E2(A_27b,c_2Ebag_2EEMPTY__BAG_2E0(A_27b),V1b_2E0) = V1b_2E0 )
      & ! [V2b1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),V3b2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)] :
          ( ( c_2Ebag_2EBAG__UNION_2E2(A_27c,V2b1_2E0,V3b2_2E0) = c_2Ebag_2EEMPTY__BAG_2E0(A_27c) )
        <=> ( ( V2b1_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27c) )
            & ( V3b2_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27c) ) ) ) ) ).

tff(thm_2Ebag_2EBAG__DELETE__EMPTY,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ~ p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,c_2Ebag_2EEMPTY__BAG_2E0(A_27a),V0e_2E0,V1b_2E0)) ).

tff(thm_2Ebag_2EBAG__DELETE__commutes,axiom,
    ! [A_27a: $tType,V0b0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3e1_2E0: A_27a,V4e2_2E0: A_27a] :
      ( ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b0_2E0,V3e1_2E0,V1b1_2E0))
        & p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V1b1_2E0,V4e2_2E0,V2b2_2E0)) )
     => ? [V5b_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b0_2E0,V4e2_2E0,V5b_27_2E0))
          & p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V5b_27_2E0,V3e1_2E0,V2b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__DELETE__11,axiom,
    ! [A_27a: $tType,V0b0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e1_2E0: A_27a,V2e2_2E0: A_27a,V3b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b0_2E0,V1e1_2E0,V3b1_2E0))
        & p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b0_2E0,V2e2_2E0,V4b2_2E0)) )
     => ( ( V1e1_2E0 = V2e2_2E0 )
      <=> ( V3b1_2E0 = V4b2_2E0 ) ) ) ).

tff(thm_2Ebag_2EBAG__INN__BAG__DELETE,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1n_2E0: tyop_2Enum_2Enum,V2e_2E0: A_27a] :
      ( ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V2e_2E0,V1n_2E0,V0b_2E0))
        & p(c_2Earithmetic_2E_3E_2E2(V1n_2E0,c_2Enum_2E0_2E0)) )
     => ? [V3b_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b_2E0,V2e_2E0,V3b_27_2E0)) ) ).

tff(thm_2Ebag_2EBAG__IN__BAG__DELETE,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e_2E0: A_27a] :
      ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V1e_2E0,V0b_2E0))
     => ? [V2b_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b_2E0,V1e_2E0,V2b_27_2E0)) ) ).

tff(thm_2Ebag_2EBAG__DELETE__INSERT,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a,V2b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,V2b1_2E0),V1y_2E0,V3b2_2E0))
     => ( ( ( V0x_2E0 = V1y_2E0 )
          & ( V2b1_2E0 = V3b2_2E0 ) )
        | ( ? [V4b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V2b1_2E0,V1y_2E0,V4b3_2E0))
          & ( V0x_2E0 != V1y_2E0 ) ) ) ) ).

tff(thm_2Ebag_2EBAG__DELETE__BAG__IN__up,axiom,
    ! [A_27a: $tType,V0b0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e_2E0: A_27a] :
      ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b0_2E0,V2e_2E0,V1b_2E0))
     => ! [V3e_27_2E0: A_27a] :
          ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V3e_27_2E0,V1b_2E0))
         => p(c_2Ebag_2EBAG__IN_2E2(A_27a,V3e_27_2E0,V0b0_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__DELETE__BAG__IN__down,axiom,
    ! [A_27a: $tType,V0b0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e1_2E0: A_27a,V3e2_2E0: A_27a] :
      ( ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b0_2E0,V2e1_2E0,V1b_2E0))
        & ( V2e1_2E0 != V3e2_2E0 )
        & p(c_2Ebag_2EBAG__IN_2E2(A_27a,V3e2_2E0,V0b0_2E0)) )
     => p(c_2Ebag_2EBAG__IN_2E2(A_27a,V3e2_2E0,V1b_2E0)) ) ).

tff(thm_2Ebag_2EBAG__DELETE__BAG__IN,axiom,
    ! [A_27a: $tType,V0b0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e_2E0: A_27a] :
      ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b0_2E0,V2e_2E0,V1b_2E0))
     => p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e_2E0,V0b0_2E0)) ) ).

tff(thm_2Ebag_2EBAG__DELETE__concrete,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V3x_2E0: A_27a,V2e_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,V3x_2E0),V2e_2E0))
        <=> ( V3x_2E0 = V2e_2E0 ) )
     => ! [V0b0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e_2E0: A_27a] :
          ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b0_2E0,V2e_2E0,V1b_2E0))
        <=> ( p(c_2Earithmetic_2E_3E_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0b0_2E0,V2e_2E0),c_2Enum_2E0_2E0))
            & ! [V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Enum_2Enum,V1b_2E0,V3x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V3x_2E0),V2e_2E0),c_2Earithmetic_2E_2D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0b0_2E0,V2e_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),app_2E2(A_27a,tyop_2Enum_2Enum,V0b0_2E0,V3x_2E0)) ) ) ) ) ).

tff(thm_2Ebag_2EBAG__UNION__DIFF__eliminate,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b_2E0,V0c_2E0),V0c_2E0) = V1b_2E0 )
      & ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0c_2E0,V1b_2E0),V0c_2E0) = V1b_2E0 ) ) ).

tff(thm_2Ebag_2EBAG__INSERT__EQUAL,axiom,
    ! [A_27a: $tType,V0b_2E0: A_27a,V1a_2E0: A_27a,V2N_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3M_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1a_2E0,V3M_2E0) = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0b_2E0,V2N_2E0) )
    <=> ( ( ( V3M_2E0 = V2N_2E0 )
          & ( V1a_2E0 = V0b_2E0 ) )
        | ? [V4k_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
            ( ( V3M_2E0 = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0b_2E0,V4k_2E0) )
            & ( V2N_2E0 = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1a_2E0,V4k_2E0) ) ) ) ) ).

tff(thm_2Ebag_2EBAG__DELETE__TWICE,axiom,
    ! [A_27a: $tType,V0b0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e1_2E0: A_27a,V2e2_2E0: A_27a,V3b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b0_2E0,V1e1_2E0,V3b1_2E0))
        & p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b0_2E0,V2e2_2E0,V4b2_2E0))
        & ( V3b1_2E0 != V4b2_2E0 ) )
     => ? [V5b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V3b1_2E0,V2e2_2E0,V5b_2E0))
          & p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V4b2_2E0,V1e1_2E0,V5b_2E0)) ) ) ).

tff(thm_2Ebag_2ESING__BAG__THM,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a] : p(c_2Ebag_2ESING__BAG_2E1(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)))) ).

tff(thm_2Ebag_2EEL__BAG__11,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
      ( ( c_2Ebag_2EEL__BAG_2E1(A_27a,V0x_2E0) = c_2Ebag_2EEL__BAG_2E1(A_27a,V1y_2E0) )
     => ( V0x_2E0 = V1y_2E0 ) ) ).

tff(thm_2Ebag_2EEL__BAG__INSERT__squeeze,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2y_2E0: A_27a] :
      ( ( c_2Ebag_2EEL__BAG_2E1(A_27a,V0x_2E0) = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2y_2E0,V1b_2E0) )
     => ( ( V0x_2E0 = V2y_2E0 )
        & ( V1b_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) ) ).

tff(thm_2Ebag_2ESING__EL__BAG,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a] : p(c_2Ebag_2ESING__BAG_2E1(A_27a,c_2Ebag_2EEL__BAG_2E1(A_27a,V0e_2E0))) ).

tff(thm_2Ebag_2EBAG__INSERT__UNION,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e_2E0: A_27a] : ( c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1e_2E0,V0b_2E0) = c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EEL__BAG_2E1(A_27a,V1e_2E0),V0b_2E0) ) ).

tff(thm_2Ebag_2EBAG__INSERT__EQ__UNION,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V3b_2E0) = c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b1_2E0,V2b2_2E0) )
     => ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V1b1_2E0))
        | p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V2b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__DELETE__SING,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e_2E0: A_27a] :
      ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b_2E0,V1e_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)))
     => p(c_2Ebag_2ESING__BAG_2E1(A_27a,V0b_2E0)) ) ).

tff(thm_2Ebag_2ENOT__IN__EMPTY__BAG,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ~ p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0x_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a))) ).

tff(thm_2Ebag_2EBAG__INN__EMPTY__BAG,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V0e_2E0,V1n_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)))
    <=> ( V1n_2E0 = c_2Enum_2E0_2E0 ) ) ).

tff(thm_2Ebag_2EMEMBER__NOT__EMPTY,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ? [V1x_2E0: A_27a] : p(c_2Ebag_2EBAG__IN_2E2(A_27a,V1x_2E0,V0b_2E0))
    <=> ( V0b_2E0 != c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__LEQ,axiom,
    ! [A_27a: $tType,V0b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b1_2E0,V0b2_2E0))
    <=> ! [V2x_2E0: A_27a] : p(c_2Earithmetic_2E_3C_3D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V1b1_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V0b2_2E0,V2x_2E0))) ) ).

tff(thm_2Ebag_2ESUB__BAG__EMPTY,axiom,
    ! [A_27a: $tType] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EEMPTY__BAG_2E0(A_27a),V0b_2E0))
      & ! [V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)))
        <=> ( V1b_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__REFL,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b_2E0,V0b_2E0)) ).

tff(thm_2Ebag_2EPSUB__BAG__IRREFL,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ~ p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,V0b_2E0,V0b_2E0)) ).

tff(thm_2Ebag_2ESUB__BAG__ANTISYM,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
        & p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b2_2E0,V0b1_2E0)) )
     => ( V0b1_2E0 = V1b2_2E0 ) ) ).

tff(thm_2Ebag_2EPSUB__BAG__ANTISYM,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ~ ( p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
        & p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,V1b2_2E0,V0b1_2E0)) ) ).

tff(thm_2Ebag_2ESUB__BAG__TRANS,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
        & p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b2_2E0,V2b3_2E0)) )
     => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V2b3_2E0)) ) ).

tff(thm_2Ebag_2EPSUB__BAG__TRANS,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
        & p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,V1b2_2E0,V2b3_2E0)) )
     => p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,V0b1_2E0,V2b3_2E0)) ) ).

tff(thm_2Ebag_2EPSUB__BAG__SUB__BAG,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
     => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0)) ) ).

tff(thm_2Ebag_2EPSUB__BAG__NOT__EQ,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
     => ( V0b1_2E0 != V1b2_2E0 ) ) ).

tff(thm_2Ebag_2EBAG__DIFF__EMPTY,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0b_2E0,V0b_2E0) = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) )
      & ! [V1b_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DIFF_2E2(A_27b,V1b_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27b)) = V1b_2E0 )
      & ! [V2b_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DIFF_2E2(A_27c,c_2Ebag_2EEMPTY__BAG_2E0(A_27c),V2b_2E0) = c_2Ebag_2EEMPTY__BAG_2E0(A_27c) )
      & ! [V3b1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),V4b2_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27d,V3b1_2E0,V4b2_2E0))
         => ( c_2Ebag_2EBAG__DIFF_2E2(A_27d,V3b1_2E0,V4b2_2E0) = c_2Ebag_2EEMPTY__BAG_2E0(A_27d) ) ) ) ).

tff(thm_2Ebag_2EBAG__DIFF__EMPTY__simple,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0b_2E0,V0b_2E0) = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) )
      & ! [V1b_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DIFF_2E2(A_27b,V1b_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27b)) = V1b_2E0 )
      & ! [V2b_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DIFF_2E2(A_27c,c_2Ebag_2EEMPTY__BAG_2E0(A_27c),V2b_2E0) = c_2Ebag_2EEMPTY__BAG_2E0(A_27c) ) ) ).

tff(thm_2Ebag_2EBAG__DIFF__EQ__EMPTY,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1b_2E0,V0c_2E0) = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) )
    <=> p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b_2E0,V0c_2E0)) ) ).

tff(thm_2Ebag_2EBAG__DIFF__INSERT__same,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,V1b1_2E0),c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,V2b2_2E0)) = c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1b1_2E0,V2b2_2E0) ) ).

tff(thm_2Ebag_2EBAG__DIFF__INSERT,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ~ p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0x_2E0,V1b1_2E0))
     => ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,V2b2_2E0),V1b1_2E0) = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V2b2_2E0,V1b1_2E0)) ) ) ).

tff(thm_2Ebag_2ENOT__IN__BAG__DIFF,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ~ p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0x_2E0,V1b1_2E0))
     => ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1b1_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,V2b2_2E0)) = c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1b1_2E0,V2b2_2E0) ) ) ).

tff(thm_2Ebag_2EBAG__IN__DIFF__I,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V2b1_2E0))
        & ~ p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V1b2_2E0)) )
     => p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V2b1_2E0,V1b2_2E0))) ) ).

tff(thm_2Ebag_2EBAG__IN__DIFF__E,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V2b1_2E0,V1b2_2E0)))
     => p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V2b1_2E0)) ) ).

tff(thm_2Ebag_2EBAG__UNION__DIFF,axiom,
    ! [A_27a: $tType,V0X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Z_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V2Z_2E0,V1Y_2E0))
     => ( ( c_2Ebag_2EBAG__UNION_2E2(A_27a,V0X_2E0,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1Y_2E0,V2Z_2E0)) = c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0X_2E0,V1Y_2E0),V2Z_2E0) )
        & ( c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1Y_2E0,V2Z_2E0),V0X_2E0) = c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0X_2E0,V1Y_2E0),V2Z_2E0) ) ) ) ).

tff(thm_2Ebag_2EBAG__DIFF__2L,axiom,
    ! [A_27a: $tType,V0X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Z_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0X_2E0,V1Y_2E0),V2Z_2E0) = c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0X_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1Y_2E0,V2Z_2E0)) ) ).

tff(thm_2Ebag_2EBAG__DIFF__2R,axiom,
    ! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2C_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V2C_2E0,V1B_2E0))
     => ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0A_2E0,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1B_2E0,V2C_2E0)) = c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0A_2E0,V2C_2E0),V1B_2E0) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__BAG__DIFF,axiom,
    ! [A_27a: $tType,V0X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Y_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3Z_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4W_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0X_2E0,V1Y_2E0),c_2Ebag_2EBAG__DIFF_2E2(A_27a,V3Z_2E0,V4W_2E0)))
     => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0X_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1Y_2E0,V2Y_27_2E0)),c_2Ebag_2EBAG__DIFF_2E2(A_27a,V3Z_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V4W_2E0,V2Y_27_2E0)))) ) ).

tff(thm_2Ebag_2EBAG__DIFF__UNION__eliminate,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V2b3_2E0)) = c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1b2_2E0,V2b3_2E0) )
      & ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V2b3_2E0,V0b1_2E0)) = c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1b2_2E0,V2b3_2E0) )
      & ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b2_2E0,V0b1_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V2b3_2E0)) = c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1b2_2E0,V2b3_2E0) )
      & ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b2_2E0,V0b1_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V2b3_2E0,V0b1_2E0)) = c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1b2_2E0,V2b3_2E0) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__UNION__eliminate,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V2b3_2E0)) = c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b2_2E0,V2b3_2E0) )
      & ( c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V2b3_2E0,V0b1_2E0)) = c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b2_2E0,V2b3_2E0) )
      & ( c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b2_2E0,V0b1_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V2b3_2E0)) = c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b2_2E0,V2b3_2E0) )
      & ( c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b2_2E0,V0b1_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V2b3_2E0,V0b1_2E0)) = c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b2_2E0,V2b3_2E0) ) ) ).

tff(thm_2Ebag_2Emove__BAG__UNION__over__eq,axiom,
    ! [A_27a: $tType,V0X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Z_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2EBAG__UNION_2E2(A_27a,V0X_2E0,V1Y_2E0) = V2Z_2E0 )
     => ( V0X_2E0 = c_2Ebag_2EBAG__DIFF_2E2(A_27a,V2Z_2E0,V1Y_2E0) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__UNION,axiom,
    ! [A_27a: $tType] :
      ( ! [V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
         => ! [V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b2_2E0,V2b_2E0))) )
      & ! [V3b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V3b1_2E0,V4b2_2E0))
         => ! [V5b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V3b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V5b_2E0,V4b2_2E0))) )
      & ! [V6b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V7b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V8b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V6b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V7b2_2E0,V8b3_2E0)))
         => ! [V9b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V6b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V7b2_2E0,V9b_2E0),V8b3_2E0))) )
      & ! [V10b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V11b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V12b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V10b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V11b2_2E0,V12b3_2E0)))
         => ! [V13b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V10b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V13b_2E0,V11b2_2E0),V12b3_2E0))) )
      & ! [V14b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V15b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V16b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V14b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V16b3_2E0,V15b2_2E0)))
         => ! [V17b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V14b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V16b3_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V15b2_2E0,V17b_2E0)))) )
      & ! [V18b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V19b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V20b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V18b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V20b3_2E0,V19b2_2E0)))
         => ! [V21b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V18b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V20b3_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V21b_2E0,V19b2_2E0)))) )
      & ! [V22b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V23b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V24b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V25b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V22b1_2E0,V24b3_2E0))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V23b2_2E0,V25b4_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V22b1_2E0,V23b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V24b3_2E0,V25b4_2E0))) ) )
      & ! [V26b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V27b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V28b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V29b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V26b1_2E0,V29b4_2E0))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V27b2_2E0,V28b3_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V26b1_2E0,V27b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V28b3_2E0,V29b4_2E0))) ) )
      & ! [V30b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V31b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V32b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V33b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V34b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V30b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V32b3_2E0,V34b5_2E0)))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V31b2_2E0,V33b4_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V30b1_2E0,V31b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V32b3_2E0,V33b4_2E0),V34b5_2E0))) ) )
      & ! [V35b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V36b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V37b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V38b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V39b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V35b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V38b4_2E0,V39b5_2E0)))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V36b2_2E0,V37b3_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V35b1_2E0,V36b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V37b3_2E0,V38b4_2E0),V39b5_2E0))) ) )
      & ! [V40b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V41b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V42b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V43b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V44b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V41b2_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V42b3_2E0,V44b5_2E0)))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V40b1_2E0,V43b4_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V40b1_2E0,V41b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V42b3_2E0,V43b4_2E0),V44b5_2E0))) ) )
      & ! [V45b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V46b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V47b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V48b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V49b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V46b2_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V48b4_2E0,V49b5_2E0)))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V45b1_2E0,V47b3_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V45b1_2E0,V46b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V47b3_2E0,V48b4_2E0),V49b5_2E0))) ) )
      & ! [V50b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V51b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V52b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V53b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V54b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V50b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V54b5_2E0,V52b3_2E0)))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V51b2_2E0,V53b4_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V51b2_2E0,V50b1_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V54b5_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V52b3_2E0,V53b4_2E0)))) ) )
      & ! [V55b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V56b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V57b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V58b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V59b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V55b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V59b5_2E0,V58b4_2E0)))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V56b2_2E0,V57b3_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V56b2_2E0,V55b1_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V59b5_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V57b3_2E0,V58b4_2E0)))) ) )
      & ! [V60b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V61b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V62b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V63b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V64b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V61b2_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V64b5_2E0,V62b3_2E0)))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V60b1_2E0,V63b4_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V61b2_2E0,V60b1_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V64b5_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V62b3_2E0,V63b4_2E0)))) ) )
      & ! [V65b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V66b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V67b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V68b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V69b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V66b2_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V69b5_2E0,V68b4_2E0)))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V65b1_2E0,V67b3_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V66b2_2E0,V65b1_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V69b5_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V67b3_2E0,V68b4_2E0)))) ) )
      & ! [V70b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V71b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V72b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V73b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V74b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V70b1_2E0,V71b2_2E0),V73b4_2E0))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V72b3_2E0,V74b5_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V70b1_2E0,V72b3_2E0),V71b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V73b4_2E0,V74b5_2E0))) ) )
      & ! [V75b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V76b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V77b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V78b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V79b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V75b1_2E0,V76b2_2E0),V79b5_2E0))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V77b3_2E0,V78b4_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V75b1_2E0,V77b3_2E0),V76b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V78b4_2E0,V79b5_2E0))) ) )
      & ! [V80b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V81b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V82b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V83b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V84b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V82b3_2E0,V81b2_2E0),V83b4_2E0))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V80b1_2E0,V84b5_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V80b1_2E0,V82b3_2E0),V81b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V83b4_2E0,V84b5_2E0))) ) )
      & ! [V85b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V86b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V87b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V88b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V89b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V87b3_2E0,V86b2_2E0),V89b5_2E0))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V85b1_2E0,V88b4_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V85b1_2E0,V87b3_2E0),V86b2_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V88b4_2E0,V89b5_2E0))) ) )
      & ! [V90b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V91b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V92b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V93b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V94b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V91b2_2E0,V90b1_2E0),V93b4_2E0))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V92b3_2E0,V94b5_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V91b2_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V90b1_2E0,V92b3_2E0)),c_2Ebag_2EBAG__UNION_2E2(A_27a,V94b5_2E0,V93b4_2E0))) ) )
      & ! [V95b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V96b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V97b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V98b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V99b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V96b2_2E0,V95b1_2E0),V99b5_2E0))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V97b3_2E0,V98b4_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V96b2_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V95b1_2E0,V97b3_2E0)),c_2Ebag_2EBAG__UNION_2E2(A_27a,V99b5_2E0,V98b4_2E0))) ) )
      & ! [V100b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V101b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V102b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V103b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V104b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V101b2_2E0,V102b3_2E0),V103b4_2E0))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V100b1_2E0,V104b5_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V101b2_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V100b1_2E0,V102b3_2E0)),c_2Ebag_2EBAG__UNION_2E2(A_27a,V104b5_2E0,V103b4_2E0))) ) )
      & ! [V105b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V106b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V107b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V108b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V109b5_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V106b2_2E0,V107b3_2E0),V109b5_2E0))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V105b1_2E0,V108b4_2E0))
           => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V106b2_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V105b1_2E0,V107b3_2E0)),c_2Ebag_2EBAG__UNION_2E2(A_27a,V109b5_2E0,V108b4_2E0))) ) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__EL__BAG,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EEL__BAG_2E1(A_27a,V0e_2E0),V1b_2E0) = c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V1b_2E0) ) ).

tff(thm_2Ebag_2ESUB__BAG__INSERT,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V1b1_2E0),c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V2b2_2E0)) = c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b1_2E0,V2b2_2E0) ) ).

tff(thm_2Ebag_2ESUB__BAG__INSERT__I,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e_2E0: A_27a] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b_2E0,V1c_2E0))
     => p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2e_2E0,V1c_2E0))) ) ).

tff(thm_2Ebag_2ENOT__IN__SUB__BAG__INSERT,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e_2E0: A_27a] :
      ( ~ p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e_2E0,V0b1_2E0))
     => ( c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2e_2E0,V1b2_2E0)) = c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__BAG__IN,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,V1b1_2E0),V2b2_2E0))
     => p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0x_2E0,V2b2_2E0)) ) ).

tff(thm_2Ebag_2ESUB__BAG__EXISTS,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
    <=> ? [V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( V1b2_2E0 = c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V2b_2E0) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__UNION__DIFF,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V2b3_2E0))
     => ( c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b2_2E0,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V2b3_2E0,V0b1_2E0)) = c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0),V2b3_2E0) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__UNION__down,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0),V2b3_2E0))
     => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V2b3_2E0))
        & p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b2_2E0,V2b3_2E0)) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__DIFF,axiom,
    ! [A_27a: $tType] :
      ( ! [V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
         => ! [V2b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0b1_2E0,V2b3_2E0),V1b2_2E0)) )
      & ! [V3b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V6b4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V4b2_2E0,V3b1_2E0))
         => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V6b4_2E0,V5b3_2E0))
           => ( c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V3b1_2E0,V4b2_2E0),c_2Ebag_2EBAG__DIFF_2E2(A_27a,V5b3_2E0,V6b4_2E0)) = c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V3b1_2E0,V6b4_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V4b2_2E0,V5b3_2E0)) ) ) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__PSUB__BAG,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
    <=> ( p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
        | ( V0b1_2E0 = V1b2_2E0 ) ) ) ).

tff(thm_2Ebag_2EBAG__DELETE__PSUB__BAG,axiom,
    ! [A_27a: $tType,V0b0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e_2E0: A_27a,V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__DELETE_2E3(A_27a,V0b0_2E0,V1e_2E0,V2b_2E0))
     => p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,V2b_2E0,V0b0_2E0)) ) ).

tff(thm_2Ebag_2ESET__OF__EMPTY,axiom,
    ! [A_27a: $tType] : ( c_2Ebag_2EBAG__OF__SET_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ).

tff(thm_2Ebag_2EBAG__IN__BAG__OF__SET,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: A_27a] : ( c_2Ebag_2EBAG__IN_2E2(A_27a,V1p_2E0,c_2Ebag_2EBAG__OF__SET_2E1(A_27a,V0P_2E0)) = c_2Ebool_2EIN_2E2(A_27a,V1p_2E0,V0P_2E0) ) ).

tff(thm_2Ebag_2EBAG__OF__EMPTY,axiom,
    ! [A_27a: $tType] : ( c_2Ebag_2ESET__OF__BAG_2E1(A_27a,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).

tff(thm_2Ebag_2ESET__BAG__I,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebag_2ESET__OF__BAG_2E1(A_27a,c_2Ebag_2EBAG__OF__SET_2E1(A_27a,V0s_2E0)) = V0s_2E0 ) ).

tff(thm_2Ebag_2ESUB__BAG__SET,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
     => p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0b1_2E0),c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V1b2_2E0))) ) ).

tff(thm_2Ebag_2ESET__OF__BAG__UNION,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2ESET__OF__BAG_2E1(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0b1_2E0),c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V1b2_2E0)) ) ).

tff(thm_2Ebag_2ESET__OF__BAG__MERGE,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2ESET__OF__BAG_2E1(A_27a,c_2Ebag_2EBAG__MERGE_2E2(A_27a,V0b1_2E0,V1b2_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0b1_2E0),c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V1b2_2E0)) ) ).

tff(thm_2Ebag_2ESET__OF__BAG__INSERT,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2ESET__OF__BAG_2E1(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V1b_2E0)) = c_2Epred__set_2EINSERT_2E2(A_27a,V0e_2E0,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V1b_2E0)) ) ).

tff(thm_2Ebag_2ESET__OF__EL__BAG,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a] : ( c_2Ebag_2ESET__OF__BAG_2E1(A_27a,c_2Ebag_2EEL__BAG_2E1(A_27a,V0e_2E0)) = c_2Epred__set_2EINSERT_2E2(A_27a,V0e_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) ) ).

tff(thm_2Ebag_2ESET__OF__BAG__DIFF__SUBSET__down,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0b1_2E0),c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V1b2_2E0)),c_2Ebag_2ESET__OF__BAG_2E1(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0b1_2E0,V1b2_2E0)))) ).

tff(thm_2Ebag_2ESET__OF__BAG__DIFF__SUBSET__up,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0b1_2E0,V1b2_2E0)),c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0b1_2E0))) ).

tff(thm_2Ebag_2EIN__SET__OF__BAG,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V1b_2E0)) = c_2Ebag_2EBAG__IN_2E2(A_27a,V0x_2E0,V1b_2E0) ) ).

tff(thm_2Ebag_2ESET__OF__BAG__EQ__EMPTY,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( ( c_2Epred__set_2EEMPTY_2E0(A_27a) = c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0b_2E0) )
      <=> ( V0b_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) )
      & ( ( c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0b_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
      <=> ( V0b_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) ) ).

tff(thm_2Ebag_2EBAG__DISJOINT__EMPTY,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,V0b_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)))
      & p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,c_2Ebag_2EEMPTY__BAG_2E0(A_27a),V0b_2E0)) ) ).

tff(thm_2Ebag_2EBAG__DISJOINT__DIFF,axiom,
    ! [A_27a: $tType,V0B1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1B2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0B1_2E0,V1B2_2E0),c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1B2_2E0,V0B1_2E0))) ).

tff(thm_2Ebag_2EBAG__DISJOINT__BAG__IN,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,V0b1_2E0,V1b2_2E0))
    <=> ! [V2e_2E0: A_27a] :
          ( ~ p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e_2E0,V0b1_2E0))
          | ~ p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e_2E0,V1b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__DISJOINT__BAG__INSERT,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e1_2E0: A_27a] :
          ( p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2e1_2E0,V0b1_2E0),V1b2_2E0))
        <=> ( ~ p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e1_2E0,V1b2_2E0))
            & p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,V0b1_2E0,V1b2_2E0)) ) )
      & ! [V3b1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V4b2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V5e2_2E0: A_27b] :
          ( p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27b,V3b1_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27b,V5e2_2E0,V4b2_2E0)))
        <=> ( ~ p(c_2Ebag_2EBAG__IN_2E2(A_27b,V5e2_2E0,V3b1_2E0))
            & p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27b,V3b1_2E0,V4b2_2E0)) ) ) ) ).

tff(thm_2Ebag_2EBAG__DISJOINT__BAG__UNION,axiom,
    ! [A_27a: $tType,V0b3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,V2b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b2_2E0,V0b3_2E0)))
      <=> ( p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,V2b1_2E0,V1b2_2E0))
          & p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,V2b1_2E0,V0b3_2E0)) ) )
      & ( p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V2b1_2E0,V1b2_2E0),V0b3_2E0))
      <=> ( p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,V2b1_2E0,V0b3_2E0))
          & p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,V1b2_2E0,V0b3_2E0)) ) ) ) ).

tff(thm_2Ebag_2EFINITE__EMPTY__BAG,axiom,
    ! [A_27a: $tType] : p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,c_2Ebag_2EEMPTY__BAG_2E0(A_27a))) ).

tff(thm_2Ebag_2EFINITE__BAG__INSERT,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b_2E0))
     => ! [V1e_2E0: A_27a] : p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1e_2E0,V0b_2E0))) ) ).

tff(thm_2Ebag_2EFINITE__BAG__INDUCT,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,V0P_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)))
        & ! [V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
            ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,V0P_2E0,V1b_2E0))
           => ! [V2e_2E0: A_27a] : p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,V0P_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2e_2E0,V1b_2E0))) ) )
     => ! [V3b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V3b_2E0))
         => p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,V0P_2E0,V3b_2E0)) ) ) ).

tff(thm_2Ebag_2ESTRONG__FINITE__BAG__INDUCT,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,V0P_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)))
        & ! [V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
            ( ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b_2E0))
              & p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,V0P_2E0,V1b_2E0)) )
           => ! [V2e_2E0: A_27a] : p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,V0P_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2e_2E0,V1b_2E0))) ) )
     => ! [V3b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V3b_2E0))
         => p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,V0P_2E0,V3b_2E0)) ) ) ).

tff(thm_2Ebag_2EFINITE__BAG__THM,axiom,
    ! [A_27a: $tType] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)))
      & ! [V0e_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2EFINITE__BAG_2E1(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V1b_2E0)) = c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b_2E0) ) ) ).

tff(thm_2Ebag_2EFINITE__BAG__DIFF,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b1_2E0))
     => ! [V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0b1_2E0,V1b2_2E0))) ) ).

tff(thm_2Ebag_2EFINITE__BAG__DIFF__dual,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b1_2E0))
     => ! [V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1b2_2E0,V0b1_2E0)))
         => p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b2_2E0)) ) ) ).

tff(thm_2Ebag_2EFINITE__BAG__UNION,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0)))
    <=> ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b1_2E0))
        & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b2_2E0)) ) ) ).

tff(thm_2Ebag_2EFINITE__SUB__BAG,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b1_2E0))
     => ! [V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b2_2E0,V0b1_2E0))
         => p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__CARD__EMPTY,axiom,
    ! [A_27a: $tType] : ( c_2Ebag_2EBAG__CARD_2E1(A_27a,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)) = c_2Enum_2E0_2E0 ) ).

tff(thm_2Ebag_2EBCARD__0,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b_2E0))
     => ( ( c_2Ebag_2EBAG__CARD_2E1(A_27a,V0b_2E0) = c_2Enum_2E0_2E0 )
      <=> ( V0b_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) ) ).

tff(thm_2Ebag_2EBAG__CARD__THM,axiom,
    ! [A_27a: $tType] :
      ( ( c_2Ebag_2EBAG__CARD_2E1(A_27a,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)) = c_2Enum_2E0_2E0 )
      & ! [V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b_2E0))
         => ! [V1e_2E0: A_27a] : ( c_2Ebag_2EBAG__CARD_2E1(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1e_2E0,V0b_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Ebag_2EBAG__CARD_2E1(A_27a,V0b_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ) ).

tff(thm_2Ebag_2EBAG__CARD__UNION,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b1_2E0))
        & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b2_2E0)) )
     => ( c_2Ebag_2EBAG__CARD_2E1(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Ebag_2EBAG__CARD_2E1(A_27a,V0b1_2E0),c_2Ebag_2EBAG__CARD_2E1(A_27a,V1b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBCARD__SUC,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b_2E0))
     => ! [V1n_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Ebag_2EBAG__CARD_2E1(A_27a,V0b_2E0) = c_2Enum_2ESUC_2E1(V1n_2E0) )
        <=> ? [V2b0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3e_2E0: A_27a] :
              ( ( V0b_2E0 = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V3e_2E0,V2b0_2E0) )
              & ( c_2Ebag_2EBAG__CARD_2E1(A_27a,V2b0_2E0) = V1n_2E0 ) ) ) ) ).

tff(thm_2Ebag_2EBAG__CARD__BAG__INN,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b_2E0))
     => ! [V1n_2E0: tyop_2Enum_2Enum,V2e_2E0: A_27a] :
          ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V2e_2E0,V1n_2E0,V0b_2E0))
         => p(c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,c_2Ebag_2EBAG__CARD_2E1(A_27a,V0b_2E0))) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__DIFF__EQ,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
     => ( V1b2_2E0 = c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1b2_2E0,V0b1_2E0)) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__CARD,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b2_2E0))
        & p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0)) )
     => p(c_2Earithmetic_2E_3C_3D_2E2(c_2Ebag_2EBAG__CARD_2E1(A_27a,V0b1_2E0),c_2Ebag_2EBAG__CARD_2E1(A_27a,V1b2_2E0))) ) ).

tff(thm_2Ebag_2EBAG__CARD__DIFF,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b_2E0))
     => ! [V1c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V1c_2E0,V0b_2E0))
         => ( c_2Ebag_2EBAG__CARD_2E1(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0b_2E0,V1c_2E0)) = c_2Earithmetic_2E_2D_2E2(c_2Ebag_2EBAG__CARD_2E1(A_27a,V0b_2E0),c_2Ebag_2EBAG__CARD_2E1(A_27a,V1c_2E0)) ) ) ) ).

tff(thm_2Ebag_2EBAG__FILTER__EMPTY,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebag_2EBAG__FILTER_2E2(A_27a,V0P_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)) = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ).

tff(thm_2Ebag_2EBAG__FILTER__BAG__INSERT,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebag_2EBAG__FILTER_2E2(A_27a,V2P_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V1b_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V0e_2E0),c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,c_2Ebag_2EBAG__FILTER_2E2(A_27a,V2P_2E0,V1b_2E0)),c_2Ebag_2EBAG__FILTER_2E2(A_27a,V2P_2E0,V1b_2E0)) ) ).

tff(thm_2Ebag_2EFINITE__BAG__FILTER,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b_2E0))
     => p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,c_2Ebag_2EBAG__FILTER_2E2(A_27a,V0P_2E0,V1b_2E0))) ) ).

tff(thm_2Ebag_2EBAG__INN__BAG__FILTER,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1e_2E0: A_27a,V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V1e_2E0,V0n_2E0,c_2Ebag_2EBAG__FILTER_2E2(A_27a,V3P_2E0,V2b_2E0)))
    <=> ( ( V0n_2E0 = c_2Enum_2E0_2E0 )
        | ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_2E0,V1e_2E0))
          & p(c_2Ebag_2EBAG__INN_2E3(A_27a,V1e_2E0,V0n_2E0,V2b_2E0)) ) ) ) ).

tff(thm_2Ebag_2EBAG__IN__BAG__FILTER,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,c_2Ebag_2EBAG__FILTER_2E2(A_27a,V2P_2E0,V1b_2E0)))
    <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V0e_2E0))
        & p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V1b_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__FILTER__FILTER,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2P_2E0),V1Q_2E0),V3a_2E0))
        <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3a_2E0))
            & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3a_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebag_2EBAG__FILTER_2E2(A_27a,V2P_2E0,c_2Ebag_2EBAG__FILTER_2E2(A_27a,V1Q_2E0,V0b_2E0)) = c_2Ebag_2EBAG__FILTER_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2P_2E0),V1Q_2E0),V0b_2E0) ) ) ).

tff(thm_2Ebag_2EBAG__FILTER__SUB__BAG,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__FILTER_2E2(A_27a,V0P_2E0,V1b_2E0),V1b_2E0)) ).

tff(thm_2Ebag_2ESET__OF__BAG__EQ__INSERT,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( c_2Epred__set_2EINSERT_2E2(A_27a,V1e_2E0,V2s_2E0) = c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0b_2E0) )
    <=> ? [V3b0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4eb_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( ( V0b_2E0 = c_2Ebag_2EBAG__UNION_2E2(A_27a,V4eb_2E0,V3b0_2E0) )
          & ( V2s_2E0 = c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V3b0_2E0) )
          & ! [V5e_27_2E0: A_27a] :
              ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V5e_27_2E0,V4eb_2E0))
             => ( V5e_27_2E0 = V1e_2E0 ) )
          & ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V1e_2E0,V2s_2E0))
           => p(c_2Ebag_2EBAG__IN_2E2(A_27a,V1e_2E0,V4eb_2E0)) ) ) ) ).

tff(thm_2Ebag_2EFINITE__SET__OF__BAG,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Epred__set_2EFINITE_2E1(A_27a,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0b_2E0)) = c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b_2E0) ) ).

tff(thm_2Ebag_2EBAG__IMAGE__EMPTY,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27a,V0f_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)) = c_2Ebag_2EEMPTY__BAG_2E0(A_27b) ) ).

tff(thm_2Ebag_2EBAG__IMAGE__FINITE__INSERT,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2e_2E0: A_27a] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b_2E0))
     => ( c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27a,V1f_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V2e_2E0,V0b_2E0)) = c_2Ebag_2EBAG__INSERT_2E2(A_27b,app_2E2(A_27a,A_27b,V1f_2E0,V2e_2E0),c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27a,V1f_2E0,V0b_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__IMAGE__FINITE__UNION,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b1_2E0))
        & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b2_2E0)) )
     => ( c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27a,V2f_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0)) = c_2Ebag_2EBAG__UNION_2E2(A_27b,c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27a,V2f_2E0,V0b1_2E0),c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27a,V2f_2E0,V1b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__IMAGE__FINITE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b_2E0))
     => p(c_2Ebag_2EFINITE__BAG_2E1(A_27b,c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27a,V0f_2E0,V1b_2E0))) ) ).

tff(thm_2Ebag_2EBAG__IMAGE__COMPOSE,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),V2b_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27c,V2b_2E0))
     => ( c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27c,c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,V0f_2E0,V1g_2E0),V2b_2E0) = c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27a,V0f_2E0,c_2Ebag_2EBAG__IMAGE_2E2(A_27a,A_27c,V1g_2E0,V2b_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__IMAGE__FINITE__I,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b_2E0))
     => ( c_2Ebag_2EBAG__IMAGE_2E2(A_27a,A_27a,c_2Ecombin_2EI_2E0(A_27a),V0b_2E0) = V0b_2E0 ) ) ).

tff(thm_2Ebag_2EBAG__IN__FINITE__BAG__IMAGE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V2b_2E0))
     => ( p(c_2Ebag_2EBAG__IN_2E2(A_27b,V0x_2E0,c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27a,V1f_2E0,V2b_2E0)))
      <=> ? [V3y_2E0: A_27a] :
            ( ( app_2E2(A_27a,A_27b,V1f_2E0,V3y_2E0) = V0x_2E0 )
            & p(c_2Ebag_2EBAG__IN_2E2(A_27a,V3y_2E0,V2b_2E0)) ) ) ) ).

tff(thm_2Ebag_2EBAG__IMAGE__EQ__EMPTY,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b_2E0))
     => ( ( c_2Ebag_2EBAG__IMAGE_2E2(A_27b,A_27a,V0f_2E0,V1b_2E0) = c_2Ebag_2EEMPTY__BAG_2E0(A_27b) )
      <=> ( V1b_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) ) ).

tff(thm_2Ebag_2EBAG__INSERT__CHOICE__REST,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( V0b_2E0 != c_2Ebag_2EEMPTY__BAG_2E0(A_27a) )
     => ( V0b_2E0 = c_2Ebag_2EBAG__INSERT_2E2(A_27a,c_2Ebag_2EBAG__CHOICE_2E1(A_27a,V0b_2E0),c_2Ebag_2EBAG__REST_2E1(A_27a,V0b_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__CHOICE__SING,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Ebag_2EBAG__CHOICE_2E1(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a))) = V0x_2E0 ) ).

tff(thm_2Ebag_2EBAG__REST__SING,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Ebag_2EBAG__REST_2E1(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a))) = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ).

tff(thm_2Ebag_2ESUB__BAG__REST,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__REST_2E1(A_27a,V0b_2E0),V0b_2E0)) ).

tff(thm_2Ebag_2EPSUB__BAG__REST,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( V0b_2E0 != c_2Ebag_2EEMPTY__BAG_2E0(A_27a) )
     => p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__REST_2E1(A_27a,V0b_2E0),V0b_2E0)) ) ).

tff(thm_2Ebag_2ESUB__BAG__UNION__MONO,axiom,
    ! [A_27a: $tType] :
      ( ! [V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0x_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0x_2E0,V1y_2E0)))
      & ! [V2x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V2x_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V3y_2E0,V2x_2E0))) ) ).

tff(thm_2Ebag_2EPSUB__BAG__CARD,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b2_2E0))
        & p(c_2Ebag_2EPSUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0)) )
     => p(c_2Eprim__rec_2E_3C_2E2(c_2Ebag_2EBAG__CARD_2E1(A_27a,V0b1_2E0),c_2Ebag_2EBAG__CARD_2E1(A_27a,V1b2_2E0))) ) ).

tff(thm_2Ebag_2EEL__BAG__BAG__INSERT,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1x_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)) = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0y_2E0,V2b_2E0) )
    <=> ( ( V1x_2E0 = V0y_2E0 )
        & ( V2b_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) ) ).

tff(thm_2Ebag_2EEL__BAG__SUB__BAG,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)),V1b_2E0) = c_2Ebag_2EBAG__IN_2E2(A_27a,V0x_2E0,V1b_2E0) ) ).

tff(thm_2Ebag_2EITBAG__IND,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( ! [V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3acc_2E0: A_27b] :
          ( ( ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V2b_2E0))
              & ( V2b_2E0 != c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) )
           => p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,c_2Ebag_2EBAG__REST_2E1(A_27a,V2b_2E0)),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,c_2Ebag_2EBAG__CHOICE_2E1(A_27a,V2b_2E0)),V3acc_2E0))) )
         => p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,V2b_2E0),V3acc_2E0)) )
     => ! [V4v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5v1_2E0: A_27b] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,V4v_2E0),V5v1_2E0)) ) ).

tff(thm_2Ebag_2EITBAG__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,F0_2E0,V0b_2E0))
        <=> ( V0b_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2acc_2E0: A_27b] :
          ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b_2E0))
         => ( c_2Ebag_2EITBAG_2E3(A_27a,A_27b,V1f_2E0,V0b_2E0,V2acc_2E0) = c_2Ebool_2ECOND_2E3(A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,F0_2E0,V0b_2E0),V2acc_2E0,c_2Ebag_2EITBAG_2E3(A_27a,A_27b,V1f_2E0,c_2Ebag_2EBAG__REST_2E1(A_27a,V0b_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V1f_2E0,c_2Ebag_2EBAG__CHOICE_2E1(A_27a,V0b_2E0)),V2acc_2E0))) ) ) ) ).

tff(thm_2Ebag_2EITBAG__EMPTY,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1acc_2E0: A_27b] : ( c_2Ebag_2EITBAG_2E3(A_27a,A_27b,V0f_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a),V1acc_2E0) = V1acc_2E0 ) ).

tff(thm_2Ebag_2EITBAG__INSERT,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3acc_2E0: A_27b] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b_2E0))
     => ( c_2Ebag_2EITBAG_2E3(A_27a,A_27b,V2f_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,V1b_2E0),V3acc_2E0) = c_2Ebag_2EITBAG_2E3(A_27a,A_27b,V2f_2E0,c_2Ebag_2EBAG__REST_2E1(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,V1b_2E0)),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V2f_2E0,c_2Ebag_2EBAG__CHOICE_2E1(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0x_2E0,V1b_2E0))),V3acc_2E0)) ) ) ).

tff(thm_2Ebag_2ECOMMUTING__ITBAG__INSERT,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a,V4z_2E0: A_27b] : ( app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V2x_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V3y_2E0),V4z_2E0)) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V3y_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V2x_2E0),V4z_2E0)) )
        & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b_2E0)) )
     => ! [V5x_2E0: A_27a,V6a_2E0: A_27b] : ( c_2Ebag_2EITBAG_2E3(A_27a,A_27b,V0f_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V5x_2E0,V1b_2E0),V6a_2E0) = c_2Ebag_2EITBAG_2E3(A_27a,A_27b,V0f_2E0,V1b_2E0,app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V5x_2E0),V6a_2E0)) ) ) ).

tff(thm_2Ebag_2ECOMMUTING__ITBAG__RECURSES,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,V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3a_2E0: A_27b] :
      ( ( ! [V4x_2E0: A_27a,V5y_2E0: A_27a,V6z_2E0: A_27b] : ( app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V4x_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V5y_2E0),V6z_2E0)) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V5y_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V4x_2E0),V6z_2E0)) )
        & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V2b_2E0)) )
     => ( c_2Ebag_2EITBAG_2E3(A_27a,A_27b,V0f_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1e_2E0,V2b_2E0),V3a_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V1e_2E0),c_2Ebag_2EITBAG_2E3(A_27a,A_27b,V0f_2E0,V2b_2E0,V3a_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__GEN__SUM__EMPTY,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EBAG__GEN__SUM_2E2(c_2Ebag_2EEMPTY__BAG_2E0(tyop_2Enum_2Enum),V0n_2E0) = V0n_2E0 ) ).

tff(thm_2Ebag_2EBAG__GEN__PROD__EMPTY,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EBAG__GEN__PROD_2E2(c_2Ebag_2EEMPTY__BAG_2E0(tyop_2Enum_2Enum),V0n_2E0) = V0n_2E0 ) ).

tff(thm_2Ebag_2EBAG__GEN__SUM__TAILREC,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V0b_2E0))
     => ! [V1x_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EBAG__GEN__SUM_2E2(c_2Ebag_2EBAG__INSERT_2E2(tyop_2Enum_2Enum,V1x_2E0,V0b_2E0),V2a_2E0) = c_2Ebag_2EBAG__GEN__SUM_2E2(V0b_2E0,c_2Earithmetic_2E_2B_2E2(V1x_2E0,V2a_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__GEN__SUM__REC,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V0b_2E0))
     => ! [V1x_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EBAG__GEN__SUM_2E2(c_2Ebag_2EBAG__INSERT_2E2(tyop_2Enum_2Enum,V1x_2E0,V0b_2E0),V2a_2E0) = c_2Earithmetic_2E_2B_2E2(V1x_2E0,c_2Ebag_2EBAG__GEN__SUM_2E2(V0b_2E0,V2a_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__GEN__PROD__TAILREC,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V0b_2E0))
     => ! [V1x_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EBAG__GEN__PROD_2E2(c_2Ebag_2EBAG__INSERT_2E2(tyop_2Enum_2Enum,V1x_2E0,V0b_2E0),V2a_2E0) = c_2Ebag_2EBAG__GEN__PROD_2E2(V0b_2E0,c_2Earithmetic_2E_2A_2E2(V1x_2E0,V2a_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__GEN__PROD__REC,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V0b_2E0))
     => ! [V1x_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum] : ( c_2Ebag_2EBAG__GEN__PROD_2E2(c_2Ebag_2EBAG__INSERT_2E2(tyop_2Enum_2Enum,V1x_2E0,V0b_2E0),V2a_2E0) = c_2Earithmetic_2E_2A_2E2(V1x_2E0,c_2Ebag_2EBAG__GEN__PROD_2E2(V0b_2E0,V2a_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__GEN__PROD__EQ__1,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V0b_2E0))
     => ! [V1e_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Ebag_2EBAG__GEN__PROD_2E2(V0b_2E0,V1e_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
         => ( V1e_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ) ).

tff(thm_2Ebag_2EBAG__GEN__PROD__ALL__ONES,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V0b_2E0))
     => ( ( c_2Ebag_2EBAG__GEN__PROD_2E2(V0b_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
       => ! [V1x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Ebag_2EBAG__IN_2E2(tyop_2Enum_2Enum,V1x_2E0,V0b_2E0))
           => ( V1x_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ) ) ).

tff(thm_2Ebag_2EBAG__GEN__PROD__POSITIVE,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V0b_2E0))
     => ( ! [V1x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Ebag_2EBAG__IN_2E2(tyop_2Enum_2Enum,V1x_2E0,V0b_2E0))
           => p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V1x_2E0)) )
       => p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Ebag_2EBAG__GEN__PROD_2E2(V0b_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) ).

tff(thm_2Ebag_2EBAG__EVERY__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ebag_2EBAG__EVERY_2E2(A_27a,V0P_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)))
      & ! [V1P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2e_2E0: A_27b,V3b_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2EBAG__EVERY_2E2(A_27b,V1P_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27b,V2e_2E0,V3b_2E0)))
        <=> ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,V1P_2E0,V2e_2E0))
            & p(c_2Ebag_2EBAG__EVERY_2E2(A_27b,V1P_2E0,V3b_2E0)) ) ) ) ).

tff(thm_2Ebag_2EBAG__EVERY__UNION,axiom,
    ! [A_27a: $tType,V0b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebag_2EBAG__EVERY_2E2(A_27a,V2P_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b1_2E0,V0b2_2E0)))
    <=> ( p(c_2Ebag_2EBAG__EVERY_2E2(A_27a,V2P_2E0,V1b1_2E0))
        & p(c_2Ebag_2EBAG__EVERY_2E2(A_27a,V2P_2E0,V0b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__EVERY__MERGE,axiom,
    ! [A_27a: $tType,V0b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebag_2EBAG__EVERY_2E2(A_27a,V2P_2E0,c_2Ebag_2EBAG__MERGE_2E2(A_27a,V1b1_2E0,V0b2_2E0)))
    <=> ( p(c_2Ebag_2EBAG__EVERY_2E2(A_27a,V2P_2E0,V1b1_2E0))
        & p(c_2Ebag_2EBAG__EVERY_2E2(A_27a,V2P_2E0,V0b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__EVERY__SET,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0)) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebag_2EBAG__EVERY_2E2(A_27a,V1P_2E0,V0b_2E0) = c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0b_2E0),c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0))) ) ) ).

tff(thm_2Ebag_2EBAG__FILTER__EQ__EMPTY,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( c_2Ebag_2EBAG__FILTER_2E2(A_27a,V1P_2E0,V0b_2E0) = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) )
    <=> p(c_2Ebag_2EBAG__EVERY_2E2(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V1P_2E0),V0b_2E0)) ) ).

tff(thm_2Ebag_2ESET__OF__BAG__IMAGE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V1b_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Ebag_2ESET__OF__BAG_2E1(A_27a,c_2Ebag_2EBAG__IMAGE_2E2(A_27a,A_27b,V0f_2E0,V1b_2E0)) = c_2Epred__set_2EIMAGE_2E2(A_27b,A_27a,V0f_2E0,c_2Ebag_2ESET__OF__BAG_2E1(A_27b,V1b_2E0)) ) ).

tff(thm_2Ebag_2EBAG__IMAGE__FINITE__RESTRICTED__I,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V2e_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0f_2E0),V2e_2E0))
        <=> ( app_2E2(A_27a,A_27a,V0f_2E0,V2e_2E0) = V2e_2E0 ) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b_2E0))
            & p(c_2Ebag_2EBAG__EVERY_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0f_2E0),V1b_2E0)) )
         => ( c_2Ebag_2EBAG__IMAGE_2E2(A_27a,A_27a,V0f_2E0,V1b_2E0) = V1b_2E0 ) ) ) ).

tff(thm_2Ebag_2EBAG__ALL__DISTINCT__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)))
      & ! [V0e_2E0: A_27b,V1b_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] :
          ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27b,c_2Ebag_2EBAG__INSERT_2E2(A_27b,V0e_2E0,V1b_2E0)))
        <=> ( ~ p(c_2Ebag_2EBAG__IN_2E2(A_27b,V0e_2E0,V1b_2E0))
            & p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27b,V1b_2E0)) ) ) ) ).

tff(thm_2Ebag_2EBAG__ALL__DISTINCT__BAG__MERGE,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,c_2Ebag_2EBAG__MERGE_2E2(A_27a,V0b1_2E0,V1b2_2E0)))
    <=> ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V0b1_2E0))
        & p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V1b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__ALL__DISTINCT__BAG__UNION,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b1_2E0,V1b2_2E0)))
    <=> ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V0b1_2E0))
        & p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V1b2_2E0))
        & p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,V0b1_2E0,V1b2_2E0)) ) ) ).

tff(thm_2Ebag_2EBAG__ALL__DISTINCT__DIFF,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V0b1_2E0))
     => p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0b1_2E0,V1b2_2E0))) ) ).

tff(thm_2Ebag_2EBAG__ALL__DISTINCT__DELETE,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V0b_2E0))
    <=> ! [V1e_2E0: A_27a] :
          ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V1e_2E0,V0b_2E0))
         => ~ p(c_2Ebag_2EBAG__IN_2E2(A_27a,V1e_2E0,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0b_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1e_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a))))) ) ) ).

tff(thm_2Ebag_2EBAG__ALL__DISTINCT__SET,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V0b_2E0))
    <=> ( c_2Ebag_2EBAG__OF__SET_2E1(A_27a,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0b_2E0)) = V0b_2E0 ) ) ).

tff(thm_2Ebag_2EBAG__ALL__DISTINCT__BAG__OF__SET,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,c_2Ebag_2EBAG__OF__SET_2E1(A_27a,V0s_2E0))) ).

tff(thm_2Ebag_2EBAG__IN__BAG__DIFF__ALL__DISTINCT,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e_2E0: A_27a] :
      ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V0b1_2E0))
     => ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e_2E0,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0b1_2E0,V1b2_2E0)))
      <=> ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e_2E0,V0b1_2E0))
          & ~ p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e_2E0,V1b2_2E0)) ) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__ALL__DISTINCT,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V0b1_2E0))
     => ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V0b1_2E0,V1b2_2E0))
      <=> ! [V2x_2E0: A_27a] :
            ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2x_2E0,V0b1_2E0))
           => p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2x_2E0,V1b2_2E0)) ) ) ) ).

tff(thm_2Ebag_2EBAG__ALL__DISTINCT__BAG__INN,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1n_2E0: tyop_2Enum_2Enum,V2e_2E0: A_27a] :
      ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V0b_2E0))
     => ( p(c_2Ebag_2EBAG__INN_2E3(A_27a,V2e_2E0,V1n_2E0,V0b_2E0))
      <=> ( ( V1n_2E0 = c_2Enum_2E0_2E0 )
          | ( ( V1n_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
            & p(c_2Ebag_2EBAG__IN_2E2(A_27a,V2e_2E0,V0b_2E0)) ) ) ) ) ).

tff(thm_2Ebag_2EBAG__ALL__DISTINCT__EXTENSION,axiom,
    ! [A_27a: $tType,V0b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V0b1_2E0))
        & p(c_2Ebag_2EBAG__ALL__DISTINCT_2E1(A_27a,V1b2_2E0)) )
     => ( ( V0b1_2E0 = V1b2_2E0 )
      <=> ! [V2x_2E0: A_27a] : ( c_2Ebag_2EBAG__IN_2E2(A_27a,V2x_2E0,V0b1_2E0) = c_2Ebag_2EBAG__IN_2E2(A_27a,V2x_2E0,V1b2_2E0) ) ) ) ).

tff(thm_2Ebag_2ENOT__BAG__IN,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1x_2E0: A_27a] :
      ( ( app_2E2(A_27a,tyop_2Enum_2Enum,V0b_2E0,V1x_2E0) = c_2Enum_2E0_2E0 )
    <=> ~ p(c_2Ebag_2EBAG__IN_2E2(A_27a,V1x_2E0,V0b_2E0)) ) ).

tff(thm_2Ebag_2EBAG__UNION__EQ__LEFT,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2d_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b_2E0,V1c_2E0) = c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b_2E0,V2d_2E0) )
     => ( V1c_2E0 = V2d_2E0 ) ) ).

tff(thm_2Ebag_2EBAG__IN__DIVIDES,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1x_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V0b_2E0))
        & p(c_2Ebag_2EBAG__IN_2E2(tyop_2Enum_2Enum,V1x_2E0,V0b_2E0)) )
     => p(c_2Edivides_2Edivides_2E2(V1x_2E0,c_2Ebag_2EBAG__GEN__PROD_2E2(V0b_2E0,V2a_2E0))) ) ).

tff(thm_2Ebag_2EBAG__GEN__PROD__UNION__LEM,axiom,
    ! [V0b1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V0b1_2E0))
     => ! [V1b2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2a_2E0: tyop_2Enum_2Enum,V3b_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V1b2_2E0))
         => ( c_2Ebag_2EBAG__GEN__PROD_2E2(c_2Ebag_2EBAG__UNION_2E2(tyop_2Enum_2Enum,V0b1_2E0,V1b2_2E0),c_2Earithmetic_2E_2A_2E2(V2a_2E0,V3b_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2Ebag_2EBAG__GEN__PROD_2E2(V0b1_2E0,V2a_2E0),c_2Ebag_2EBAG__GEN__PROD_2E2(V1b2_2E0,V3b_2E0)) ) ) ) ).

tff(thm_2Ebag_2EBAG__GEN__PROD__UNION,axiom,
    ! [V0b1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1b2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V0b1_2E0))
        & p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V1b2_2E0)) )
     => ( c_2Ebag_2EBAG__GEN__PROD_2E2(c_2Ebag_2EBAG__UNION_2E2(tyop_2Enum_2Enum,V0b1_2E0,V1b2_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Earithmetic_2E_2A_2E2(c_2Ebag_2EBAG__GEN__PROD_2E2(V0b1_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ebag_2EBAG__GEN__PROD_2E2(V1b2_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ) ).

tff(thm_2Ebag_2EBIG__BAG__UNION__EMPTY,axiom,
    ! [A_27a: $tType] : ( c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))) = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ).

tff(thm_2Ebag_2EBIG__BAG__UNION__INSERT,axiom,
    ! [A_27a: $tType,V0sob_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0sob_2E0))
     => ( c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0,V0sob_2E0)) = c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b_2E0,c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,c_2Epred__set_2EDELETE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0sob_2E0,V1b_2E0))) ) ) ).

tff(thm_2Ebag_2EBIG__BAG__UNION__DELETE,axiom,
    ! [A_27a: $tType,V0sob_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0sob_2E0))
     => ( c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,c_2Epred__set_2EDELETE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0sob_2E0,V1b_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0,V0sob_2E0),c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,V0sob_2E0),V1b_2E0),c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,V0sob_2E0)) ) ) ).

tff(thm_2Ebag_2EBIG__BAG__UNION__ITSET__BAG__UNION,axiom,
    ! [A_27a: $tType,V0sob_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0sob_2E0))
     => ( c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,V0sob_2E0) = c_2Epred__set_2EITSET_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E0(A_27a),V0sob_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)) ) ) ).

tff(thm_2Ebag_2EFINITE__BIG__BAG__UNION,axiom,
    ! [A_27a: $tType,V0sob_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0sob_2E0))
        & ! [V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0,V0sob_2E0))
           => p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b_2E0)) ) )
     => p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,V0sob_2E0))) ) ).

tff(thm_2Ebag_2EBAG__IN__BIG__BAG__UNION,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1P_2E0))
     => ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,V1P_2E0)))
      <=> ? [V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
            ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V2b_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0,V1P_2E0)) ) ) ) ).

tff(thm_2Ebag_2EBIG__BAG__UNION__EQ__EMPTY__BAG,axiom,
    ! [A_27a: $tType,V0sob_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0sob_2E0))
     => ( ( c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,V0sob_2E0) = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) )
      <=> ! [V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0,V0sob_2E0))
           => ( V1b_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) ) ) ).

tff(thm_2Ebag_2EBIG__BAG__UNION__UNION,axiom,
    ! [A_27a: $tType,V0s2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s1_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0s2_2E0)) )
     => ( c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,c_2Epred__set_2EUNION_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s1_2E0,V0s2_2E0)) = c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,V1s1_2E0),c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,V0s2_2E0)),c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,c_2Epred__set_2EINTER_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s1_2E0,V0s2_2E0))) ) ) ).

tff(thm_2Ebag_2EBIG__BAG__UNION__EQ__ELEMENT,axiom,
    ! [A_27a: $tType,V0sob_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0sob_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0,V0sob_2E0)) )
     => ( ( c_2Ebag_2EBIG__BAG__UNION_2E1(A_27a,V0sob_2E0) = V1b_2E0 )
      <=> ! [V2b_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_27_2E0,V0sob_2E0))
           => ( ( V2b_27_2E0 = V1b_2E0 )
              | ( V2b_27_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) ) ) ) ).

tff(thm_2Ebag_2EBAG__NOT__LESS__EMPTY,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ~ p(c_2Ebag_2Emlt1_2E3(A_27a,V0r_2E0,V1b_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a))) ).

tff(thm_2Ebag_2ENOT__mlt__EMPTY,axiom,
    ! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ~ p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V1R_2E0),V0b_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a))) ).

tff(thm_2Ebag_2EBAG__LESS__ADD,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1a_2E0: A_27a,V2N_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3M0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2Emlt1_2E3(A_27a,V0r_2E0,V2N_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V3M0_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1a_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)))))
     => ( ? [V4M_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
            ( p(c_2Ebag_2Emlt1_2E3(A_27a,V0r_2E0,V4M_2E0,V3M0_2E0))
            & ( V2N_2E0 = c_2Ebag_2EBAG__UNION_2E2(A_27a,V4M_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1a_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a))) ) )
        | ? [V5KK_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
            ( ! [V6b_2E0: A_27a] :
                ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V6b_2E0,V5KK_2E0))
               => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0,V6b_2E0),V1a_2E0)) )
            & ( V2N_2E0 = c_2Ebag_2EBAG__UNION_2E2(A_27a,V3M0_2E0,V5KK_2E0) ) ) ) ) ).

tff(thm_2Ebag_2Emlt1__all__accessible,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
     => ! [V1M_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Erelation_2EWFP_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V0R_2E0),V1M_2E0)) ) ).

tff(thm_2Ebag_2EWF__mlt1,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
     => p(c_2Erelation_2EWF_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V0R_2E0))) ) ).

tff(thm_2Ebag_2ETC__mlt1__FINITE__BAG,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V0R_2E0),V1b1_2E0,V2b2_2E0))
     => ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b1_2E0))
        & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V2b2_2E0)) ) ) ).

tff(thm_2Ebag_2ETC__mlt1__UNION2__I,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b2_2E0))
        & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V2b1_2E0))
        & ( V1b2_2E0 != c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) )
     => p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V0R_2E0),V2b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V2b1_2E0,V1b2_2E0))) ) ).

tff(thm_2Ebag_2ETC__mlt1__UNION1__I,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b2_2E0))
        & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V2b1_2E0))
        & ( V2b1_2E0 != c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) )
     => p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V0R_2E0),V1b2_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V2b1_2E0,V1b2_2E0))) ) ).

tff(thm_2Ebag_2Emlt__NOT__REFL,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,V1R_2E0))
     => ~ p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V1R_2E0),V0a_2E0,V0a_2E0)) ) ).

tff(thm_2Ebag_2Emlt__INSERT__CANCEL__I,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V1R_2E0),V2a_2E0,V3b_2E0))
     => p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V1R_2E0),c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V2a_2E0),c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V3b_2E0))) ) ).

tff(thm_2Ebag_2Emlt1__INSERT__CANCEL,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,V3R_2E0))
     => ( c_2Ebag_2Emlt1_2E3(A_27a,V3R_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V2a_2E0),c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V1b_2E0)) = c_2Ebag_2Emlt1_2E3(A_27a,V3R_2E0,V2a_2E0,V1b_2E0) ) ) ).

tff(thm_2Ebag_2Edominates__EMPTY,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0b_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : p(c_2Ebag_2Edominates_2E3(A_27a,A_27b,V1R_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a),V0b_2E0)) ).

tff(thm_2Ebag_2Edominates__SUBSET,axiom,
    ! [A_27a: $tType,V0Y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V2R_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27a,V0Y_2E0))
        & p(c_2Ebag_2Edominates_2E3(A_27a,A_27a,V2R_2E0,V0Y_2E0,V1X_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1X_2E0,V0Y_2E0))
        & ( V1X_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
     => ? [V3x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1X_2E0))
          & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V3x_2E0),V3x_2E0)) ) ) ).

tff(thm_2Ebag_2Emlt__dominates__thm1,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
     => ! [V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V0R_2E0),V1b1_2E0,V2b2_2E0))
        <=> ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b1_2E0))
            & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V2b2_2E0))
            & ? [V3x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
                ( ( V3x_2E0 != c_2Ebag_2EEMPTY__BAG_2E0(A_27a) )
                & p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V3x_2E0,V2b2_2E0))
                & ( V1b1_2E0 = c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V2b2_2E0,V3x_2E0),V4y_2E0) )
                & p(c_2Ebag_2Edominates_2E3(A_27a,A_27a,V0R_2E0,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V4y_2E0),c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V3x_2E0))) ) ) ) ) ).

tff(thm_2Ebag_2Edominates__DIFF,axiom,
    ! [A_27a: $tType,V0y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Erelation_2EWF_2E1(A_27a,V3R_2E0))
        & p(c_2Erelation_2Etransitive_2E1(A_27a,V3R_2E0))
        & p(c_2Ebag_2Edominates_2E3(A_27a,A_27a,V3R_2E0,V1x_2E0,V0y_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27a,V2i_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2i_2E0,V1x_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2i_2E0,V0y_2E0)) )
     => p(c_2Ebag_2Edominates_2E3(A_27a,A_27a,V3R_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V1x_2E0,V2i_2E0),c_2Epred__set_2EDIFF_2E2(A_27a,V0y_2E0,V2i_2E0))) ) ).

tff(thm_2Ebag_2EBAG__INSERT__SUB__BAG__E,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V2b_2E0),V1c_2E0))
     => ( p(c_2Ebag_2EBAG__IN_2E2(A_27a,V0e_2E0,V1c_2E0))
        & p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V2b_2E0,V1c_2E0)) ) ) ).

tff(thm_2Ebag_2Ebdominates__BAG__DIFF,axiom,
    ! [A_27a: $tType,V0y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2i_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Erelation_2EWF_2E1(A_27a,V3R_2E0))
        & p(c_2Erelation_2Etransitive_2E1(A_27a,V3R_2E0))
        & p(c_2Ebag_2Edominates_2E3(A_27a,A_27a,V3R_2E0,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V1x_2E0),c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V0y_2E0)))
        & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V2i_2E0))
        & p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V2i_2E0,V1x_2E0))
        & p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V2i_2E0,V0y_2E0)) )
     => p(c_2Ebag_2Edominates_2E3(A_27a,A_27a,V3R_2E0,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1x_2E0,V2i_2E0)),c_2Ebag_2ESET__OF__BAG_2E1(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V0y_2E0,V2i_2E0)))) ) ).

tff(thm_2Ebag_2EBAG__INTER__SUB__BAG,axiom,
    ! [A_27a: $tType,V0b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__INTER_2E2(A_27a,V1b1_2E0,V0b2_2E0),V1b1_2E0))
      & p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__INTER_2E2(A_27a,V1b1_2E0,V0b2_2E0),V0b2_2E0)) ) ).

tff(thm_2Ebag_2EBAG__INTER__FINITE,axiom,
    ! [A_27a: $tType,V0b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b1_2E0))
        | p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b2_2E0)) )
     => p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,c_2Ebag_2EBAG__INTER_2E2(A_27a,V1b1_2E0,V0b2_2E0))) ) ).

tff(thm_2Ebag_2Emlt__dominates__thm2,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
        & p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0)) )
     => ! [V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
          ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V0R_2E0),V1b1_2E0,V2b2_2E0))
        <=> ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b1_2E0))
            & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V2b2_2E0))
            & ? [V3x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
                ( ( V3x_2E0 != c_2Ebag_2EEMPTY__BAG_2E0(A_27a) )
                & p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V3x_2E0,V2b2_2E0))
                & p(c_2Ebag_2EBAG__DISJOINT_2E2(A_27a,V3x_2E0,V4y_2E0))
                & ( V1b1_2E0 = c_2Ebag_2EBAG__UNION_2E2(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V2b2_2E0,V3x_2E0),V4y_2E0) )
                & p(c_2Ebag_2Edominates_2E3(A_27a,A_27a,V0R_2E0,c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V4y_2E0),c_2Ebag_2ESET__OF__BAG_2E1(A_27a,V3x_2E0))) ) ) ) ) ).

tff(thm_2Ebag_2EBAG__DIFF__INSERT__SUB__BAG,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V1c_2E0,V2b_2E0))
     => ( c_2Ebag_2EBAG__DIFF_2E2(A_27a,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V2b_2E0),V1c_2E0) = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V2b_2E0,V1c_2E0)) ) ) ).

tff(thm_2Ebag_2Emlt__INSERT__CANCEL,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V3R_2E0))
        & p(c_2Erelation_2EWF_2E1(A_27a,V3R_2E0)) )
     => ( c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V3R_2E0),c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V2a_2E0),c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,V1b_2E0)) = c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V3R_2E0),V2a_2E0,V1b_2E0) ) ) ).

tff(thm_2Ebag_2Emlt__UNION__RCANCEL__I,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V3R_2E0),V2a_2E0,V1b_2E0))
        & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0c_2E0)) )
     => p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V3R_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V2a_2E0,V0c_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b_2E0,V0c_2E0))) ) ).

tff(thm_2Ebag_2Emlt__UNION__RCANCEL,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Erelation_2EWF_2E1(A_27a,V3R_2E0))
        & p(c_2Erelation_2Etransitive_2E1(A_27a,V3R_2E0)) )
     => ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V3R_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V2a_2E0,V0c_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b_2E0,V0c_2E0)))
      <=> ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V3R_2E0),V2a_2E0,V1b_2E0))
          & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0c_2E0)) ) ) ) ).

tff(thm_2Ebag_2Emlt__UNION__LCANCEL__I,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V3R_2E0),V2a_2E0,V1b_2E0))
        & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0c_2E0)) )
     => p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V3R_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V0c_2E0,V2a_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V0c_2E0,V1b_2E0))) ) ).

tff(thm_2Ebag_2Emlt__UNION__LCANCEL,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Erelation_2EWF_2E1(A_27a,V3R_2E0))
        & p(c_2Erelation_2Etransitive_2E1(A_27a,V3R_2E0)) )
     => ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V3R_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V0c_2E0,V2a_2E0),c_2Ebag_2EBAG__UNION_2E2(A_27a,V0c_2E0,V1b_2E0)))
      <=> ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V3R_2E0),V2a_2E0,V1b_2E0))
          & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0c_2E0)) ) ) ) ).

tff(thm_2Ebag_2Emlt__UNION__CANCEL__EQN,axiom,
    ! [A_27a: $tType,V0b2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2EWF_2E1(A_27a,V2R_2E0))
     => ( ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V2R_2E0),V1b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V1b1_2E0,V0b2_2E0)))
        <=> ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b1_2E0))
            & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b2_2E0))
            & ( V0b2_2E0 != c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) )
        & ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(A_27a,V2R_2E0),V1b1_2E0,c_2Ebag_2EBAG__UNION_2E2(A_27a,V0b2_2E0,V1b1_2E0)))
        <=> ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V1b1_2E0))
            & p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V0b2_2E0))
            & ( V0b2_2E0 != c_2Ebag_2EEMPTY__BAG_2E0(A_27a) ) ) ) ) ) ).

tff(thm_2Ebag_2Emlt__UNION__EMPTY__EQN,axiom,
    p(c_2Ebool_2ET_2E0) ).

tff(thm_2Ebag_2ESUB__BAG__SING,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2ESUB__BAG_2E2(A_27a,V1b_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a))))
    <=> ( ( V1b_2E0 = c_2Ebag_2EEMPTY__BAG_2E0(A_27a) )
        | ( V1b_2E0 = c_2Ebag_2EBAG__INSERT_2E2(A_27a,V0e_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)) ) ) ) ).

tff(thm_2Ebag_2ESUB__BAG__DIFF__simple,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Ebag_2ESUB__BAG_2E2(A_27a,c_2Ebag_2EBAG__DIFF_2E2(A_27a,V1b_2E0,V0c_2E0),V1b_2E0)) ).

tff(thm_2Ebag_2EmltLT__SING0,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
      ( p(c_2Erelation_2ETC_2E3(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2Emlt1_2E1(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E0),c_2Ebag_2EBAG__INSERT_2E2(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Ebag_2EEMPTY__BAG_2E0(tyop_2Enum_2Enum)),V0b_2E0))
    <=> ( p(c_2Ebag_2EFINITE__BAG_2E1(tyop_2Enum_2Enum,V0b_2E0))
        & ( V0b_2E0 != c_2Ebag_2EBAG__INSERT_2E2(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Ebag_2EEMPTY__BAG_2E0(tyop_2Enum_2Enum)) )
        & ( V0b_2E0 != c_2Ebag_2EEMPTY__BAG_2E0(tyop_2Enum_2Enum) ) ) ) ).

tff(thm_2Ebag_2EBAG__SIZE__EMPTY,axiom,
    ! [A_27a: $tType,V0eltsize_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Ebag_2Ebag__size_2E2(A_27a,V0eltsize_2E0,c_2Ebag_2EEMPTY__BAG_2E0(A_27a)) = c_2Enum_2E0_2E0 ) ).

tff(thm_2Ebag_2EBAG__SIZE__INSERT,axiom,
    ! [A_27a: $tType,V0eltsize_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e_2E0: A_27a,V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Ebag_2EFINITE__BAG_2E1(A_27a,V2b_2E0))
     => ( c_2Ebag_2Ebag__size_2E2(A_27a,V0eltsize_2E0,c_2Ebag_2EBAG__INSERT_2E2(A_27a,V1e_2E0,V2b_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),app_2E2(A_27a,tyop_2Enum_2Enum,V0eltsize_2E0,V1e_2E0)),c_2Ebag_2Ebag__size_2E2(A_27a,V0eltsize_2E0,V2b_2E0)) ) ) ).

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