%------------------------------------------------------------------------------
% File     : ITP030_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    : list.ax [Gau19]
%          : HL4030_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    : 1104 ( 446 unt; 284 typ;   0 def)
%            Number of atoms       : 1671 (1097 equ)
%            Maximal formula atoms :   12 (   1 avg)
%            Number of connectives :  914 (  63   ~;  29   |; 328   &)
%                                         ( 193 <=>; 301  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  248 ( 143   >; 105   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  280 ( 280 usr;  25 con; 0-7 aty)
%            Number of variables   : 3918 (3502   !;  99   ?;3918   :)
%                                         ( 317  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Eind__type_2Erecspace,type,
    tyop_2Eind__type_2Erecspace: $tType > $tType ).

tff(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: $tType > $tType ).

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_2Eone_2Eone,type,
    tyop_2Eone_2Eone: $tType ).

tff(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: $tType > $tType ).

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

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

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

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

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

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

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

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

tff(c_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_2E1,type,
    c_2Earithmetic_2E_2B_2E1: 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_2E1,type,
    c_2Emin_2E_3D_2E1: 
      !>[A_27a: $tType] : ( 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_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_2Ebool_2E_3F_21_2E0,type,
    c_2Ebool_2E_3F_21_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_3F_21_2E1,type,
    c_2Ebool_2E_3F_21_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).

tff(c_2Emin_2E_40_2E1,type,
    c_2Emin_2E_40_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).

tff(c_2Elist_2EALL__DISTINCT_2E0,type,
    c_2Elist_2EALL__DISTINCT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ).

tff(c_2Elist_2EALL__DISTINCT_2E1,type,
    c_2Elist_2EALL__DISTINCT_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Ebool ) ).

tff(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Ebool_2EARB_2E0,type,
    c_2Ebool_2EARB_2E0: 
      !>[A_27a: $tType] : A_27a ).

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

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

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

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

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

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

tff(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Eind__type_2EBOTTOM_2E0,type,
    c_2Eind__type_2EBOTTOM_2E0: 
      !>[A_27a: $tType] : tyop_2Eind__type_2Erecspace(A_27a) ).

tff(c_2Ecombin_2EC_2E0,type,
    c_2Ecombin_2EC_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))) ).

tff(c_2Ecombin_2EC_2E1,type,
    c_2Ecombin_2EC_2E1: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)) ) ).

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

tff(c_2Epred__set_2ECARD_2E0,type,
    c_2Epred__set_2ECARD_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).

tff(c_2Epred__set_2ECARD_2E1,type,
    c_2Epred__set_2ECARD_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ) ).

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

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

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

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

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

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

tff(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Eind__type_2ECONSTR_2E0,type,
    c_2Eind__type_2ECONSTR_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))) ).

tff(c_2Eind__type_2ECONSTR_2E3,type,
    c_2Eind__type_2ECONSTR_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)) ) > tyop_2Eind__type_2Erecspace(A_27a) ) ).

tff(c_2Ebool_2EDATATYPE_2E0,type,
    c_2Ebool_2EDATATYPE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2EDATATYPE_2E1,type,
    c_2Ebool_2EDATATYPE_2E1: 
      !>[A_27a: $tType] : ( 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_2Elist_2EDROP_2E0,type,
    c_2Elist_2EDROP_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2EDROP_2E2,type,
    c_2Elist_2EDROP_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2EEL_2E0,type,
    c_2Elist_2EEL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)) ).

tff(c_2Elist_2EEL_2E1,type,
    c_2Elist_2EEL_2E1: 
      !>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a) ) ).

tff(c_2Elist_2EEL_2E2,type,
    c_2Elist_2EEL_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > A_27a ) ).

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_2Elist_2EEVERY_2E0,type,
    c_2Elist_2EEVERY_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Elist_2EEVERY_2E2,type,
    c_2Elist_2EEVERY_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Elist_2EEVERYi_2E0,type,
    c_2Elist_2EEVERYi_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Elist_2EEVERYi_2E2,type,
    c_2Elist_2EEVERYi_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Elist_2EEXISTS_2E0,type,
    c_2Elist_2EEXISTS_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Elist_2EEXISTS_2E2,type,
    c_2Elist_2EEXISTS_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2Eind__type_2EFCONS_2E0,type,
    c_2Eind__type_2EFCONS_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))) ).

tff(c_2Eind__type_2EFCONS_2E2,type,
    c_2Eind__type_2EFCONS_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) ).

tff(c_2Elist_2EFILTER_2E0,type,
    c_2Elist_2EFILTER_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2EFILTER_2E2,type,
    c_2Elist_2EFILTER_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2EFIND_2E0,type,
    c_2Elist_2EFIND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))) ).

tff(c_2Elist_2EFIND_2E1,type,
    c_2Elist_2EFIND_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)) ) ).

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_2Elist_2EFLAT_2E0,type,
    c_2Elist_2EFLAT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)) ).

tff(c_2Elist_2EFLAT_2E1,type,
    c_2Elist_2EFLAT_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2EFOLDL_2E0,type,
    c_2Elist_2EFOLDL_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).

tff(c_2Elist_2EFOLDL_2E3,type,
    c_2Elist_2EFOLDL_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > A_27b ) ).

tff(c_2Elist_2EFOLDL2_2E0,type,
    c_2Elist_2EFOLDL2_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a)))) ).

tff(c_2Elist_2EFOLDL2_2E4,type,
    c_2Elist_2EFOLDL2_2E4: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))) * A_27a * tyop_2Elist_2Elist(A_27b) * tyop_2Elist_2Elist(A_27c) ) > A_27a ) ).

tff(c_2Elist_2EFOLDR_2E0,type,
    c_2Elist_2EFOLDR_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).

tff(c_2Elist_2EFOLDR_2E3,type,
    c_2Elist_2EFOLDR_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > A_27b ) ).

tff(c_2Elist_2EFRONT_2E0,type,
    c_2Elist_2EFRONT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).

tff(c_2Elist_2EFRONT_2E1,type,
    c_2Elist_2EFRONT_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).

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

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

tff(c_2Elist_2EGENLIST_2E0,type,
    c_2Elist_2EGENLIST_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2EGENLIST_2E2,type,
    c_2Elist_2EGENLIST_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) * tyop_2Enum_2Enum ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2EGENLIST__AUX_2E0,type,
    c_2Elist_2EGENLIST__AUX_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))) ).

tff(c_2Elist_2EGENLIST__AUX_2E3,type,
    c_2Elist_2EGENLIST__AUX_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) * tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

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

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

tff(c_2Elist_2EHD_2E0,type,
    c_2Elist_2EHD_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a) ).

tff(c_2Elist_2EHD_2E1,type,
    c_2Elist_2EHD_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > A_27a ) ).

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

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

tff(c_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_2Elist_2EINDEX__FIND_2E0,type,
    c_2Elist_2EINDEX__FIND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))) ).

tff(c_2Elist_2EINDEX__FIND_2E2,type,
    c_2Elist_2EINDEX__FIND_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))) ) ).

tff(c_2Elist_2EINDEX__FIND_2E3,type,
    c_2Elist_2EINDEX__FIND_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)) ) ).

tff(c_2Elist_2EINDEX__OF_2E0,type,
    c_2Elist_2EINDEX__OF_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))) ).

tff(c_2Elist_2EINDEX__OF_2E1,type,
    c_2Elist_2EINDEX__OF_2E1: 
      !>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)) ) ).

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

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

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

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

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

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

tff(c_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_2Elist_2ELAST_2E0,type,
    c_2Elist_2ELAST_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a) ).

tff(c_2Elist_2ELAST_2E1,type,
    c_2Elist_2ELAST_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > A_27a ) ).

tff(c_2Elist_2ELEN_2E0,type,
    c_2Elist_2ELEN_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Elist_2ELEN_2E2,type,
    c_2Elist_2ELEN_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ) ).

tff(c_2Elist_2ELENGTH_2E0,type,
    c_2Elist_2ELENGTH_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).

tff(c_2Elist_2ELENGTH_2E1,type,
    c_2Elist_2ELENGTH_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).

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_2Elist_2ELIST__APPLY_2E0,type,
    c_2Elist_2ELIST__APPLY_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2ELIST__APPLY_2E2,type,
    c_2Elist_2ELIST__APPLY_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)) * tyop_2Elist_2Elist(A_27b) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2ELIST__BIND_2E0,type,
    c_2Elist_2ELIST__BIND_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2ELIST__BIND_2E2,type,
    c_2Elist_2ELIST__BIND_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(A_27b) * tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2ELIST__GUARD_2E0,type,
    c_2Elist_2ELIST__GUARD_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Eone_2Eone)) ).

tff(c_2Elist_2ELIST__GUARD_2E1,type,
    c_2Elist_2ELIST__GUARD_2E1: tyop_2Emin_2Ebool > tyop_2Elist_2Elist(tyop_2Eone_2Eone) ).

tff(c_2Elist_2ELIST__IGNORE__BIND_2E0,type,
    c_2Elist_2ELIST__IGNORE__BIND_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2ELIST__IGNORE__BIND_2E2,type,
    c_2Elist_2ELIST__IGNORE__BIND_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(A_27b) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2ELIST__LIFT2_2E0,type,
    c_2Elist_2ELIST__LIFT2_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)))) ).

tff(c_2Elist_2ELIST__LIFT2_2E3,type,
    c_2Elist_2ELIST__LIFT2_2E3: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)) * tyop_2Elist_2Elist(A_27b) * tyop_2Elist_2Elist(A_27c) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2ELIST__REL_2E0,type,
    c_2Elist_2ELIST__REL_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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))) ).

tff(c_2Elist_2ELIST__REL_2E3,type,
    c_2Elist_2ELIST__REL_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27b) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Elist_2ELIST__TO__SET_2E0,type,
    c_2Elist_2ELIST__TO__SET_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Elist_2ELIST__TO__SET_2E1,type,
    c_2Elist_2ELIST__TO__SET_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Elist_2ELIST__TO__SET_2E2,type,
    c_2Elist_2ELIST__TO__SET_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Elist_2ELLEX_2E0,type,
    c_2Elist_2ELLEX_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))) ).

tff(c_2Elist_2ELLEX_2E1,type,
    c_2Elist_2ELLEX_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ) ).

tff(c_2Elist_2ELLEX_2E3,type,
    c_2Elist_2ELLEX_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Elist_2ELRC_2E0,type,
    c_2Elist_2ELRC_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).

tff(c_2Elist_2ELRC_2E4,type,
    c_2Elist_2ELRC_2E4: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Elist_2ELUPDATE_2E0,type,
    c_2Elist_2ELUPDATE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))) ).

tff(c_2Elist_2ELUPDATE_2E3,type,
    c_2Elist_2ELUPDATE_2E3: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2EMAP_2E0,type,
    c_2Elist_2EMAP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).

tff(c_2Elist_2EMAP_2E1,type,
    c_2Elist_2EMAP_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,A_27b) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)) ) ).

tff(c_2Elist_2EMAP_2E2,type,
    c_2Elist_2EMAP_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27b) ) ).

tff(c_2Elist_2EMAP2_2E0,type,
    c_2Elist_2EMAP2_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)))) ).

tff(c_2Elist_2EMAP2_2E3,type,
    c_2Elist_2EMAP2_2E3: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)) * tyop_2Elist_2Elist(A_27b) * tyop_2Elist_2Elist(A_27c) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Earithmetic_2EMIN_2E0,type,
    c_2Earithmetic_2EMIN_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2EMIN_2E2,type,
    c_2Earithmetic_2EMIN_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: 
      !>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).

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

tff(c_2Earithmetic_2ENRC_2E0,type,
    c_2Earithmetic_2ENRC_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).

tff(c_2Earithmetic_2ENRC_2E4,type,
    c_2Earithmetic_2ENRC_2E4: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Enum_2Enum * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Elist_2ENULL_2E0,type,
    c_2Elist_2ENULL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ).

tff(c_2Elist_2ENULL_2E1,type,
    c_2Elist_2ENULL_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Ebool ) ).

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_2Ewhile_2EOLEAST_2E0,type,
    c_2Ewhile_2EOLEAST_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)) ).

tff(c_2Ewhile_2EOLEAST_2E1,type,
    c_2Ewhile_2EOLEAST_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Eoption_2Eoption(tyop_2Enum_2Enum) ).

tff(c_2Eoption_2EOPTION__BIND_2E0,type,
    c_2Eoption_2EOPTION__BIND_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))) ).

tff(c_2Eoption_2EOPTION__BIND_2E2,type,
    c_2Eoption_2EOPTION__BIND_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption(A_27b) * tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)) ) > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Eoption_2EOPTION__MAP_2E0,type,
    c_2Eoption_2EOPTION__MAP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))) ).

tff(c_2Eoption_2EOPTION__MAP_2E1,type,
    c_2Eoption_2EOPTION__MAP_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,A_27b) > tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)) ) ).

tff(c_2Elist_2EOPT__MMAP_2E0,type,
    c_2Elist_2EOPT__MMAP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))) ).

tff(c_2Elist_2EOPT__MMAP_2E2,type,
    c_2Elist_2EOPT__MMAP_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)) * tyop_2Elist_2Elist(A_27b) ) > tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)) ) ).

tff(c_2Elist_2EPAD__LEFT_2E0,type,
    c_2Elist_2EPAD__LEFT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))) ).

tff(c_2Elist_2EPAD__LEFT_2E3,type,
    c_2Elist_2EPAD__LEFT_2E3: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2EPAD__RIGHT_2E0,type,
    c_2Elist_2EPAD__RIGHT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))) ).

tff(c_2Elist_2EPAD__RIGHT_2E3,type,
    c_2Elist_2EPAD__RIGHT_2E3: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Eprim__rec_2EPRE_2E0,type,
    c_2Eprim__rec_2EPRE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Eprim__rec_2EPRE_2E1,type,
    c_2Eprim__rec_2EPRE_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Erelation_2ERC_2E0,type,
    c_2Erelation_2ERC_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_2ERC_2E1,type,
    c_2Erelation_2ERC_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).

tff(c_2Epred__set_2EREST_2E0,type,
    c_2Epred__set_2EREST_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2EREST_2E1,type,
    c_2Epred__set_2EREST_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Elist_2EREV_2E0,type,
    c_2Elist_2EREV_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2EREV_2E2,type,
    c_2Elist_2EREV_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2EREVERSE_2E0,type,
    c_2Elist_2EREVERSE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).

tff(c_2Elist_2EREVERSE_2E1,type,
    c_2Elist_2EREVERSE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2ESET__TO__LIST_2E0,type,
    c_2Elist_2ESET__TO__LIST_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)) ).

tff(c_2Elist_2ESET__TO__LIST_2E1,type,
    c_2Elist_2ESET__TO__LIST_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2ESHORTLEX_2E0,type,
    c_2Elist_2ESHORTLEX_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))) ).

tff(c_2Elist_2ESHORTLEX_2E1,type,
    c_2Elist_2ESHORTLEX_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ) ).

tff(c_2Elist_2ESHORTLEX_2E3,type,
    c_2Elist_2ESHORTLEX_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

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

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

tff(c_2Elist_2ESNOC_2E0,type,
    c_2Elist_2ESNOC_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2ESNOC_2E2,type,
    c_2Elist_2ESNOC_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

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

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

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

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

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

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

tff(c_2Elist_2ESUM_2E0,type,
    c_2Elist_2ESUM_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum) ).

tff(c_2Elist_2ESUM_2E1,type,
    c_2Elist_2ESUM_2E1: tyop_2Elist_2Elist(tyop_2Enum_2Enum) > tyop_2Enum_2Enum ).

tff(c_2Elist_2ESUM__ACC_2E0,type,
    c_2Elist_2ESUM__ACC_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Elist_2ESUM__ACC_2E2,type,
    c_2Elist_2ESUM__ACC_2E2: ( tyop_2Elist_2Elist(tyop_2Enum_2Enum) * 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_2Elist_2ETAKE_2E0,type,
    c_2Elist_2ETAKE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2ETAKE_2E2,type,
    c_2Elist_2ETAKE_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2ETL_2E0,type,
    c_2Elist_2ETL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).

tff(c_2Elist_2ETL_2E1,type,
    c_2Elist_2ETL_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).

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

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

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

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

tff(c_2Epair_2EUNCURRY_2E2,type,
    c_2Epair_2EUNCURRY_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) * tyop_2Epair_2Eprod(A_27a,A_27b) ) > A_27c ) ).

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

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

tff(c_2Elist_2EUNIQUE_2E0,type,
    c_2Elist_2EUNIQUE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Elist_2EUNIQUE_2E2,type,
    c_2Elist_2EUNIQUE_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

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

tff(c_2Elist_2EUNZIP_2E0,type,
    c_2Elist_2EUNZIP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).

tff(c_2Elist_2EUNZIP_2E1,type,
    c_2Elist_2EUNZIP_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) > tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)) ) ).

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

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

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

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

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).

tff(c_2Elist_2EZIP_2E0,type,
    c_2Elist_2EZIP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))) ).

tff(c_2Elist_2EZIP_2E1,type,
    c_2Elist_2EZIP_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

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

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

tff(c_2Epred__set_2Ecount_2E0,type,
    c_2Epred__set_2Ecount_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

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

tff(c_2Elist_2EdropWhile_2E0,type,
    c_2Elist_2EdropWhile_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2EdropWhile_2E1,type,
    c_2Elist_2EdropWhile_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ) ).

tff(c_2Elist_2EdropWhile_2E2,type,
    c_2Elist_2EdropWhile_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2EisPREFIX_2E0,type,
    c_2Elist_2EisPREFIX_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Elist_2EisPREFIX_2E2,type,
    c_2Elist_2EisPREFIX_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Elist_2Elist__CASE_2E0,type,
    c_2Elist_2Elist__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b))) ).

tff(c_2Elist_2Elist__CASE_2E3,type,
    c_2Elist_2Elist__CASE_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)) ) > A_27b ) ).

tff(c_2Elist_2Elist__size_2E0,type,
    c_2Elist_2Elist__size_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)) ).

tff(c_2Elist_2Elist__size_2E2,type,
    c_2Elist_2Elist__size_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Enum_2Enum ) ).

tff(c_2Elist_2Enub_2E0,type,
    c_2Elist_2Enub_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).

tff(c_2Elist_2Enub_2E1,type,
    c_2Elist_2Enub_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).

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_2Elist_2EoEL_2E0,type,
    c_2Elist_2EoEL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))) ).

tff(c_2Elist_2EoEL_2E2,type,
    c_2Elist_2EoEL_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Elist_2EoHD_2E0,type,
    c_2Elist_2EoHD_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)) ).

tff(c_2Elist_2EoHD_2E1,type,
    c_2Elist_2EoHD_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Eone_2Eone_2E0,type,
    c_2Eone_2Eone_2E0: tyop_2Eone_2Eone ).

tff(c_2Eoption_2Eoption__CASE_2E0,type,
    c_2Eoption_2Eoption__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))) ).

tff(c_2Eoption_2Eoption__CASE_2E3,type,
    c_2Eoption_2Eoption__CASE_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) ) > A_27b ) ).

tff(c_2Elist_2EsplitAtPki_2E0,type,
    c_2Elist_2EsplitAtPki_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))) ).

tff(c_2Elist_2EsplitAtPki_2E2,type,
    c_2Elist_2EsplitAtPki_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)) ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a) ) ).

tff(c_2Elist_2EsplitAtPki_2E3,type,
    c_2Elist_2EsplitAtPki_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)) * tyop_2Elist_2Elist(A_27b) ) > A_27a ) ).

tff(c_2Erelation_2Etotal_2E0,type,
    c_2Erelation_2Etotal_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_2Etotal_2E1,type,
    c_2Erelation_2Etotal_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

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

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

tff(c_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(arityeq1_2Ec_2Earithmetic_2E_2B_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_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_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2E_2C_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2E_2C_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27d,axiom,
    ! [A_27a: $tType,A_27d: $tType,X0_2E0: A_27a,X1_2E0: A_27d] : ( c_2Epair_2E_2C_2E2(A_27a,A_27d,X0_2E0,X1_2E0) = app_2E2(A_27d,tyop_2Epair_2Eprod(A_27a,A_27d),app_2E2(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Epair_2E_2C_2E0(A_27a,A_27d),X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: A_27c,X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Epair_2E_2C_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29,axiom,
    ! [A_27a: $tType,A_27d: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27d)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(A_27c),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Elist_2Elist(A_27c),X1_2E0: tyop_2Elist_2Elist(A_27d)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,A_27a),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(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Emin_2E_3D_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_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(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Emin_2E_3D_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(tyop_2Enum_2Enum),X0_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_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_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_21_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E0(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(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)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_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_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EALL__DISTINCT_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Elist_2EALL__DISTINCT_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EAPPEND_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EAPPEND_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(A_27c),X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EAPPEND_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EAPPEND_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EAPPEND_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),c_2Elist_2EAPPEND_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EAPPEND_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EAPPEND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2EASSOC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27c),X0_2E0) ) ).

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

tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EC_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))] : ( c_2Ecombin_2EC_2E1(A_27a,A_27b,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EC_2E0(A_27a,A_27b,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EC_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Ecombin_2EC_2E1(A_27a,tyop_2Enum_2Enum,tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EC_2E0(A_27a,tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Ecombin_2EC_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EC_2E0(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a))] : ( c_2Ecombin_2EC_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EC_2E0(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECARD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECHOICE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Epred__set_2ECHOICE_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2ECOMM_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ebool_2ECOND_2E0(A_27a),X0_2E0),X1_2E0),X2_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_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(tyop_2Eone_2Eone),X2_2E0: tyop_2Elist_2Elist(tyop_2Eone_2Eone)] : ( c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone),app_2E2(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(tyop_2Eone_2Eone)),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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ECONS_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ECONS_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27d,axiom,
    ! [A_27d: $tType,X0_2E0: A_27d,X1_2E0: tyop_2Elist_2Elist(A_27d)] : ( c_2Elist_2ECONS_2E2(A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27d),app_2E2(A_27d,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27d)),c_2Elist_2ECONS_2E0(A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27e,axiom,
    ! [A_27e: $tType,X0_2E0: A_27e,X1_2E0: tyop_2Elist_2Elist(A_27e)] : ( c_2Elist_2ECONS_2E2(A_27e,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27e),app_2E2(A_27e,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27e)),c_2Elist_2ECONS_2E0(A_27e),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27f,axiom,
    ! [A_27f: $tType,X0_2E0: A_27f,X1_2E0: tyop_2Elist_2Elist(A_27f)] : ( c_2Elist_2ECONS_2E2(A_27f,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27f),tyop_2Elist_2Elist(A_27f),app_2E2(A_27f,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Elist_2Elist(A_27f)),c_2Elist_2ECONS_2E0(A_27f),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27g,axiom,
    ! [A_27g: $tType,X0_2E0: A_27g,X1_2E0: tyop_2Elist_2Elist(A_27g)] : ( c_2Elist_2ECONS_2E2(A_27g,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27g),tyop_2Elist_2Elist(A_27g),app_2E2(A_27g,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27g),tyop_2Elist_2Elist(A_27g)),c_2Elist_2ECONS_2E0(A_27g),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27h,axiom,
    ! [A_27h: $tType,X0_2E0: A_27h,X1_2E0: tyop_2Elist_2Elist(A_27h)] : ( c_2Elist_2ECONS_2E2(A_27h,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27h),tyop_2Elist_2Elist(A_27h),app_2E2(A_27h,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Elist_2Elist(A_27h)),c_2Elist_2ECONS_2E0(A_27h),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a))] : ( c_2Elist_2ECONS_2E2(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a))),c_2Elist_2ECONS_2E0(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27a_29_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a))] : ( c_2Elist_2ECONS_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a))),c_2Elist_2ECONS_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27c_2CA_27a_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27c_29_2Ctyop_2Emin_2Efun_28A_27b_2CA_27a_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))))] : ( c_2Elist_2ECONS_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))))),c_2Elist_2ECONS_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ECONS_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2ECONS_2E2(tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))),c_2Elist_2ECONS_2E0(tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(A_27c),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c))] : ( c_2Elist_2ECONS_2E2(tyop_2Elist_2Elist(A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c))),c_2Elist_2ECONS_2E0(tyop_2Elist_2Elist(A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2ECONS_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: tyop_2Eone_2Eone,X1_2E0: tyop_2Elist_2Elist(tyop_2Eone_2Eone)] : ( c_2Elist_2ECONS_2E2(tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone),app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),c_2Elist_2ECONS_2E0(tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ECONS_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Eind__type_2ECONSTR_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a))),c_2Eind__type_2ECONSTR_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E0(tyop_2Emin_2Ebool),X0_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_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDISJOINT_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EDISJOINT_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EDROP_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EDROP_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EDROP_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EDROP_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EDROP_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EDROP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EDROP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EEL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EEL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EEL_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),c_2Elist_2EEL_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EEL_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),A_27c,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27c),c_2Elist_2EEL_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EEL_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EEL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEVERY_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EEVERY_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EEVERY_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EEVERY_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERYi_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEVERYi_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EEVERYi_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEXISTS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EEXISTS_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EEXISTS_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),c_2Elist_2EEXISTS_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eind__type_2Erecspace(A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))),c_2Eind__type_2EFCONS_2E0(tyop_2Eind__type_2Erecspace(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFILTER_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EFILTER_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EFIND_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EFIND_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2EFIND_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_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFLAT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EFLAT_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c))] : ( c_2Elist_2EFLAT_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),tyop_2Elist_2Elist(A_27c),c_2Elist_2EFLAT_2E0(A_27c),X0_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EFOLDL_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),c_2Elist_2EFOLDL_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a))] : ( c_2Elist_2EFOLDL_2E3(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),A_27b)),c_2Elist_2EFOLDL_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),X1_2E0: A_27c,X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EFOLDL_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27c,app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27c),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27c)),c_2Elist_2EFOLDL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Elist_2EFOLDL_2E0(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EFOLDL_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Elist_2EFOLDL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),c_2Elist_2EFOLDL_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq4_2Ec_2Elist_2EFOLDL2_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X1_2E0: A_27a,X2_2E0: tyop_2Elist_2Elist(A_27b),X3_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EFOLDL2_2E4(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),A_27a,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a))),c_2Elist_2EFOLDL2_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq4_2Ec_2Elist_2EFOLDL2_2E4_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X1_2E0: A_27c,X2_2E0: tyop_2Elist_2Elist(A_27a),X3_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDL2_2E4(A_27c,A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27c,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27c)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27c))),c_2Elist_2EFOLDL2_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EFOLDR_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDR_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: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),c_2Elist_2EFOLDR_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),X1_2E0: tyop_2Elist_2Elist(A_27b),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EFOLDR_2E0(A_27a,tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EFRONT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFRONT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E0(A_27a),X0_2E0) ) ).

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

tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))] : ( c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),c_2Elist_2EGENLIST_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b)),c_2Elist_2EGENLIST_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EGENLIST_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EGENLIST_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EGENLIST__AUX_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EGENLIST__AUX_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EGENLIST__AUX_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

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

tff(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EHD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2EHD_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29,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)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = 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_2Epred__set_2EIMAGE_2E0(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),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_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2Elist_2EINDEX__FIND_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EINDEX__FIND_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),c_2Elist_2EINDEX__FIND_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EINDEX__FIND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EINDEX__FIND_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),c_2Elist_2EINDEX__FIND_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EINDEX__OF_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Elist_2EINDEX__OF_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Elist_2EINDEX__OF_2E0(A_27a),X0_2E0) ) ).

tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(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_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27b),X0_2E0),X1_2E0) ) ).

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

tff(arityeq3_2Ec_2Epred__set_2EITSET_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_2Emin_2Ebool),X2_2E0: A_27b] : ( c_2Epred__set_2EITSET_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_2Emin_2Ebool),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_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b)),c_2Epred__set_2EITSET_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Ecombin_2EK_2E1(A_27a,tyop_2Enum_2Enum,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EK_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))] : ( c_2Ecombin_2EK_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E0(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ecombin_2EK_2E1(tyop_2Elist_2Elist(A_27a),A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EK_2E0(tyop_2Elist_2Elist(A_27a),A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELAST_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELAST_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2ELAST_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELAST_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELAST_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2ELAST_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELEN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ELEN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elist_2ELEN_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELENGTH_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ELENGTH_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))] : ( c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Ebool_2ELET_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__APPLY_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ELIST__APPLY_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__APPLY_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),c_2Elist_2ELIST__APPLY_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ELIST__APPLY_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ELIST__APPLY_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a))] : ( c_2Elist_2ELIST__APPLY_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ELIST__APPLY_2E0(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2Elist_2ELIST__APPLY_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a))),c_2Elist_2ELIST__APPLY_2E0(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27c_29_2Ctyop_2Emin_2Efun_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a))] : ( c_2Elist_2ELIST__APPLY_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ELIST__APPLY_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELIST__BIND_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ELIST__BIND_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELIST__BIND_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ELIST__BIND_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(A_27c),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELIST__BIND_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ELIST__BIND_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(A_27c),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2ELIST__BIND_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ELIST__BIND_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELIST__BIND_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ELIST__BIND_2E0(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELIST__BIND_2E2(A_27a,tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ELIST__BIND_2E0(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__GUARD_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Elist_2ELIST__GUARD_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ELIST__GUARD_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__IGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__IGNORE__BIND_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ELIST__IGNORE__BIND_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__LIFT2_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: tyop_2Elist_2Elist(A_27b),X2_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ELIST__LIFT2_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__LIFT2_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_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_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_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_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27a,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27b),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__REL_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27c),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__REL_2E3(A_27c,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27c,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27c),X2_2E0: tyop_2Elist_2Elist(A_27d)] : ( c_2Elist_2ELIST__REL_2E3(A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27e_20mono_2EA_27f,axiom,
    ! [A_27e: $tType,A_27f: $tType,X0_2E0: tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27e),X2_2E0: tyop_2Elist_2Elist(A_27f)] : ( c_2Elist_2ELIST__REL_2E3(A_27e,A_27f,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27f),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27e),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27e,A_27f),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27g_20mono_2EA_27h,axiom,
    ! [A_27g: $tType,A_27h: $tType,X0_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27g),X2_2E0: tyop_2Elist_2Elist(A_27h)] : ( c_2Elist_2ELIST__REL_2E3(A_27g,A_27h,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27h),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27g),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27g),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27g,A_27h),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ELIST__TO__SET_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: A_27a] : ( c_2Elist_2ELIST__TO__SET_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELLEX_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Elist_2ELLEX_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E0(A_27a),X0_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELLEX_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_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELLEX_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq4_2Ec_2Elist_2ELRC_2E4_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_2Elist_2Elist(A_27a),X2_2E0: A_27a,X3_2E0: A_27a] : ( c_2Elist_2ELRC_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Elist_2ELRC_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELUPDATE_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELUPDATE_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELUPDATE_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ELUPDATE_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a))] : ( c_2Elist_2ELUPDATE_2E3(tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)))),c_2Elist_2ELUPDATE_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27b),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b))] : ( c_2Elist_2ELUPDATE_2E3(tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b))),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)))),c_2Elist_2ELUPDATE_2E0(tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Elist_2EMAP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c)] : ( c_2Elist_2EMAP_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E0(A_27a,A_27c),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EMAP_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Elist_2EMAP_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(A_27b,A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_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_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c)] : ( c_2Elist_2EMAP_2E1(A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E0(A_27b,A_27c),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d)),c_2Elist_2EMAP_2E0(A_27b,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a))),c_2Elist_2EMAP_2E0(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP_2E2(A_27b,tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0(A_27b,tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP_2E2(A_27b,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EMAP_2E0(A_27b,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EMAP_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EMAP_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Elist_2EMAP_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EMAP_2E0(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27d),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27d)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27d_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d))),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP2_2E3(A_27c,A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EMAP2_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: tyop_2Elist_2Elist(A_27b),X2_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EMAP2_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP2_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27f_20mono_2EA_27d_20mono_2EA_27e,axiom,
    ! [A_27d: $tType,A_27e: $tType,A_27f: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),X1_2E0: tyop_2Elist_2Elist(A_27d),X2_2E0: tyop_2Elist_2Elist(A_27e)] : ( c_2Elist_2EMAP2_2E3(A_27f,A_27d,A_27e,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27f),app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27f)),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27f))),c_2Elist_2EMAP2_2E0(A_27f,A_27d,A_27e),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2EMIN_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMIN_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_2EMIN_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq4_2Ec_2Earithmetic_2ENRC_2E4_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_2Enum_2Enum,X2_2E0: A_27a,X3_2E0: A_27a] : ( c_2Earithmetic_2ENRC_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Earithmetic_2ENRC_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ENULL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ENULL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E0(A_27a),X0_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(arityeq1_2Ec_2Ewhile_2EOLEAST_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ewhile_2EOLEAST_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( c_2Eoption_2EOPTION__BIND_2E2(tyop_2Elist_2Elist(A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Eoption_2EOPTION__BIND_2E0(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( c_2Eoption_2EOPTION__BIND_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Eoption_2EOPTION__BIND_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Eoption_2EOPTION__MAP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a)] : ( c_2Eoption_2EOPTION__MAP_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum)] : ( c_2Eoption_2EOPTION__MAP_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EOPT__MMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EOPT__MMAP_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b))),c_2Elist_2EOPT__MMAP_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EOPT__MMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EOPT__MMAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Elist_2EOPT__MMAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EPAD__LEFT_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EPAD__LEFT_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EPAD__LEFT_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EPAD__RIGHT_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EPAD__RIGHT_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EPAD__RIGHT_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2EPRE_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2ERC_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_2ERC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2ERC_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERC_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EREST_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EREV_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREV_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREV_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EREVERSE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EREVERSE_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ESET__TO__LIST_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2ESET__TO__LIST_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ESHORTLEX_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Elist_2ESHORTLEX_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E0(A_27a),X0_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2ESHORTLEX_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_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ESHORTLEX_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

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

tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))] : ( c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ESNOC_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ESNOC_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ESNOC_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ESNOC_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ESNOC_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2ESNOC_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

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

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b] : ( c_2Eoption_2ESOME_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ESUM_2E1,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ESUM_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Elist_2ESUM_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ESUM__ACC_2E2,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ESUM__ACC_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elist_2ESUM__ACC_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ESUM__IMAGE_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ETAKE_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ETAKE_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ETAKE_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ETAKE_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2ETAKE_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ETL_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),c_2Elist_2ETL_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Emin_2Ebool),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2EUNCURRY_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,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_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2EUNCURRY_2E2(A_27a,A_27b,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Epair_2EUNCURRY_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),X0_2E0) ) ).

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

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

tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EUNIQUE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EUNIQUE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EUNIQUE_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EUNZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EUNZIP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E0(A_27a,A_27b),X0_2E0) ) ).

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

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),c_2Erelation_2EWFREC_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EZIP_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Elist_2EZIP_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EZIP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27d,axiom,
    ! [A_27a: $tType,A_27d: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d))] : ( c_2Elist_2EZIP_2E1(A_27a,A_27d,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EZIP_2E0(A_27a,A_27d),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EZIP_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Elist_2EZIP_2E0(A_27b,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EZIP_2E1(A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Elist_2EZIP_2E0(A_27c,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d))] : ( c_2Elist_2EZIP_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2EZIP_2E0(A_27c,A_27d),X0_2E0) ) ).

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

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

tff(arityeq1_2Ec_2Elist_2EdropWhile_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EdropWhile_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EdropWhile_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EdropWhile_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EdropWhile_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EdropWhile_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EisPREFIX_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EisPREFIX_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EisPREFIX_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))] : ( c_2Elist_2Elist__CASE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b)),c_2Elist_2Elist__CASE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Elist_2Elist__CASE_2E3(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Elist_2Elist__CASE_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)))] : ( c_2Elist_2Elist__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2Elist__CASE_2E0(A_27a,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2Elist__size_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2Elist__size_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2Elist__size_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2Enub_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2Enub_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a)] : ( c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),c_2Ecombin_2Eo_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,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_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a),X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b)] : ( c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d)),c_2Ecombin_2Eo_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27c,tyop_2Elist_2Elist(A_27a),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2Eo_2E0(A_27c,tyop_2Elist_2Elist(A_27a),A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))] : ( c_2Ecombin_2Eo_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),c_2Ecombin_2Eo_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b))] : ( c_2Ecombin_2Eo_2E2(A_27c,tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2Eo_2E0(A_27c,tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b))] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))] : ( c_2Ecombin_2Eo_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c))),c_2Ecombin_2Eo_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27c_29,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c))] : ( c_2Ecombin_2Eo_2E2(A_27b,tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c))),c_2Ecombin_2Eo_2E0(A_27b,tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28A_27c_29,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c))] : ( c_2Ecombin_2Eo_2E2(A_27b,tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),c_2Ecombin_2Eo_2E0(A_27b,tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),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_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))] : ( c_2Ecombin_2Eo_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Ecombin_2Eo_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))] : ( c_2Ecombin_2Eo_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Ecombin_2Eo_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EoEL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EoEL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2EoEL_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EoHD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EoHD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoHD_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EoHD_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EoHD_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27b),c_2Elist_2EoHD_2E0(A_27b),X0_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a),app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a)),c_2Eoption_2Eoption__CASE_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EsplitAtPki_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EsplitAtPki_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),c_2Elist_2EsplitAtPki_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EsplitAtPki_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))] : ( c_2Elist_2EsplitAtPki_2E2(tyop_2Elist_2Elist(A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EsplitAtPki_2E0(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EsplitAtPki_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EsplitAtPki_2E3(tyop_2Elist_2Elist(A_27a),A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EsplitAtPki_2E0(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EsplitAtPki_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EsplitAtPki_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Elist_2EsplitAtPki_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2Etotal_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_2Etotal_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_2Etotal_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etotal_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E0(tyop_2Elist_2Elist(A_27a)),X0_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_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E0(tyop_2Elist_2Elist(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_2Elist_2ESUM__ACC__DEF,axiom,
    ( ! [V0acc_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ESUM__ACC_2E2(c_2Elist_2ENIL_2E0(tyop_2Enum_2Enum),V0acc_2E0) = V0acc_2E0 )
    & ! [V1h_2E0: tyop_2Enum_2Enum,V2t_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),V3acc_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ESUM__ACC_2E2(c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,V1h_2E0,V2t_2E0),V3acc_2E0) = c_2Elist_2ESUM__ACC_2E2(V2t_2E0,c_2Earithmetic_2E_2B_2E2(V1h_2E0,V3acc_2E0)) ) ) ).

tff(thm_2Elist_2EREV__DEF,axiom,
    ! [A_27a: $tType] :
      ( ! [V0acc_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREV_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V0acc_2E0) = V0acc_2E0 )
      & ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Elist_2Elist(A_27a),V3acc_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREV_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V2t_2E0),V3acc_2E0) = c_2Elist_2EREV_2E2(A_27a,V2t_2E0,c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V3acc_2E0)) ) ) ).

tff(thm_2Elist_2ELEN__DEF,axiom,
    ! [A_27a: $tType] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ELEN_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V0n_2E0) = V0n_2E0 )
      & ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Elist_2Elist(A_27a),V3n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ELEN_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V2t_2E0),V3n_2E0) = c_2Elist_2ELEN_2E2(A_27a,V2t_2E0,c_2Earithmetic_2E_2B_2E2(V3n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ) ).

tff(thm_2Elist_2EPAD__RIGHT,axiom,
    ! [A_27a: $tType,V0c_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum,V2s_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EPAD__RIGHT_2E3(A_27a,V0c_2E0,V1n_2E0,V2s_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,V2s_2E0,c_2Elist_2EGENLIST_2E2(A_27a,c_2Ecombin_2EK_2E1(A_27a,tyop_2Enum_2Enum,V0c_2E0),c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V2s_2E0)))) ) ).

tff(thm_2Elist_2EPAD__LEFT,axiom,
    ! [A_27a: $tType,V0c_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum,V2s_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EPAD__LEFT_2E3(A_27a,V0c_2E0,V1n_2E0,V2s_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EGENLIST_2E2(A_27a,c_2Ecombin_2EK_2E1(A_27a,tyop_2Enum_2Enum,V0c_2E0),c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V2s_2E0))),V2s_2E0) ) ).

tff(thm_2Elist_2EGENLIST__AUX,axiom,
    ! [A_27a: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EGENLIST__AUX_2E3(A_27a,V0f_2E0,c_2Enum_2E0_2E0,V1l_2E0) = V1l_2E0 )
      & ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3n_2E0: tyop_2Enum_2Enum,V4l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EGENLIST__AUX_2E3(A_27a,V2f_2E0,c_2Enum_2ESUC_2E1(V3n_2E0),V4l_2E0) = c_2Elist_2EGENLIST__AUX_2E3(A_27a,V2f_2E0,V3n_2E0,c_2Elist_2ECONS_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V2f_2E0,V3n_2E0),V4l_2E0)) ) ) ).

tff(thm_2Elist_2EGENLIST,axiom,
    ! [A_27a: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Elist_2EGENLIST_2E2(A_27a,V0f_2E0,c_2Enum_2E0_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,c_2Enum_2ESUC_2E1(V2n_2E0)) = c_2Elist_2ESNOC_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V2n_2E0),c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,V2n_2E0)) ) ) ).

tff(thm_2Elist_2ESNOC,axiom,
    ! [A_27a: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)) )
      & ! [V1x_2E0: A_27a,V2x_27_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_27_2E0,V3l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V2x_27_2E0,c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V3l_2E0)) ) ) ).

tff(thm_2Elist_2EisPREFIX,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))] :
      ( ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Elist_2Elist(A_27a),V4h_27_2E0: A_27a,V5t_27_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),F0_2E0,V1h_2E0),V2t_2E0),V4h_27_2E0),V5t_27_2E0))
        <=> ( ( V1h_2E0 = V4h_27_2E0 )
            & p(c_2Elist_2EisPREFIX_2E2(A_27a,V2t_2E0,V5t_27_2E0)) ) )
     => ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V0l_2E0) = c_2Ebool_2ET_2E0 )
        & ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Elist_2Elist(A_27a),V3l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V2t_2E0),V3l_2E0) = c_2Elist_2Elist__CASE_2E3(A_27a,tyop_2Emin_2Ebool,V3l_2E0,c_2Ebool_2EF_2E0,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),F0_2E0,V1h_2E0),V2t_2E0)) ) ) ) ).

tff(thm_2Elist_2ESET__TO__LIST__primitive__def,axiom,
    ! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
      ( ! [V3a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F2_2E0,V3a_2E0))
        <=> ( V3a_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
     => ( ! [V2SET__TO__LIST_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),V3a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),F1_2E0,V2SET__TO__LIST_2E0),V3a_2E0) = c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),c_2Epred__set_2EFINITE_2E1(A_27a,V3a_2E0),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F2_2E0,V3a_2E0),c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,c_2Epred__set_2ECHOICE_2E1(A_27a,V3a_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a),V2SET__TO__LIST_2E0,c_2Epred__set_2EREST_2E1(A_27a,V3a_2E0)))),c_2Ebool_2EARB_2E0(tyop_2Elist_2Elist(A_27a)))) )
       => ( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
              ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0))
            <=> ( p(c_2Erelation_2EWF_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0))
                & ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                    ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
                      & ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
                   => p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0R_2E0,c_2Epred__set_2EREST_2E1(A_27a,V1s_2E0)),V1s_2E0)) ) ) )
         => ( c_2Elist_2ESET__TO__LIST_2E0(A_27a) = c_2Erelation_2EWFREC_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a),c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ).

tff(thm_2Elist_2ELRC__def,axiom,
    ! [A_27a: $tType] :
      ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
          ( p(c_2Elist_2ELRC_2E4(A_27a,V0R_2E0,c_2Elist_2ENIL_2E0(A_27a),V1x_2E0,V2y_2E0))
        <=> ( V1x_2E0 = V2y_2E0 ) )
      & ! [V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4h_2E0: A_27a,V5t_2E0: tyop_2Elist_2Elist(A_27a),V6x_2E0: A_27a,V7y_2E0: A_27a] :
          ( p(c_2Elist_2ELRC_2E4(A_27a,V3R_2E0,c_2Elist_2ECONS_2E2(A_27a,V4h_2E0,V5t_2E0),V6x_2E0,V7y_2E0))
        <=> ( ( V6x_2E0 = V4h_2E0 )
            & ? [V8z_2E0: A_27a] :
                ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3R_2E0,V6x_2E0),V8z_2E0))
                & p(c_2Elist_2ELRC_2E4(A_27a,V3R_2E0,V5t_2E0,V8z_2E0,V7y_2E0)) ) ) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT,axiom,
    ! [A_27a: $tType] :
      ( ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
      & ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0)))
        <=> ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V0h_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1t_2E0)))
            & p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V1t_2E0)) ) ) ) ).

tff(thm_2Elist_2EDROP__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V1n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1n_2E0))
        <=> ( V1n_2E0 = c_2Enum_2E0_2E0 ) )
     => ( ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
        & ! [V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a,V3xs_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3xs_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1n_2E0),c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3xs_2E0),c_2Elist_2EDROP_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V3xs_2E0)) ) ) ) ).

tff(thm_2Elist_2ETAKE__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V1n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1n_2E0))
        <=> ( V1n_2E0 = c_2Enum_2E0_2E0 ) )
     => ( ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
        & ! [V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a,V3xs_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,V1n_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3xs_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1n_2E0),c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Elist_2ETAKE_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V3xs_2E0))) ) ) ) ).

tff(thm_2Elist_2EFRONT__DEF,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
      ( ! [V1t_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1t_2E0))
        <=> ( V1t_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
     => ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1t_2E0),c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,c_2Elist_2EFRONT_2E1(A_27a,V1t_2E0))) ) ) ).

tff(thm_2Elist_2ELAST__DEF,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
      ( ! [V1t_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1t_2E0))
        <=> ( V1t_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
     => ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0)) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1t_2E0),V0h_2E0,c_2Elist_2ELAST_2E1(A_27a,V1t_2E0)) ) ) ).

tff(thm_2Elist_2EREVERSE__DEF,axiom,
    ! [A_27a: $tType] :
      ( ( c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V1t_2E0),c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,c_2Elist_2ENIL_2E0(A_27a))) ) ) ).

tff(thm_2Elist_2EUNZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ( c_2Elist_2EUNZIP_2E1(A_27a,A_27b,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27b)) )
      & ! [V0x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EUNZIP_2E1(A_27a,A_27b,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0,V1l_2E0)) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(A_27a,c_2Epair_2EFST_2E1(A_27a,A_27b,V0x_2E0),c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EUNZIP_2E1(A_27a,A_27b,V1l_2E0))),c_2Elist_2ECONS_2E2(A_27b,c_2Epair_2ESND_2E1(A_27a,A_27b,V0x_2E0),c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EUNZIP_2E1(A_27a,A_27b,V1l_2E0)))) ) ) ).

tff(thm_2Elist_2EZIP__def,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0l2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0(A_27a),V0l2_2E0)) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
      & ! [V1l1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V1l1_2E0,c_2Elist_2ENIL_2E0(A_27b))) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
      & ! [V2x1_2E0: A_27a,V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4x2_2E0: A_27b,V5l2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(A_27a,V2x1_2E0,V3l1_2E0),c_2Elist_2ECONS_2E2(A_27b,V4x2_2E0,V5l2_2E0))) = c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x1_2E0,V4x2_2E0),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V3l1_2E0,V5l2_2E0))) ) ) ).

tff(thm_2Elist_2Elist__size__def,axiom,
    ! [A_27a: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Elist_2Elist__size_2E2(A_27a,V0f_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Enum_2E0_2E0 )
      & ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a0_2E0: A_27a,V3a1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2Elist__size_2E2(A_27a,V1f_2E0,c_2Elist_2ECONS_2E2(A_27a,V2a0_2E0,V3a1_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V2a0_2E0),c_2Elist_2Elist__size_2E2(A_27a,V1f_2E0,V3a1_2E0))) ) ) ).

tff(thm_2Elist_2Elist__case__def,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0v_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))] : ( c_2Elist_2Elist__CASE_2E3(A_27a,A_27b,c_2Elist_2ENIL_2E0(A_27a),V0v_2E0,V1f_2E0) = V0v_2E0 )
      & ! [V2a0_2E0: A_27a,V3a1_2E0: tyop_2Elist_2Elist(A_27a),V4v_2E0: A_27b,V5f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))] : ( c_2Elist_2Elist__CASE_2E3(A_27a,A_27b,c_2Elist_2ECONS_2E2(A_27a,V2a0_2E0,V3a1_2E0),V4v_2E0,V5f_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V5f_2E0,V2a0_2E0),V3a1_2E0) ) ) ).

tff(thm_2Elist_2Elist__TY__DEF,axiom,
    ! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
      ( ! [V7n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F2_2E0,V7n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
     => ( ! [V4n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F1_2E0,V4n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
       => ( ! [V1a0_27_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
              ( p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1a0_27_2E0))
            <=> ! [V2_27list_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
                  ( ! [V3a0_27_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
                      ( ( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2E0_2E0,c_2Ebool_2EARB_2E0(A_27a),F1_2E0) )
                        | ? [V5a0_2E0: A_27a,V6a1_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
                            ( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0),V5a0_2E0,c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),V6a1_2E0,F2_2E0)) )
                            & p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27list_27_2E0,V6a1_2E0)) ) )
                     => p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27list_27_2E0,V3a0_27_2E0)) )
                 => p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27list_27_2E0,V1a0_27_2E0)) ) )
         => ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Elist_2Elist(A_27a),F0_2E0,V0rep_2E0)) ) ) ) ).

tff(thm_2Elist_2ENULL__DEF,axiom,
    ! [A_27a: $tType] :
      ( ( c_2Elist_2ENULL_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
      & ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ENULL_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0)) = c_2Ebool_2EF_2E0 ) ) ).

tff(thm_2Elist_2EHD,axiom,
    ! [A_27a: $tType,V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EHD_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0)) = V0h_2E0 ) ).

tff(thm_2Elist_2ETL__DEF,axiom,
    ! [A_27a: $tType] :
      ( ( c_2Elist_2ETL_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETL_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0)) = V1t_2E0 ) ) ).

tff(thm_2Elist_2ESUM,axiom,
    ( ( c_2Elist_2ESUM_2E1(c_2Elist_2ENIL_2E0(tyop_2Enum_2Enum)) = c_2Enum_2E0_2E0 )
    & ! [V0h_2E0: tyop_2Enum_2Enum,V1t_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ESUM_2E1(c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,V0h_2E0,V1t_2E0)) = c_2Earithmetic_2E_2B_2E2(V0h_2E0,c_2Elist_2ESUM_2E1(V1t_2E0)) ) ) ).

tff(thm_2Elist_2EAPPEND,axiom,
    ! [A_27a: $tType] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V0l_2E0) = V0l_2E0 )
      & ! [V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3h_2E0: A_27a] : ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,V1l1_2E0),V2l2_2E0) = c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)) ) ) ).

tff(thm_2Elist_2EFLAT,axiom,
    ! [A_27a: $tType] :
      ( ( c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2ENIL_2E0(tyop_2Elist_2Elist(A_27a))) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V0h_2E0: tyop_2Elist_2Elist(A_27a),V1t_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2ECONS_2E2(tyop_2Elist_2Elist(A_27a),V0h_2E0,V1t_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,V0h_2E0,c_2Elist_2EFLAT_2E1(A_27a,V1t_2E0)) ) ) ).

tff(thm_2Elist_2ELENGTH,axiom,
    ! [A_27a: $tType] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Enum_2E0_2E0 )
      & ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0)) = c_2Enum_2ESUC_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V1t_2E0)) ) ) ).

tff(thm_2Elist_2EMAP,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27b) )
      & ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0)) = c_2Elist_2ECONS_2E2(A_27b,app_2E2(A_27a,A_27b,V1f_2E0,V2h_2E0),c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,V3t_2E0)) ) ) ).

tff(thm_2Elist_2ELIST__TO__SET__DEF,axiom,
    ! [A_27a: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Elist_2ELIST__TO__SET_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V0x_2E0) = c_2Ebool_2EF_2E0 )
      & ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Elist_2Elist(A_27a),V3x_2E0: A_27a] :
          ( p(c_2Elist_2ELIST__TO__SET_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V2t_2E0),V3x_2E0))
        <=> ( ( V3x_2E0 = V1h_2E0 )
            | p(c_2Elist_2ELIST__TO__SET_2E2(A_27a,V2t_2E0,V3x_2E0)) ) ) ) ).

tff(thm_2Elist_2EFILTER,axiom,
    ! [A_27a: $tType] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2h_2E0),c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,V3t_2E0)),c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,V3t_2E0)) ) ) ).

tff(thm_2Elist_2EFOLDR,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27b] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,c_2Elist_2ENIL_2E0(A_27a)) = V1e_2E0 )
      & ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3e_2E0: A_27b,V4x_2E0: A_27a,V5l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V2f_2E0,V3e_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,V5l_2E0)) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V2f_2E0,V4x_2E0),c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V2f_2E0,V3e_2E0,V5l_2E0)) ) ) ).

tff(thm_2Elist_2EFOLDL,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V1e_2E0: A_27b] : ( c_2Elist_2EFOLDL_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,c_2Elist_2ENIL_2E0(A_27a)) = V1e_2E0 )
      & ! [V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V3e_2E0: A_27b,V4x_2E0: A_27a,V5l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,A_27b,V2f_2E0,V3e_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,V5l_2E0)) = c_2Elist_2EFOLDL_2E3(A_27a,A_27b,V2f_2E0,app_2E2(A_27a,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,V3e_2E0),V4x_2E0),V5l_2E0) ) ) ).

tff(thm_2Elist_2EEVERY__DEF,axiom,
    ! [A_27a: $tType] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
      & ! [V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Elist_2EEVERY_2E2(A_27a,V1P_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0)))
        <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2h_2E0))
            & p(c_2Elist_2EEVERY_2E2(A_27a,V1P_2E0,V3t_2E0)) ) ) ) ).

tff(thm_2Elist_2EEXISTS__DEF,axiom,
    ! [A_27a: $tType] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2EF_2E0 )
      & ! [V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Elist_2EEXISTS_2E2(A_27a,V1P_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0)))
        <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2h_2E0))
            | p(c_2Elist_2EEXISTS_2E2(A_27a,V1P_2E0,V3t_2E0)) ) ) ) ).

tff(thm_2Elist_2EEL,axiom,
    ! [A_27a: $tType] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEL_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = c_2Elist_2EHD_2E1(A_27a,V0l_2E0) )
      & ! [V1l_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EEL_2E2(A_27a,c_2Enum_2ESUC_2E1(V2n_2E0),V1l_2E0) = c_2Elist_2EEL_2E2(A_27a,V2n_2E0,c_2Elist_2ETL_2E1(A_27a,V1l_2E0)) ) ) ).

tff(thm_2Elist_2EINDEX__FIND__def,axiom,
    ! [A_27a: $tType] :
      ( ! [V0i_2E0: tyop_2Enum_2Enum,V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EINDEX__FIND_2E3(A_27a,V0i_2E0,V1P_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)) )
      & ! [V2i_2E0: tyop_2Enum_2Enum,V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4h_2E0: A_27a,V5t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EINDEX__FIND_2E3(A_27a,V2i_2E0,V3P_2E0,c_2Elist_2ECONS_2E2(A_27a,V4h_2E0,V5t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_2E0,V4h_2E0),c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,V4h_2E0)),c_2Elist_2EINDEX__FIND_2E3(A_27a,c_2Enum_2ESUC_2E1(V2i_2E0),V3P_2E0,V5t_2E0)) ) ) ).

tff(thm_2Elist_2EFIND__def,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EFIND_2E1(A_27a,V0P_2E0) = c_2Ecombin_2Eo_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2EOPTION__MAP_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a,c_2Epair_2ESND_2E0(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E2(A_27a,c_2Enum_2E0_2E0,V0P_2E0)) ) ).

tff(thm_2Elist_2EINDEX__OF__def,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Elist_2EINDEX__OF_2E1(A_27a,V0x_2E0) = c_2Ecombin_2Eo_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2EOPTION__MAP_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum,c_2Epair_2EFST_2E0(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E2(A_27a,c_2Enum_2E0_2E0,c_2Emin_2E_3D_2E1(A_27a,V0x_2E0))) ) ).

tff(thm_2Elist_2ELUPDATE__def,axiom,
    ! [A_27a: $tType] :
      ( ! [V0e_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ELUPDATE_2E3(A_27a,V0e_2E0,V1n_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V2e_2E0: A_27a,V3x_2E0: A_27a,V4l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELUPDATE_2E3(A_27a,V2e_2E0,c_2Enum_2E0_2E0,c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V4l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V2e_2E0,V4l_2E0) )
      & ! [V5e_2E0: A_27a,V6n_2E0: tyop_2Enum_2Enum,V7x_2E0: A_27a,V8l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELUPDATE_2E3(A_27a,V5e_2E0,c_2Enum_2ESUC_2E1(V6n_2E0),c_2Elist_2ECONS_2E2(A_27a,V7x_2E0,V8l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V7x_2E0,c_2Elist_2ELUPDATE_2E3(A_27a,V5e_2E0,V6n_2E0,V8l_2E0)) ) ) ).

tff(thm_2Elist_2EEVERYi__def,axiom,
    ! [A_27a: $tType] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Elist_2EEVERYi_2E2(A_27a,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
      & ! [V1P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Elist_2EEVERYi_2E2(A_27a,V1P_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0)))
        <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,c_2Enum_2E0_2E0),V2h_2E0))
            & p(c_2Elist_2EEVERYi_2E2(A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,V1P_2E0,c_2Enum_2ESUC_2E0),V3t_2E0)) ) ) ) ).

tff(thm_2Elist_2EsplitAtPki__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))))] :
      ( ! [V3k_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V4h_2E0: A_27b,V6p_2E0: tyop_2Elist_2Elist(A_27b),V7s_2E0: tyop_2Elist_2Elist(A_27b)] : ( app_2E2(tyop_2Elist_2Elist(A_27b),A_27a,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))),F0_2E0,V3k_2E0),V4h_2E0),V6p_2E0),V7s_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27a,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),V3k_2E0,c_2Elist_2ECONS_2E2(A_27b,V4h_2E0,V6p_2E0)),V7s_2E0) )
     => ( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1k_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))] : ( c_2Elist_2EsplitAtPki_2E3(A_27a,A_27b,V0P_2E0,V1k_2E0,c_2Elist_2ENIL_2E0(A_27b)) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27a,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),V1k_2E0,c_2Elist_2ENIL_2E0(A_27b)),c_2Elist_2ENIL_2E0(A_27b)) )
        & ! [V2P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3k_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V4h_2E0: A_27b,V5t_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EsplitAtPki_2E3(A_27a,A_27b,V2P_2E0,V3k_2E0,c_2Elist_2ECONS_2E2(A_27b,V4h_2E0,V5t_2E0)) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0,c_2Enum_2E0_2E0),V4h_2E0),app_2E2(tyop_2Elist_2Elist(A_27b),A_27a,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),V3k_2E0,c_2Elist_2ENIL_2E0(A_27b)),c_2Elist_2ECONS_2E2(A_27b,V4h_2E0,V5t_2E0)),c_2Elist_2EsplitAtPki_2E3(A_27a,A_27b,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,V2P_2E0,c_2Enum_2ESUC_2E0),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))),F0_2E0,V3k_2E0),V4h_2E0),V5t_2E0)) ) ) ) ).

tff(thm_2Elist_2ELIST__BIND__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27b),V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELIST__BIND_2E2(A_27a,A_27b,V0l_2E0,V1f_2E0) = c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2EMAP_2E2(A_27b,tyop_2Elist_2Elist(A_27a),V1f_2E0,V0l_2E0)) ) ).

tff(thm_2Elist_2ELIST__IGNORE__BIND__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0m1_2E0: tyop_2Elist_2Elist(A_27b),V1m2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__IGNORE__BIND_2E2(A_27a,A_27b,V0m1_2E0,V1m2_2E0) = c_2Elist_2ELIST__BIND_2E2(A_27a,A_27b,V0m1_2E0,c_2Ecombin_2EK_2E1(tyop_2Elist_2Elist(A_27a),A_27b,V1m2_2E0)) ) ).

tff(thm_2Elist_2ELIST__GUARD__def,axiom,
    ! [V0b_2E0: tyop_2Emin_2Ebool] : ( c_2Elist_2ELIST__GUARD_2E1(V0b_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Eone_2Eone),V0b_2E0,c_2Elist_2ECONS_2E2(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0,c_2Elist_2ENIL_2E0(tyop_2Eone_2Eone)),c_2Elist_2ENIL_2E0(tyop_2Eone_2Eone)) ) ).

tff(thm_2Elist_2ELIST__APPLY__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0fs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),V1xs_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__APPLY_2E2(A_27a,A_27b,V0fs_2E0,V1xs_2E0) = c_2Elist_2ELIST__BIND_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0fs_2E0,c_2Ecombin_2EC_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E0(A_27b,A_27a),V1xs_2E0)) ) ).

tff(thm_2Elist_2ELIST__LIFT2__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1xs_2E0: tyop_2Elist_2Elist(A_27b),V2ys_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ELIST__LIFT2_2E3(A_27a,A_27b,A_27c,V0f_2E0,V1xs_2E0,V2ys_2E0) = c_2Elist_2ELIST__APPLY_2E2(A_27a,A_27c,c_2Elist_2EMAP_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),V0f_2E0,V1xs_2E0),V2ys_2E0) ) ).

tff(thm_2Elist_2ESHORTLEX__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),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_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))))] :
      ( ! [V4t1_2E0: tyop_2Elist_2Elist(A_27a),V7t2_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F1_2E0,V4t1_2E0),V7t2_2E0))
        <=> ( c_2Elist_2ELENGTH_2E1(A_27a,V4t1_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V7t2_2E0) ) )
     => ( ! [V3h1_2E0: A_27a,V6h2_2E0: A_27a] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F2_2E0,V3h1_2E0),V6h2_2E0))
          <=> ( V3h1_2E0 = V6h2_2E0 ) )
       => ( ! [V4t1_2E0: tyop_2Elist_2Elist(A_27a),V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3h1_2E0: A_27a,V6h2_2E0: A_27a,V7t2_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(A_27a),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_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),F0_2E0,V4t1_2E0),V2R_2E0),V3h1_2E0),V6h2_2E0),V7t2_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V4t1_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V7t2_2E0)),c_2Ebool_2ET_2E0,c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F1_2E0,V4t1_2E0),V7t2_2E0),c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V3h1_2E0),V6h2_2E0),c_2Ebool_2ET_2E0,c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F2_2E0,V3h1_2E0),V6h2_2E0),c_2Elist_2ESHORTLEX_2E3(A_27a,V2R_2E0,V4t1_2E0,V7t2_2E0),c_2Ebool_2EF_2E0)),c_2Ebool_2EF_2E0)) )
         => ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
                ( p(c_2Elist_2ESHORTLEX_2E3(A_27a,V0R_2E0,c_2Elist_2ENIL_2E0(A_27a),V1l2_2E0))
              <=> ( V1l2_2E0 != c_2Elist_2ENIL_2E0(A_27a) ) )
            & ! [V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3h1_2E0: A_27a,V4t1_2E0: tyop_2Elist_2Elist(A_27a),V5l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ESHORTLEX_2E3(A_27a,V2R_2E0,c_2Elist_2ECONS_2E2(A_27a,V3h1_2E0,V4t1_2E0),V5l2_2E0) = c_2Elist_2Elist__CASE_2E3(A_27a,tyop_2Emin_2Ebool,V5l2_2E0,c_2Ebool_2EF_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(A_27a),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_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),F0_2E0,V4t1_2E0),V2R_2E0),V3h1_2E0)) ) ) ) ) ) ).

tff(thm_2Elist_2ELLEX__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))))] :
      ( ! [V3h1_2E0: A_27a,V6h2_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V3h1_2E0),V6h2_2E0))
        <=> ( V3h1_2E0 = V6h2_2E0 ) )
     => ( ! [V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3h1_2E0: A_27a,V4t1_2E0: tyop_2Elist_2Elist(A_27a),V6h2_2E0: A_27a,V7t2_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),F0_2E0,V2R_2E0),V3h1_2E0),V4t1_2E0),V6h2_2E0),V7t2_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V3h1_2E0),V6h2_2E0),c_2Ebool_2ET_2E0,c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V3h1_2E0),V6h2_2E0),c_2Elist_2ELLEX_2E3(A_27a,V2R_2E0,V4t1_2E0,V7t2_2E0),c_2Ebool_2EF_2E0)) )
       => ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
              ( p(c_2Elist_2ELLEX_2E3(A_27a,V0R_2E0,c_2Elist_2ENIL_2E0(A_27a),V1l2_2E0))
            <=> ( V1l2_2E0 != c_2Elist_2ENIL_2E0(A_27a) ) )
          & ! [V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3h1_2E0: A_27a,V4t1_2E0: tyop_2Elist_2Elist(A_27a),V5l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELLEX_2E3(A_27a,V2R_2E0,c_2Elist_2ECONS_2E2(A_27a,V3h1_2E0,V4t1_2E0),V5l2_2E0) = c_2Elist_2Elist__CASE_2E3(A_27a,tyop_2Emin_2Ebool,V5l2_2E0,c_2Ebool_2EF_2E0,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),F0_2E0,V2R_2E0),V3h1_2E0),V4t1_2E0)) ) ) ) ) ).

tff(thm_2Elist_2Enub__def,axiom,
    ! [A_27a: $tType] :
      ( ( c_2Elist_2Enub_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2Enub_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1l_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)),c_2Elist_2Enub_2E1(A_27a,V1l_2E0),c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2Enub_2E1(A_27a,V1l_2E0))) ) ) ).

tff(thm_2Elist_2EdropWhile__def,axiom,
    ! [A_27a: $tType] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EdropWhile_2E2(A_27a,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EdropWhile_2E2(A_27a,V1P_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2h_2E0),c_2Elist_2EdropWhile_2E2(A_27a,V1P_2E0,V3t_2E0),c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0)) ) ) ).

tff(thm_2Elist_2EUNIQUE__DEF,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1L_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EUNIQUE_2E2(A_27a,V0e_2E0,V1L_2E0))
    <=> ? [V2L1_2E0: tyop_2Elist_2Elist(A_27a),V3L2_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2L1_2E0,c_2Elist_2ECONS_2E2(A_27a,V0e_2E0,c_2Elist_2ENIL_2E0(A_27a))),V3L2_2E0) = V1L_2E0 )
          & ~ p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2L1_2E0)))
          & ~ p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V3L2_2E0))) ) ) ).

tff(thm_2Elist_2EOPT__MMAP__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))))] :
      ( ! [V4h_2E0: A_27a,V5t_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),F1_2E0,V4h_2E0),V5t_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(A_27a,V4h_2E0,V5t_2E0)) )
     => ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V3t0_2E0: tyop_2Elist_2Elist(A_27b),V4h_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F0_2E0,V1f_2E0),V3t0_2E0),V4h_2E0) = c_2Eoption_2EOPTION__BIND_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EOPT__MMAP_2E2(A_27a,A_27b,V1f_2E0,V3t0_2E0),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),F1_2E0,V4h_2E0)) )
       => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))] : ( c_2Elist_2EOPT__MMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2ENIL_2E0(A_27b)) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a)) )
          & ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2h0_2E0: A_27b,V3t0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EOPT__MMAP_2E2(A_27a,A_27b,V1f_2E0,c_2Elist_2ECONS_2E2(A_27b,V2h0_2E0,V3t0_2E0)) = c_2Eoption_2EOPTION__BIND_2E2(tyop_2Elist_2Elist(A_27a),A_27a,app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),V1f_2E0,V2h0_2E0),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F0_2E0,V1f_2E0),V3t0_2E0)) ) ) ) ) ).

tff(thm_2Elist_2EoHD__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)))] :
      ( ! [V1h_2E0: A_27a,V2v1_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),F0_2E0,V1h_2E0),V2v1_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V1h_2E0) )
     => ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EoHD_2E1(A_27a,V0l_2E0) = c_2Elist_2Elist__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27a),V0l_2E0,c_2Eoption_2ENONE_2E0(A_27a),F0_2E0) ) ) ).

tff(thm_2Elist_2EoEL__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V1n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1n_2E0))
        <=> ( V1n_2E0 = c_2Enum_2E0_2E0 ) )
     => ( ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EoEL_2E2(A_27a,V0n_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(A_27a) )
        & ! [V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a,V3xs_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EoEL_2E2(A_27a,V1n_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3xs_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1n_2E0),c_2Eoption_2ESOME_2E1(A_27a,V2x_2E0),c_2Elist_2EoEL_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V3xs_2E0)) ) ) ) ).

tff(thm_2Elist_2EEXISTS__LIST,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
      ( ? [V1l_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1l_2E0))
    <=> ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)))
        | ? [V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0))) ) ) ).

tff(thm_2Elist_2ESUM__SUM__ACC,axiom,
    ! [V0L_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ESUM_2E1(V0L_2E0) = c_2Elist_2ESUM__ACC_2E2(V0L_2E0,c_2Enum_2E0_2E0) ) ).

tff(thm_2Elist_2ESUM__ACC__SUM__LEM,axiom,
    ! [V0L_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ESUM__ACC_2E2(V0L_2E0,V1n_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Elist_2ESUM_2E1(V0L_2E0),V1n_2E0) ) ).

tff(thm_2Elist_2EREVERSE__REV,axiom,
    ! [A_27a: $tType,V0L_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,V0L_2E0) = c_2Elist_2EREV_2E2(A_27a,V0L_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ).

tff(thm_2Elist_2ELENGTH__LEN,axiom,
    ! [A_27a: $tType,V0L_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,V0L_2E0) = c_2Elist_2ELEN_2E2(A_27a,V0L_2E0,c_2Enum_2E0_2E0) ) ).

tff(thm_2Elist_2EREV__REVERSE__LEM,axiom,
    ! [A_27a: $tType,V0L1_2E0: tyop_2Elist_2Elist(A_27a),V1L2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREV_2E2(A_27a,V0L1_2E0,V1L2_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V0L1_2E0),V1L2_2E0) ) ).

tff(thm_2Elist_2ELEN__LENGTH__LEM,axiom,
    ! [A_27a: $tType,V0L_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ELEN_2E2(A_27a,V0L_2E0,V1n_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0L_2E0),V1n_2E0) ) ).

tff(thm_2Elist_2EINFINITE__LIST__UNIV,axiom,
    ! [A_27a: $tType] : ~ p(c_2Epred__set_2EFINITE_2E1(tyop_2Elist_2Elist(A_27a),c_2Epred__set_2EUNIV_2E0(tyop_2Elist_2Elist(A_27a)))) ).

tff(thm_2Elist_2EMAP__ZIP__SAME,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),tyop_2Emin_2Efun(A_27a,A_27b),F0_2E0,V1f_2E0),V2x_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b,V1f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V2x_2E0)) )
     => ! [V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b,V1f_2E0,c_2Elist_2EZIP_2E1(A_27a,A_27a,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V0ls_2E0,V0ls_2E0))) = c_2Elist_2EMAP_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),tyop_2Emin_2Efun(A_27a,A_27b),F0_2E0,V1f_2E0),V0ls_2E0) ) ) ).

tff(thm_2Elist_2EFOLDL__ZIP__SAME,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),V3x_2E0: A_27b,V4y_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0,V1f_2E0),V3x_2E0),V4y_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f_2E0,V3x_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27a,V4y_2E0,V4y_2E0)) )
     => ! [V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),V2e_2E0: A_27b] : ( c_2Elist_2EFOLDL_2E3(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b,V1f_2E0,V2e_2E0,c_2Elist_2EZIP_2E1(A_27a,A_27a,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V0ls_2E0,V0ls_2E0))) = c_2Elist_2EFOLDL_2E3(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0,V1f_2E0),V2e_2E0,V0ls_2E0) ) ) ).

tff(thm_2Elist_2EFOLDL__UNION__BIGUNION__paired,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))))] :
      ( ! [V3s_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V4x_2E0: A_27a,V5y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F1_2E0,V3s_2E0),V0f_2E0),V4x_2E0),V5y_2E0) = c_2Epred__set_2EUNION_2E2(A_27c,V3s_2E0,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V0f_2E0,V4x_2E0),V5y_2E0)) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V3s_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V3s_2E0) = c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F1_2E0,V3s_2E0),V0f_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V1ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2s_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Elist_2EFOLDL_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2s_2E0,V1ls_2E0) = c_2Epred__set_2EUNION_2E2(A_27c,V2s_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27c,c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V0f_2E0),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V1ls_2E0)))) ) ) ) ).

tff(thm_2Elist_2EFOLDL__UNION__BIGUNION,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V3s_2E0),V4x_2E0) = c_2Epred__set_2EUNION_2E2(A_27b,V3s_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0f_2E0,V4x_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1ls_2E0: tyop_2Elist_2Elist(A_27a),V2s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Emin_2Efun(A_27b,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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V2s_2E0,V1ls_2E0) = c_2Epred__set_2EUNION_2E2(A_27b,V2s_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0f_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1ls_2E0)))) ) ) ).

tff(thm_2Elist_2EREVERSE__GENLIST,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0n_2E0: tyop_2Enum_2Enum,V2m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0,V1f_2E0),V0n_2E0),V2m_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Earithmetic_2E_2D_2E2(c_2Eprim__rec_2EPRE_2E1(V0n_2E0),V2m_2E0)) )
     => ! [V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,V0n_2E0)) = c_2Elist_2EGENLIST_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0,V1f_2E0),V0n_2E0),V0n_2E0) ) ) ).

tff(thm_2Elist_2EEL__REVERSE,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
     => ( c_2Elist_2EEL_2E2(A_27a,V0n_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) = c_2Elist_2EEL_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0)),V1l_2E0) ) ) ).

tff(thm_2Elist_2ESUM__IMAGE__eq__SUM__MAP__SET__TO__LIST,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V1f_2E0,V0s_2E0) = c_2Elist_2ESUM_2E1(c_2Elist_2EMAP_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,c_2Elist_2ESET__TO__LIST_2E1(A_27a,V0s_2E0))) ) ) ).

tff(thm_2Elist_2ESUM__MAP__FOLDL,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0: tyop_2Enum_2Enum,V3e_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(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_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),F0_2E0,V0f_2E0),V2a_2E0),V3e_2E0) = c_2Earithmetic_2E_2B_2E2(V2a_2E0,app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V3e_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1ls_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ESUM_2E1(c_2Elist_2EMAP_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1ls_2E0)) = c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),F0_2E0,V0f_2E0),c_2Enum_2E0_2E0,V1ls_2E0) ) ) ).

tff(thm_2Elist_2ESUM__APPEND,axiom,
    ! [V0l1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l2_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ESUM_2E1(c_2Elist_2EAPPEND_2E2(tyop_2Enum_2Enum,V0l1_2E0,V1l2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Elist_2ESUM_2E1(V0l1_2E0),c_2Elist_2ESUM_2E1(V1l2_2E0)) ) ).

tff(thm_2Elist_2ESUM__SNOC,axiom,
    ! [V0x_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ESUM_2E1(c_2Elist_2ESNOC_2E2(tyop_2Enum_2Enum,V0x_2E0,V1l_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Elist_2ESUM_2E1(V1l_2E0),V0x_2E0) ) ).

tff(thm_2Elist_2EFOLDL__SNOC,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V1e_2E0: A_27b,V2x_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,c_2Elist_2ESNOC_2E2(A_27a,V2x_2E0,V3l_2E0)) = app_2E2(A_27a,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,c_2Elist_2EFOLDL_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,V3l_2E0)),V2x_2E0) ) ).

tff(thm_2Elist_2EALL__DISTINCT__GENLIST,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
      ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,V0n_2E0)))
    <=> ! [V2m1_2E0: tyop_2Enum_2Enum,V3m2_2E0: tyop_2Enum_2Enum] :
          ( ( p(c_2Eprim__rec_2E_3C_2E2(V2m1_2E0,V0n_2E0))
            & p(c_2Eprim__rec_2E_3C_2E2(V3m2_2E0,V0n_2E0))
            & ( app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V2m1_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V3m2_2E0) ) )
         => ( V2m1_2E0 = V3m2_2E0 ) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT__SNOC,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1l_2E0)))
    <=> ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)))
        & p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V1l_2E0)) ) ) ).

tff(thm_2Elist_2EMEM__GENLIST,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EGENLIST_2E2(A_27a,V2f_2E0,V1n_2E0))))
    <=> ? [V3m_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(V3m_2E0,V1n_2E0))
          & ( V0x_2E0 = app_2E2(tyop_2Enum_2Enum,A_27a,V2f_2E0,V3m_2E0) ) ) ) ).

tff(thm_2Elist_2EGENLIST__NUMERALS,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
      ( ( c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,c_2Enum_2E0_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
      & ( c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,c_2Earithmetic_2ENUMERAL_2E1(V0n_2E0)) = c_2Elist_2EGENLIST__AUX_2E3(A_27a,V1f_2E0,c_2Earithmetic_2ENUMERAL_2E1(V0n_2E0),c_2Elist_2ENIL_2E0(A_27a)) ) ) ).

tff(thm_2Elist_2EGENLIST__GENLIST__AUX,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(A_27a,V0f_2E0,V1n_2E0) = c_2Elist_2EGENLIST__AUX_2E3(A_27a,V0f_2E0,V1n_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ).

tff(thm_2Elist_2ENULL__GENLIST,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
      ( p(c_2Elist_2ENULL_2E1(A_27a,c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,V0n_2E0)))
    <=> ( V0n_2E0 = c_2Enum_2E0_2E0 ) ) ).

tff(thm_2Elist_2EGENLIST__CONS,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,c_2Enum_2ESUC_2E1(V0n_2E0)) = c_2Elist_2ECONS_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Enum_2E0_2E0),c_2Elist_2EGENLIST_2E2(A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum,V1f_2E0,c_2Enum_2ESUC_2E0),V0n_2E0)) ) ).

tff(thm_2Elist_2EZIP__GENLIST,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b))))] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V3x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b))),F0_2E0,V0l_2E0),V1f_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27b,c_2Elist_2EEL_2E2(A_27a,V3x_2E0,V0l_2E0),app_2E2(tyop_2Enum_2Enum,A_27b,V1f_2E0,V3x_2E0)) )
     => ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V2n_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) = V2n_2E0 )
         => ( c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l_2E0,c_2Elist_2EGENLIST_2E2(A_27b,V1f_2E0,V2n_2E0))) = c_2Elist_2EGENLIST_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b))),F0_2E0,V0l_2E0),V1f_2E0),V2n_2E0) ) ) ) ).

tff(thm_2Elist_2ETL__GENLIST,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ETL_2E1(A_27a,c_2Elist_2EGENLIST_2E2(A_27a,V0f_2E0,c_2Enum_2ESUC_2E1(V1n_2E0))) = c_2Elist_2EGENLIST_2E2(A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum,V0f_2E0,c_2Enum_2ESUC_2E0),V1n_2E0) ) ).

tff(thm_2Elist_2EEXISTS__GENLIST,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Elist_2EEXISTS_2E2(A_27a,V1P_2E0,c_2Elist_2EGENLIST_2E2(A_27a,V0f_2E0,V2n_2E0)))
    <=> ? [V3i_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(V3i_2E0,V2n_2E0))
          & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,app_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,V3i_2E0))) ) ) ).

tff(thm_2Elist_2EEVERY__GENLIST,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Elist_2EEVERY_2E2(A_27a,V1P_2E0,c_2Elist_2EGENLIST_2E2(A_27a,V0f_2E0,V2n_2E0)))
    <=> ! [V3i_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(V3i_2E0,V2n_2E0))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,app_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,V3i_2E0))) ) ) ).

tff(thm_2Elist_2EGENLIST__APPEND,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2b_2E0: tyop_2Enum_2Enum,V3t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0,V0f_2E0),V2b_2E0),V3t_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,c_2Earithmetic_2E_2B_2E2(V3t_2E0,V2b_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(A_27a,V0f_2E0,c_2Earithmetic_2E_2B_2E2(V1a_2E0,V2b_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EGENLIST_2E2(A_27a,V0f_2E0,V2b_2E0),c_2Elist_2EGENLIST_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0,V0f_2E0),V2b_2E0),V1a_2E0)) ) ) ).

tff(thm_2Elist_2EGENLIST__FUN__EQ,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
      ( ( c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,V0n_2E0) = c_2Elist_2EGENLIST_2E2(A_27a,V2g_2E0,V0n_2E0) )
    <=> ! [V3x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(V3x_2E0,V0n_2E0))
         => ( app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V3x_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V2g_2E0,V3x_2E0) ) ) ) ).

tff(thm_2Elist_2EHD__GENLIST__COR,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
      ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
     => ( c_2Elist_2EHD_2E1(A_27a,c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,V0n_2E0)) = app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Enum_2E0_2E0) ) ) ).

tff(thm_2Elist_2EHD__GENLIST,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Elist_2EHD_2E1(A_27a,c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,c_2Enum_2ESUC_2E1(V0n_2E0))) = app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Enum_2E0_2E0) ) ).

tff(thm_2Elist_2EEL__GENLIST,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V2x_2E0,V1n_2E0))
     => ( c_2Elist_2EEL_2E2(A_27a,V2x_2E0,c_2Elist_2EGENLIST_2E2(A_27a,V0f_2E0,V1n_2E0)) = app_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,V2x_2E0) ) ) ).

tff(thm_2Elist_2EMAP__GENLIST,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2EGENLIST_2E2(A_27a,V1g_2E0,V2n_2E0)) = c_2Elist_2EGENLIST_2E2(A_27b,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27b,A_27a,V0f_2E0,V1g_2E0),V2n_2E0) ) ).

tff(thm_2Elist_2EGENLIST__AUX__compute,axiom,
    ! [A_27a: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EGENLIST__AUX_2E3(A_27a,V0f_2E0,c_2Enum_2E0_2E0,V1l_2E0) = V1l_2E0 )
      & ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3n_2E0: tyop_2Enum_2Enum,V4l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EGENLIST__AUX_2E3(A_27a,V2f_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),V4l_2E0) = c_2Elist_2EGENLIST__AUX_2E3(A_27a,V2f_2E0,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ECONS_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V2f_2E0,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V4l_2E0)) )
      & ! [V5f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V6n_2E0: tyop_2Enum_2Enum,V7l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EGENLIST__AUX_2E3(A_27a,V5f_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V6n_2E0)),V7l_2E0) = c_2Elist_2EGENLIST__AUX_2E3(A_27a,V5f_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V6n_2E0)),c_2Elist_2ECONS_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V5f_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V6n_2E0))),V7l_2E0)) ) ) ).

tff(thm_2Elist_2ELENGTH__GENLIST,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EGENLIST_2E2(A_27a,V0f_2E0,V1n_2E0)) = V1n_2E0 ) ).

tff(thm_2Elist_2ESNOC__CASES,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( V0ll_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
      | ? [V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( V0ll_2E0 = c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V2l_2E0) ) ) ).

tff(thm_2Elist_2ESNOC__INDUCT,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)))
        & ! [V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1l_2E0))
           => ! [V2x_2E0: A_27a] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ESNOC_2E2(A_27a,V2x_2E0,V1l_2E0))) ) )
     => ! [V3l_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V3l_2E0)) ) ).

tff(thm_2Elist_2ESNOC__Axiom,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0e_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)))] :
    ? [V2fn_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)] :
      ( ( app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V2fn_2E0,c_2Elist_2ENIL_2E0(A_27a)) = V0e_2E0 )
      & ! [V3x_2E0: A_27a,V4l_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V2fn_2E0,c_2Elist_2ESNOC_2E2(A_27a,V3x_2E0,V4l_2E0)) = app_2E2(A_27b,A_27b,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0,V3x_2E0),V4l_2E0),app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V2fn_2E0,V4l_2E0)) ) ) ).

tff(thm_2Elist_2EREVERSE__SNOC,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) ) ).

tff(thm_2Elist_2EREVERSE__SNOC__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ( c_2Elist_2EREVERSE_2E1(A_27b,c_2Elist_2ENIL_2E0(A_27b)) = c_2Elist_2ENIL_2E0(A_27b) )
      & ! [V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1l_2E0)) = c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) ) ) ).

tff(thm_2Elist_2ESNOC__11,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: tyop_2Elist_2Elist(A_27a),V2a_2E0: A_27a,V3b_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1y_2E0) = c_2Elist_2ESNOC_2E2(A_27a,V2a_2E0,V3b_2E0) )
    <=> ( ( V0x_2E0 = V2a_2E0 )
        & ( V1y_2E0 = V3b_2E0 ) ) ) ).

tff(thm_2Elist_2EMEM__SNOC,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V2l_2E0))))
    <=> ( ( V0y_2E0 = V1x_2E0 )
        | p(c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2l_2E0))) ) ) ).

tff(thm_2Elist_2EEXISTS__SNOC,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V2l_2E0)))
    <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0))
        | p(c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,V2l_2E0)) ) ) ).

tff(thm_2Elist_2EEVERY__SNOC,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V2l_2E0)))
    <=> ( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V2l_2E0))
        & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0)) ) ) ).

tff(thm_2Elist_2EAPPEND__SNOC,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a,V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V2l2_2E0)) = c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V2l2_2E0)) ) ).

tff(thm_2Elist_2EEL__LENGTH__SNOC,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a] : ( c_2Elist_2EEL_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V0l_2E0)) = V1x_2E0 ) ).

tff(thm_2Elist_2EEL__SNOC,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
     => ! [V2x_2E0: A_27a] : ( c_2Elist_2EEL_2E2(A_27a,V0n_2E0,c_2Elist_2ESNOC_2E2(A_27a,V2x_2E0,V1l_2E0)) = c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0) ) ) ).

tff(thm_2Elist_2EMAP__SNOC,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V2l_2E0)) = c_2Elist_2ESNOC_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0),c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V2l_2E0)) ) ).

tff(thm_2Elist_2ELIST__TO__SET__SNOC,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1ls_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1ls_2E0)) = c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1ls_2E0)) ) ).

tff(thm_2Elist_2ESNOC__APPEND,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1l_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,V1l_2E0,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a))) ) ).

tff(thm_2Elist_2EFRONT__SNOC,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1l_2E0)) = V1l_2E0 ) ).

tff(thm_2Elist_2ELAST__SNOC,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1l_2E0)) = V0x_2E0 ) ).

tff(thm_2Elist_2ELENGTH__SNOC,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1l_2E0)) = c_2Enum_2ESUC_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)) ) ).

tff(thm_2Elist_2EisPREFIX__CONSR,axiom,
    ! [A_27a: $tType,V0ys_2E0: tyop_2Elist_2Elist(A_27a),V1y_2E0: A_27a,V2x_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EisPREFIX_2E2(A_27a,V2x_2E0,c_2Elist_2ECONS_2E2(A_27a,V1y_2E0,V0ys_2E0)))
    <=> ( ( V2x_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
        | ? [V3xs_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( ( V2x_2E0 = c_2Elist_2ECONS_2E2(A_27a,V1y_2E0,V3xs_2E0) )
            & p(c_2Elist_2EisPREFIX_2E2(A_27a,V3xs_2E0,V0ys_2E0)) ) ) ) ).

tff(thm_2Elist_2EisPREFIX__NILR,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EisPREFIX_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)))
    <=> ( V0x_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ).

tff(thm_2Elist_2EisPREFIX__THM,axiom,
    ! [A_27a: $tType,V0t2_2E0: tyop_2Elist_2Elist(A_27a),V1t1_2E0: tyop_2Elist_2Elist(A_27a),V2t_2E0: tyop_2Elist_2Elist(A_27a),V3l_2E0: tyop_2Elist_2Elist(A_27a),V4h2_2E0: A_27a,V5h1_2E0: A_27a,V6h_2E0: A_27a] :
      ( ( c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V3l_2E0) = c_2Ebool_2ET_2E0 )
      & ( c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V6h_2E0,V2t_2E0),c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2EF_2E0 )
      & ( p(c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V5h1_2E0,V1t1_2E0),c_2Elist_2ECONS_2E2(A_27a,V4h2_2E0,V0t2_2E0)))
      <=> ( ( V5h1_2E0 = V4h2_2E0 )
          & p(c_2Elist_2EisPREFIX_2E2(A_27a,V1t1_2E0,V0t2_2E0)) ) ) ) ).

tff(thm_2Elist_2EITSET__eq__FOLDL__SET__TO__LIST,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2a_2E0: A_27b] : ( c_2Epred__set_2EITSET_2E3(A_27a,A_27b,V1f_2E0,V0s_2E0,V2a_2E0) = c_2Elist_2EFOLDL_2E3(A_27a,A_27b,c_2Ecombin_2EC_2E1(A_27a,A_27b,A_27b,V1f_2E0),V2a_2E0,c_2Elist_2ESET__TO__LIST_2E1(A_27a,V0s_2E0)) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT__SET__TO__LIST,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2ESET__TO__LIST_2E1(A_27a,V0s_2E0))) ) ).

tff(thm_2Elist_2ESET__TO__LIST__SING,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Elist_2ESET__TO__LIST_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) = c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ).

tff(thm_2Elist_2EMEM__SET__TO__LIST,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ! [V1x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ESET__TO__LIST_2E1(A_27a,V0s_2E0))) = c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0) ) ) ).

tff(thm_2Elist_2ESET__TO__LIST__IN__MEM,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ! [V1x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0) = c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ESET__TO__LIST_2E1(A_27a,V0s_2E0))) ) ) ).

tff(thm_2Elist_2ESET__TO__LIST__CARD,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2ESET__TO__LIST_2E1(A_27a,V0s_2E0)) = c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) ) ) ).

tff(thm_2Elist_2ESET__TO__LIST__INV,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ESET__TO__LIST_2E1(A_27a,V0s_2E0)) = V0s_2E0 ) ) ).

tff(thm_2Elist_2ESET__TO__LIST__EMPTY,axiom,
    ! [A_27a: $tType] : ( c_2Elist_2ESET__TO__LIST_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) ) ).

tff(thm_2Elist_2ESET__TO__LIST__IND,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
              & ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
           => p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EREST_2E1(A_27a,V1s_2E0))) )
         => p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V1s_2E0)) )
     => ! [V2v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V2v_2E0)) ) ).

tff(thm_2Elist_2ESET__TO__LIST__THM,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0))
        <=> ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
     => ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
         => ( c_2Elist_2ESET__TO__LIST_2E1(A_27a,V0s_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0),c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,c_2Epred__set_2ECHOICE_2E1(A_27a,V0s_2E0),c_2Elist_2ESET__TO__LIST_2E1(A_27a,c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0)))) ) ) ) ).

tff(thm_2Elist_2ELIST__TO__SET__FILTER,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)) )
     => ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,V0l_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,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)),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0)) ) ) ).

tff(thm_2Elist_2ELIST__TO__SET__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27b,c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V1l_2E0)) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)) ) ).

tff(thm_2Elist_2ELIST__TO__SET__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Elist_2Elist(A_27b),V1h_2E0: A_27b] :
      ( ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
      & ( c_2Elist_2ELIST__TO__SET_2E1(A_27b,c_2Elist_2ECONS_2E2(A_27b,V1h_2E0,V0t_2E0)) = c_2Epred__set_2EINSERT_2E2(A_27b,V1h_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27b,V0t_2E0)) ) ) ).

tff(thm_2Elist_2ELIST__TO__SET__REVERSE,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V0ls_2E0)) = c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0ls_2E0) ) ).

tff(thm_2Elist_2ECARD__LIST__TO__SET__ALL__DISTINCT,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0ls_2E0)) = c_2Elist_2ELENGTH_2E1(A_27a,V0ls_2E0) )
     => p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0ls_2E0)) ) ).

tff(thm_2Elist_2EALL__DISTINCT__CARD__LIST__TO__SET,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0ls_2E0))
     => ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0ls_2E0)) = c_2Elist_2ELENGTH_2E1(A_27a,V0ls_2E0) ) ) ).

tff(thm_2Elist_2ECARD__LIST__TO__SET,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0ls_2E0)),c_2Elist_2ELENGTH_2E1(A_27a,V0ls_2E0))) ).

tff(thm_2Elist_2EINJ__MAP__EQ__IFF,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EUNION_2E2(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l1_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2l2_2E0)),c_2Epred__set_2EUNIV_2E0(A_27b)))
     => ( ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V1l1_2E0) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V2l2_2E0) )
      <=> ( V1l1_2E0 = V2l2_2E0 ) ) ) ).

tff(thm_2Elist_2EINJ__MAP__EQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EUNION_2E2(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l1_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2l2_2E0)),c_2Epred__set_2EUNIV_2E0(A_27b)))
        & ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V1l1_2E0) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V2l2_2E0) ) )
     => ( V1l1_2E0 = V2l2_2E0 ) ) ).

tff(thm_2Elist_2ESUM__MAP__MEM__bound,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1x_2E0: A_27a,V2ls_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2ls_2E0)))
     => p(c_2Earithmetic_2E_3C_3D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1x_2E0),c_2Elist_2ESUM_2E1(c_2Elist_2EMAP_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2ls_2E0)))) ) ).

tff(thm_2Elist_2ESUM__IMAGE__LIST__TO__SET__upper__bound,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1ls_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1ls_2E0)),c_2Elist_2ESUM_2E1(c_2Elist_2EMAP_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1ls_2E0)))) ).

tff(thm_2Elist_2EFINITE__LIST__TO__SET,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0))) ).

tff(thm_2Elist_2ELIST__TO__SET__EQ__EMPTY,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
      <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
      & ( ( c_2Epred__set_2EEMPTY_2E0(A_27a) = c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0) )
      <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ) ).

tff(thm_2Elist_2EUNION__APPEND,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l1_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0)) = c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) ) ).

tff(thm_2Elist_2ELIST__TO__SET__APPEND,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l1_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0)) ) ).

tff(thm_2Elist_2ELRC__MEM__right,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2t_2E0: tyop_2Elist_2Elist(A_27a),V3h_2E0: A_27a,V4e_2E0: A_27a,V5R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Elist_2ELRC_2E4(A_27a,V5R_2E0,c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,V2t_2E0),V1x_2E0,V0y_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V4e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2t_2E0))) )
     => ? [V6z_2E0: A_27a,V7p_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5R_2E0,V6z_2E0),V4e_2E0))
          & p(c_2Elist_2ELRC_2E4(A_27a,V5R_2E0,V7p_2E0,V1x_2E0,V6z_2E0)) ) ) ).

tff(thm_2Elist_2ELRC__MEM,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2ls_2E0: tyop_2Elist_2Elist(A_27a),V3e_2E0: A_27a,V4R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Elist_2ELRC_2E4(A_27a,V4R_2E0,V2ls_2E0,V1x_2E0,V0y_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V3e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2ls_2E0))) )
     => ? [V5z_2E0: A_27a,V6t_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4R_2E0,V3e_2E0),V5z_2E0))
          & p(c_2Elist_2ELRC_2E4(A_27a,V4R_2E0,V6t_2E0,V5z_2E0,V0y_2E0)) ) ) ).

tff(thm_2Elist_2ENRC__LRC,axiom,
    ! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2n_2E0: tyop_2Enum_2Enum,V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Earithmetic_2ENRC_2E4(A_27a,V3R_2E0,V2n_2E0,V1x_2E0,V0y_2E0))
    <=> ? [V4ls_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Elist_2ELRC_2E4(A_27a,V3R_2E0,V4ls_2E0,V1x_2E0,V0y_2E0))
          & ( c_2Elist_2ELENGTH_2E1(A_27a,V4ls_2E0) = V2n_2E0 ) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT__FLAT__REVERSE,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2EREVERSE_2E1(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) = c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EFLAT_2E1(A_27a,V0xs_2E0)) ) ).

tff(thm_2Elist_2EALL__DISTINCT__REVERSE,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V0l_2E0)) = c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0l_2E0) ) ).

tff(thm_2Elist_2EALL__DISTINCT__ZIP__SWAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( ( p(c_2Elist_2EALL__DISTINCT_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))))
        & ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) ) )
     => p(c_2Elist_2EALL__DISTINCT_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Elist_2EZIP_2E1(A_27b,A_27a,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),V1l2_2E0,V0l1_2E0)))) ) ).

tff(thm_2Elist_2EALL__DISTINCT__ZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0l1_2E0))
        & ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) ) )
     => p(c_2Elist_2EALL__DISTINCT_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0)))) ) ).

tff(thm_2Elist_2EALL__DISTINCT__SING,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)))) ).

tff(thm_2Elist_2EALL__DISTINCT__APPEND,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)))
    <=> ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0l1_2E0))
        & p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V1l2_2E0))
        & ! [V2e_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V2e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l1_2E0)))
           => ~ p(c_2Ebool_2EIN_2E2(A_27a,V2e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0))) ) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT__EL__IMP,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1n1_2E0: tyop_2Enum_2Enum,V2n2_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0l_2E0))
        & p(c_2Eprim__rec_2E_3C_2E2(V1n1_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)))
        & p(c_2Eprim__rec_2E_3C_2E2(V2n2_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0))) )
     => ( ( c_2Elist_2EEL_2E2(A_27a,V1n1_2E0,V0l_2E0) = c_2Elist_2EEL_2E2(A_27a,V2n2_2E0,V0l_2E0) )
      <=> ( V1n1_2E0 = V2n2_2E0 ) ) ) ).

tff(thm_2Elist_2EEL__ALL__DISTINCT__EL__EQ,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0l_2E0))
    <=> ! [V1n1_2E0: tyop_2Enum_2Enum,V2n2_2E0: tyop_2Enum_2Enum] :
          ( ( p(c_2Eprim__rec_2E_3C_2E2(V1n1_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)))
            & p(c_2Eprim__rec_2E_3C_2E2(V2n2_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0))) )
         => ( ( c_2Elist_2EEL_2E2(A_27a,V1n1_2E0,V0l_2E0) = c_2Elist_2EEL_2E2(A_27a,V2n2_2E0,V0l_2E0) )
          <=> ( V1n1_2E0 = V2n2_2E0 ) ) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1ls_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27b,c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V1ls_2E0)))
     => p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V1ls_2E0)) ) ).

tff(thm_2Elist_2EFILTER__ALL__DISTINCT,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V1l_2E0))
     => p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l_2E0))) ) ).

tff(thm_2Elist_2EALL__DISTINCT__FILTER,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0l_2E0))
    <=> ! [V1x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0)))
         => ( c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V1x_2E0),V0l_2E0) = c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ) ) ).

tff(thm_2Elist_2EEVERY2__mono,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( ! [V4x_2E0: A_27a,V5y_2E0: A_27b] :
          ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3R1_2E0,V4x_2E0),V5y_2E0))
         => p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2R2_2E0,V4x_2E0),V5y_2E0)) )
     => ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V3R1_2E0,V1l1_2E0,V0l2_2E0))
       => p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V2R2_2E0,V1l1_2E0,V0l2_2E0)) ) ) ).

tff(thm_2Elist_2EEVERY2__LENGTH,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0P_2E0,V1l1_2E0,V2l2_2E0))
     => ( c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V2l2_2E0) ) ) ).

tff(thm_2Elist_2EEVERY2__EVERY,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V2f_2E0,V0l1_2E0,V1l2_2E0))
    <=> ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
        & p(c_2Elist_2EEVERY_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Ebool,V2f_2E0),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0)))) ) ) ).

tff(thm_2Elist_2EMAP__EQ__EVERY2,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))))] :
      ( ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V4x_2E0: A_27a,V5y_2E0: A_27c] :
          ( p(app_2E2(A_27c,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),F0_2E0,V0f1_2E0),V1f2_2E0),V4x_2E0),V5y_2E0))
        <=> ( app_2E2(A_27a,A_27b,V0f1_2E0,V4x_2E0) = app_2E2(A_27c,A_27b,V1f2_2E0,V5y_2E0) ) )
     => ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27c)] :
          ( ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f1_2E0,V2l1_2E0) = c_2Elist_2EMAP_2E2(A_27c,A_27b,V1f2_2E0,V3l2_2E0) )
        <=> ( ( c_2Elist_2ELENGTH_2E1(A_27a,V2l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27c,V3l2_2E0) )
            & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),F0_2E0,V0f1_2E0),V1f2_2E0),V2l1_2E0,V3l2_2E0)) ) ) ) ).

tff(thm_2Elist_2EEVERY2__cong,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l1_27_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3l2_27_2E0: tyop_2Elist_2Elist(A_27b),V4P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( ( ( V0l1_2E0 = V1l1_27_2E0 )
        & ( V2l2_2E0 = V3l2_27_2E0 )
        & ! [V6x_2E0: A_27a,V7y_2E0: A_27b] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l1_27_2E0)))
              & p(c_2Ebool_2EIN_2E2(A_27b,V7y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27b,V3l2_27_2E0))) )
           => ( app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4P_2E0,V6x_2E0),V7y_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_27_2E0,V6x_2E0),V7y_2E0) ) ) )
     => ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4P_2E0,V0l1_2E0,V2l2_2E0) = c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V5P_27_2E0,V1l1_27_2E0,V3l2_27_2E0) ) ) ).

tff(thm_2Elist_2EFOLDL2__FOLDL,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)))] :
      ( ! [V2f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V4a_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),F0_2E0,V2f_2E0),V4a_2E0) = c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,A_27c,app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0,V4a_2E0)) )
     => ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
         => ! [V2f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V3a_2E0: A_27c] : ( c_2Elist_2EFOLDL2_2E4(A_27c,A_27a,A_27b,V2f_2E0,V3a_2E0,V0l1_2E0,V1l2_2E0) = c_2Elist_2EFOLDL_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),F0_2E0,V2f_2E0),V3a_2E0,c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) ) ) ) ).

tff(thm_2Elist_2EFOLDL2__cong,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l1_27_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3l2_27_2E0: tyop_2Elist_2Elist(A_27b),V4a_2E0: A_27c,V5a_27_2E0: A_27c,V6f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V7f_27_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))] :
      ( ( ( V0l1_2E0 = V1l1_27_2E0 )
        & ( V2l2_2E0 = V3l2_27_2E0 )
        & ( V4a_2E0 = V5a_27_2E0 )
        & ! [V8z_2E0: A_27c,V9b_2E0: A_27a,V10c_2E0: A_27b] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V9b_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l1_27_2E0)))
              & p(c_2Ebool_2EIN_2E2(A_27b,V10c_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27b,V3l2_27_2E0))) )
           => ( app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V6f_2E0,V8z_2E0),V9b_2E0),V10c_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V7f_27_2E0,V8z_2E0),V9b_2E0),V10c_2E0) ) ) )
     => ( c_2Elist_2EFOLDL2_2E4(A_27c,A_27a,A_27b,V6f_2E0,V4a_2E0,V0l1_2E0,V2l2_2E0) = c_2Elist_2EFOLDL2_2E4(A_27c,A_27a,A_27b,V7f_27_2E0,V5a_27_2E0,V1l1_27_2E0,V3l2_27_2E0) ) ) ).

tff(thm_2Elist_2EFOLDL2__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1cs_2E0: tyop_2Elist_2Elist(A_27c),V2c_2E0: A_27c,V3bs_2E0: tyop_2Elist_2Elist(A_27b),V4b_2E0: A_27b,V5a_2E0: A_27a] : ( c_2Elist_2EFOLDL2_2E4(A_27a,A_27b,A_27c,V0f_2E0,V5a_2E0,c_2Elist_2ECONS_2E2(A_27b,V4b_2E0,V3bs_2E0),c_2Elist_2ECONS_2E2(A_27c,V2c_2E0,V1cs_2E0)) = c_2Elist_2EFOLDL2_2E4(A_27a,A_27b,A_27c,V0f_2E0,app_2E2(A_27c,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_2E0,V5a_2E0),V4b_2E0),V2c_2E0),V3bs_2E0,V1cs_2E0) )
      & ! [V6f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V7cs_2E0: tyop_2Elist_2Elist(A_27c),V8a_2E0: A_27a] : ( c_2Elist_2EFOLDL2_2E4(A_27a,A_27b,A_27c,V6f_2E0,V8a_2E0,c_2Elist_2ENIL_2E0(A_27b),V7cs_2E0) = V8a_2E0 )
      & ! [V9v7_2E0: tyop_2Elist_2Elist(A_27b),V10v6_2E0: A_27b,V11f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V12a_2E0: A_27a] : ( c_2Elist_2EFOLDL2_2E4(A_27a,A_27b,A_27c,V11f_2E0,V12a_2E0,c_2Elist_2ECONS_2E2(A_27b,V10v6_2E0,V9v7_2E0),c_2Elist_2ENIL_2E0(A_27c)) = V12a_2E0 ) ) ).

tff(thm_2Elist_2EFOLDL2__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))))] :
      ( ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V2a_2E0: A_27a,V3b_2E0: A_27b,V4bs_2E0: tyop_2Elist_2Elist(A_27b),V5c_2E0: A_27c,V6cs_2E0: tyop_2Elist_2Elist(A_27c)] :
            ( p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0,V1f_2E0),app_2E2(A_27c,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0,V2a_2E0),V3b_2E0),V5c_2E0)),V4bs_2E0),V6cs_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0,V1f_2E0),V2a_2E0),c_2Elist_2ECONS_2E2(A_27b,V3b_2E0,V4bs_2E0)),c_2Elist_2ECONS_2E2(A_27c,V5c_2E0,V6cs_2E0))) )
        & ! [V7f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V8a_2E0: A_27a,V9cs_2E0: tyop_2Elist_2Elist(A_27c)] : p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0,V7f_2E0),V8a_2E0),c_2Elist_2ENIL_2E0(A_27b)),V9cs_2E0))
        & ! [V10f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V11a_2E0: A_27a,V12v6_2E0: A_27b,V13v7_2E0: tyop_2Elist_2Elist(A_27b)] : p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0,V10f_2E0),V11a_2E0),c_2Elist_2ECONS_2E2(A_27b,V12v6_2E0,V13v7_2E0)),c_2Elist_2ENIL_2E0(A_27c))) )
     => ! [V14v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V15v1_2E0: A_27a,V16v2_2E0: tyop_2Elist_2Elist(A_27b),V17v3_2E0: tyop_2Elist_2Elist(A_27c)] : p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0,V14v_2E0),V15v1_2E0),V16v2_2E0),V17v3_2E0)) ) ).

tff(thm_2Elist_2EDROP__NIL,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
      ( ( c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,V0ls_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
    <=> p(c_2Earithmetic_2E_3E_3D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0ls_2E0))) ) ).

tff(thm_2Elist_2EMEM__DROP,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1ls_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EDROP_2E2(A_27a,V2n_2E0,V1ls_2E0))))
    <=> ( ( p(c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1ls_2E0)))
          & ( V0x_2E0 = c_2Elist_2EEL_2E2(A_27a,V2n_2E0,V1ls_2E0) ) )
        | p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EDROP_2E2(A_27a,c_2Enum_2ESUC_2E1(V2n_2E0),V1ls_2E0)))) ) ) ).

tff(thm_2Elist_2ELENGTH__DROP,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,V1l_2E0)) = c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0) ) ).

tff(thm_2Elist_2ETAKE__DROP,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V1l_2E0),c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,V1l_2E0)) = V1l_2E0 ) ).

tff(thm_2Elist_2EDROP__0,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = V0l_2E0 ) ).

tff(thm_2Elist_2ETAKE__APPEND2,axiom,
    ! [A_27a: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eprim__rec_2E_3C_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0),V2n_2E0))
     => ( c_2Elist_2ETAKE_2E2(A_27a,V2n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V0l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,c_2Elist_2ETAKE_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V2n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)),V0l2_2E0)) ) ) ).

tff(thm_2Elist_2ETAKE__APPEND1,axiom,
    ! [A_27a: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
     => ( c_2Elist_2ETAKE_2E2(A_27a,V2n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V0l2_2E0)) = c_2Elist_2ETAKE_2E2(A_27a,V2n_2E0,V1l1_2E0) ) ) ).

tff(thm_2Elist_2EMAP__TAKE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2ETAKE_2E2(A_27a,V1n_2E0,V2l_2E0)) = c_2Elist_2ETAKE_2E2(A_27b,V1n_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V2l_2E0)) ) ).

tff(thm_2Elist_2ELENGTH__TAKE,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
     => ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V1l_2E0)) = V0n_2E0 ) ) ).

tff(thm_2Elist_2ETAKE__LENGTH__ID,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),V0l_2E0) = V0l_2E0 ) ).

tff(thm_2Elist_2ETAKE__0,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = c_2Elist_2ENIL_2E0(A_27a) ) ).

tff(thm_2Elist_2EDROP__cons,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a,V2n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V2n_2E0))
     => ( c_2Elist_2EDROP_2E2(A_27a,V2n_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V0xs_2E0)) = c_2Elist_2EDROP_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0xs_2E0) ) ) ).

tff(thm_2Elist_2EDROP__nil,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) ) ).

tff(thm_2Elist_2ETAKE__cons,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a,V2n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V2n_2E0))
     => ( c_2Elist_2ETAKE_2E2(A_27a,V2n_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V0xs_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ETAKE_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0xs_2E0)) ) ) ).

tff(thm_2Elist_2ETAKE__nil,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) ) ).

tff(thm_2Elist_2ELAST__APPEND__CONS,axiom,
    ! [A_27a: $tType,V0h_2E0: A_27a,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V2l2_2E0))) = c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V2l2_2E0)) ) ).

tff(thm_2Elist_2ELAST__CONS__cond,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
      ( ! [V0t_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V0t_2E0))
        <=> ( V0t_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
     => ! [V0t_2E0: tyop_2Elist_2Elist(A_27a),V1h_2E0: A_27a] : ( c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V0t_2E0)) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V0t_2E0),V1h_2E0,c_2Elist_2ELAST_2E1(A_27a,V0t_2E0)) ) ) ).

tff(thm_2Elist_2EAPPEND__FRONT__LAST,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( V0l_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
     => ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EFRONT_2E1(A_27a,V0l_2E0),c_2Elist_2ECONS_2E2(A_27a,c_2Elist_2ELAST_2E1(A_27a,V0l_2E0),c_2Elist_2ENIL_2E0(A_27a))) = V0l_2E0 ) ) ).

tff(thm_2Elist_2EFRONT__CONS__EQ__NIL,axiom,
    ! [A_27a: $tType] :
      ( ! [V0x_2E0: A_27a,V1xs_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1xs_2E0)) = c_2Elist_2ENIL_2E0(A_27a) )
        <=> ( V1xs_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
      & ! [V2x_2E0: A_27a,V3xs_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2ENIL_2E0(A_27a) = c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3xs_2E0)) )
        <=> ( V3xs_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
      & ! [V4x_2E0: A_27a,V5xs_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ENULL_2E1(A_27a,c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,V5xs_2E0))) = c_2Elist_2ENULL_2E1(A_27a,V5xs_2E0) ) ) ).

tff(thm_2Elist_2ELENGTH__FRONT__CONS,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1xs_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1xs_2E0))) = c_2Elist_2ELENGTH_2E1(A_27a,V1xs_2E0) ) ).

tff(thm_2Elist_2EFRONT__CONS,axiom,
    ! [A_27a: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a))) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ECONS_2E2(A_27a,V2y_2E0,V3z_2E0))) = c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2y_2E0,V3z_2E0))) ) ) ).

tff(thm_2Elist_2ELAST__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( V0l_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
     => ( c_2Elist_2ELAST_2E1(A_27b,c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,V0l_2E0)) = app_2E2(A_27a,A_27b,V1f_2E0,c_2Elist_2ELAST_2E1(A_27a,V0l_2E0)) ) ) ).

tff(thm_2Elist_2ELAST__EL,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( V0ls_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
     => ( c_2Elist_2ELAST_2E1(A_27a,V0ls_2E0) = c_2Elist_2EEL_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V0ls_2E0)),V0ls_2E0) ) ) ).

tff(thm_2Elist_2ELAST__CONS,axiom,
    ! [A_27a: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a))) = V0x_2E0 )
      & ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ECONS_2E2(A_27a,V2y_2E0,V3z_2E0))) = c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2y_2E0,V3z_2E0)) ) ) ).

tff(thm_2Elist_2EFILTER__REVERSE,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V0l_2E0)) = c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,V0l_2E0)) ) ).

tff(thm_2Elist_2EREVERSE__EQ__SING,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1e_2E0: A_27a] :
      ( ( c_2Elist_2EREVERSE_2E1(A_27a,V0l_2E0) = c_2Elist_2ECONS_2E2(A_27a,V1e_2E0,c_2Elist_2ENIL_2E0(A_27a)) )
    <=> ( V0l_2E0 = c_2Elist_2ECONS_2E2(A_27a,V1e_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ) ).

tff(thm_2Elist_2EREVERSE__EQ__NIL,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2EREVERSE_2E1(A_27a,V0l_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
    <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ).

tff(thm_2Elist_2ELENGTH__REVERSE,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V0l_2E0)) = c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) ) ).

tff(thm_2Elist_2EMEM__REVERSE,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V0l_2E0))) = c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0)) ) ).

tff(thm_2Elist_2EREVERSE__11,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2EREVERSE_2E1(A_27a,V0l1_2E0) = c_2Elist_2EREVERSE_2E1(A_27a,V1l2_2E0) )
    <=> ( V0l1_2E0 = V1l2_2E0 ) ) ).

tff(thm_2Elist_2EREVERSE__REVERSE,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V0l_2E0)) = V0l_2E0 ) ).

tff(thm_2Elist_2EREVERSE__APPEND,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V1l2_2E0),c_2Elist_2EREVERSE_2E1(A_27a,V0l1_2E0)) ) ).

tff(thm_2Elist_2ELIST__REL__EVERY__ZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,V1l1_2E0,V2l2_2E0))
    <=> ( ( c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V2l2_2E0) )
        & p(c_2Elist_2EEVERY_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Ebool,V0R_2E0),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V1l1_2E0,V2l2_2E0)))) ) ) ).

tff(thm_2Elist_2ESUM__MAP__PLUS__ZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0h_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),V3ls1_2E0: tyop_2Elist_2Elist(A_27a),V4ls2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( ( ( c_2Elist_2ELENGTH_2E1(A_27a,V3ls1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V4ls2_2E0) )
        & ! [V5x_2E0: A_27a,V6y_2E0: A_27b] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum,V2f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V5x_2E0,V6y_2E0)) = c_2Earithmetic_2E_2B_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V1g_2E0,V5x_2E0),app_2E2(A_27b,tyop_2Enum_2Enum,V0h_2E0,V6y_2E0)) ) )
     => ( c_2Elist_2ESUM_2E1(c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum,V2f_2E0,c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V3ls1_2E0,V4ls2_2E0)))) = c_2Earithmetic_2E_2B_2E2(c_2Elist_2ESUM_2E1(c_2Elist_2EMAP_2E2(A_27a,tyop_2Enum_2Enum,V1g_2E0,V3ls1_2E0)),c_2Elist_2ESUM_2E1(c_2Elist_2EMAP_2E2(A_27b,tyop_2Enum_2Enum,V0h_2E0,V4ls2_2E0))) ) ) ).

tff(thm_2Elist_2EMEM__EL,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0)))
    <=> ? [V2n_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)))
          & ( V1x_2E0 = c_2Elist_2EEL_2E2(A_27a,V2n_2E0,V0l_2E0) ) ) ) ).

tff(thm_2Elist_2EMAP__ZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2g_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27c)] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V0l2_2E0) )
     => ( ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V1l1_2E0,V0l2_2E0))) = V1l1_2E0 )
        & ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V1l1_2E0,V0l2_2E0))) = V0l2_2E0 )
        & ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27a,V3f_2E0,c_2Epair_2EFST_2E0(A_27a,A_27b)),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V1l1_2E0,V0l2_2E0))) = c_2Elist_2EMAP_2E2(A_27a,A_27c,V3f_2E0,V1l1_2E0) )
        & ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d,c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d,A_27b,V2g_2E0,c_2Epair_2ESND_2E0(A_27a,A_27b)),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V1l1_2E0,V0l2_2E0))) = c_2Elist_2EMAP_2E2(A_27b,A_27d,V2g_2E0,V0l2_2E0) ) ) ) ).

tff(thm_2Elist_2EMAP2__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
     => ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2Elist_2EMAP2_2E3(A_27c,A_27a,A_27b,V2f_2E0,V0l1_2E0,V1l2_2E0) = c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,A_27c,V2f_2E0),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) ) ) ).

tff(thm_2Elist_2EMAP2__ZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
     => ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2Elist_2EMAP2_2E3(A_27c,A_27a,A_27b,V2f_2E0,V0l1_2E0,V1l2_2E0) = c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,A_27c,V2f_2E0),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) ) ) ).

tff(thm_2Elist_2EEL__ZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b),V2n_2E0: tyop_2Enum_2Enum] :
      ( ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
        & p(c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0))) )
     => ( c_2Elist_2EEL_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V2n_2E0,c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) = c_2Epair_2E_2C_2E2(A_27a,A_27b,c_2Elist_2EEL_2E2(A_27a,V2n_2E0,V0l1_2E0),c_2Elist_2EEL_2E2(A_27b,V2n_2E0,V1l2_2E0)) ) ) ).

tff(thm_2Elist_2EMEM__ZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b),V2p_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
     => ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0)))))
      <=> ? [V3n_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Eprim__rec_2E_3C_2E2(V3n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0)))
            & ( V2p_2E0 = c_2Epair_2E_2C_2E2(A_27a,A_27b,c_2Elist_2EEL_2E2(A_27a,V3n_2E0,V0l1_2E0),c_2Elist_2EEL_2E2(A_27b,V3n_2E0,V1l2_2E0)) ) ) ) ) ).

tff(thm_2Elist_2EZIP__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)))] :
      ( ! [V3f2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5p_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),F1_2E0,V3f2_2E0),V5p_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27d,c_2Epair_2EFST_2E1(A_27a,A_27b,V5p_2E0),app_2E2(A_27b,A_27d,V3f2_2E0,c_2Epair_2ESND_2E1(A_27a,A_27b,V5p_2E0))) )
     => ( ! [V2f1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V4p_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),F0_2E0,V2f1_2E0),V4p_2E0) = c_2Epair_2E_2C_2E2(A_27c,A_27b,app_2E2(A_27a,A_27c,V2f1_2E0,c_2Epair_2EFST_2E1(A_27a,A_27b,V4p_2E0)),c_2Epair_2ESND_2E1(A_27a,A_27b,V4p_2E0)) )
       => ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b),V2f1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V3f2_2E0: tyop_2Emin_2Efun(A_27b,A_27d)] :
            ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
           => ( ( c_2Elist_2EZIP_2E1(A_27c,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(A_27a,A_27c,V2f1_2E0,V0l1_2E0),V1l2_2E0)) = c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),F0_2E0,V2f1_2E0),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) )
              & ( c_2Elist_2EZIP_2E1(A_27a,A_27d,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d),V0l1_2E0,c_2Elist_2EMAP_2E2(A_27b,A_27d,V3f2_2E0,V1l2_2E0))) = c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),F1_2E0,V3f2_2E0),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) ) ) ) ) ) ).

tff(thm_2Elist_2EUNZIP__ZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
     => ( c_2Elist_2EUNZIP_2E1(A_27a,A_27b,c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0) ) ) ).

tff(thm_2Elist_2EZIP__UNZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Elist_2EUNZIP_2E1(A_27a,A_27b,V0l_2E0)) = V0l_2E0 ) ).

tff(thm_2Elist_2ELENGTH__UNZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0pl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EUNZIP_2E1(A_27a,A_27b,V0pl_2E0))) = c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0pl_2E0) )
      & ( c_2Elist_2ELENGTH_2E1(A_27b,c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EUNZIP_2E1(A_27a,A_27b,V0pl_2E0))) = c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0pl_2E0) ) ) ).

tff(thm_2Elist_2ELENGTH__ZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
     => ( ( c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) = c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) )
        & ( c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) ) ) ) ).

tff(thm_2Elist_2EUNZIP__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0L_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EUNZIP_2E1(A_27a,A_27b,V0L_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0L_2E0),c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),V0L_2E0)) ) ).

tff(thm_2Elist_2EUNZIP__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))))))] :
      ( ! [V1x_2E0: A_27a,V0y_2E0: A_27b,V3L1_2E0: tyop_2Elist_2Elist(A_27a),V4L2_2E0: tyop_2Elist_2Elist(A_27b)] : ( app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))))),F0_2E0,V1x_2E0),V0y_2E0),V3L1_2E0),V4L2_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V3L1_2E0),c_2Elist_2ECONS_2E2(A_27b,V0y_2E0,V4L2_2E0)) )
     => ! [V0y_2E0: A_27b,V1x_2E0: A_27a,V2t_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
          ( ( c_2Elist_2EUNZIP_2E1(A_27a,A_27b,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27b)) )
          & ( c_2Elist_2EUNZIP_2E1(A_27a,A_27b,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0),V2t_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))))),F0_2E0,V1x_2E0),V0y_2E0)),c_2Elist_2EUNZIP_2E1(A_27a,A_27b,V2t_2E0)) ) ) ) ).

tff(thm_2Elist_2EZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
      ( ( c_2Elist_2EZIP_2E1(A_27c,A_27d,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d),c_2Elist_2ENIL_2E0(A_27c),c_2Elist_2ENIL_2E0(A_27d))) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27c,A_27d)) )
      & ! [V0x1_2E0: A_27a,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2x2_2E0: A_27b,V3l2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(A_27a,V0x1_2E0,V1l1_2E0),c_2Elist_2ECONS_2E2(A_27b,V2x2_2E0,V3l2_2E0))) = c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V0x1_2E0,V2x2_2E0),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V1l1_2E0,V3l2_2E0))) ) ) ).

tff(thm_2Elist_2EEVERY__MONOTONIC,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
     => ! [V3l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V3l_2E0))
         => p(c_2Elist_2EEVERY_2E2(A_27a,V1Q_2E0,V3l_2E0)) ) ) ).

tff(thm_2Elist_2EEVERY__CONG,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( ( V0l1_2E0 = V1l2_2E0 )
        & ! [V4x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0)))
           => ( app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V4x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_27_2E0,V4x_2E0) ) ) )
     => ( c_2Elist_2EEVERY_2E2(A_27a,V2P_2E0,V0l1_2E0) = c_2Elist_2EEVERY_2E2(A_27a,V3P_27_2E0,V1l2_2E0) ) ) ).

tff(thm_2Elist_2EEXISTS__CONG,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( ( V0l1_2E0 = V1l2_2E0 )
        & ! [V4x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0)))
           => ( app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V4x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_27_2E0,V4x_2E0) ) ) )
     => ( c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,V0l1_2E0) = c_2Elist_2EEXISTS_2E2(A_27a,V3P_27_2E0,V1l2_2E0) ) ) ).

tff(thm_2Elist_2EMAP2__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l1_27_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3l2_27_2E0: tyop_2Elist_2Elist(A_27b),V4f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V5f_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))] :
      ( ( ( V0l1_2E0 = V1l1_27_2E0 )
        & ( V2l2_2E0 = V3l2_27_2E0 )
        & ! [V6x_2E0: A_27a,V7y_2E0: A_27b] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l1_27_2E0)))
              & p(c_2Ebool_2EIN_2E2(A_27b,V7y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27b,V3l2_27_2E0))) )
           => ( app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V4f_2E0,V6x_2E0),V7y_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V5f_27_2E0,V6x_2E0),V7y_2E0) ) ) )
     => ( c_2Elist_2EMAP2_2E3(A_27c,A_27a,A_27b,V4f_2E0,V0l1_2E0,V2l2_2E0) = c_2Elist_2EMAP2_2E3(A_27c,A_27a,A_27b,V5f_27_2E0,V1l1_27_2E0,V3l2_27_2E0) ) ) ).

tff(thm_2Elist_2EMAP__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3f_27_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( ( V0l1_2E0 = V1l2_2E0 )
        & ! [V4x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0)))
           => ( app_2E2(A_27a,A_27b,V2f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V3f_27_2E0,V4x_2E0) ) ) )
     => ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V2f_2E0,V0l1_2E0) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V3f_27_2E0,V1l2_2E0) ) ) ).

tff(thm_2Elist_2EFOLDL__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1l_27_2E0: tyop_2Elist_2Elist(A_27a),V2b_2E0: A_27b,V3b_27_2E0: A_27b,V4f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V5f_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))] :
      ( ( ( V0l_2E0 = V1l_27_2E0 )
        & ( V2b_2E0 = V3b_27_2E0 )
        & ! [V6x_2E0: A_27a,V7a_2E0: A_27b] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_27_2E0)))
           => ( app_2E2(A_27a,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0,V7a_2E0),V6x_2E0) = app_2E2(A_27a,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27b),V5f_27_2E0,V7a_2E0),V6x_2E0) ) ) )
     => ( c_2Elist_2EFOLDL_2E3(A_27a,A_27b,V4f_2E0,V2b_2E0,V0l_2E0) = c_2Elist_2EFOLDL_2E3(A_27a,A_27b,V5f_27_2E0,V3b_27_2E0,V1l_27_2E0) ) ) ).

tff(thm_2Elist_2EFOLDR__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1l_27_2E0: tyop_2Elist_2Elist(A_27a),V2b_2E0: A_27b,V3b_27_2E0: A_27b,V4f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V5f_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))] :
      ( ( ( V0l_2E0 = V1l_27_2E0 )
        & ( V2b_2E0 = V3b_27_2E0 )
        & ! [V6x_2E0: A_27a,V7a_2E0: A_27b] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_27_2E0)))
           => ( app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V4f_2E0,V6x_2E0),V7a_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V5f_27_2E0,V6x_2E0),V7a_2E0) ) ) )
     => ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V4f_2E0,V2b_2E0,V0l_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V5f_27_2E0,V3b_27_2E0,V1l_27_2E0) ) ) ).

tff(thm_2Elist_2Elist__size__cong,axiom,
    ! [A_27a: $tType,V0M_2E0: tyop_2Elist_2Elist(A_27a),V1N_2E0: tyop_2Elist_2Elist(A_27a),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
      ( ( ( V0M_2E0 = V1N_2E0 )
        & ! [V4x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1N_2E0)))
           => ( app_2E2(A_27a,tyop_2Enum_2Enum,V2f_2E0,V4x_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,V3f_27_2E0,V4x_2E0) ) ) )
     => ( c_2Elist_2Elist__size_2E2(A_27a,V2f_2E0,V0M_2E0) = c_2Elist_2Elist__size_2E2(A_27a,V3f_27_2E0,V1N_2E0) ) ) ).

tff(thm_2Elist_2ELIST__REL__SPLIT2,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0xs2_2E0: tyop_2Elist_2Elist(A_27a),V1P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2xs1_2E0: tyop_2Elist_2Elist(A_27a),V3zs_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( p(c_2Elist_2ELIST__REL_2E3(A_27b,A_27a,V1P_2E0,V3zs_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2xs1_2E0,V0xs2_2E0)))
    <=> ? [V4ys1_2E0: tyop_2Elist_2Elist(A_27b),V5ys2_2E0: tyop_2Elist_2Elist(A_27b)] :
          ( ( V3zs_2E0 = c_2Elist_2EAPPEND_2E2(A_27b,V4ys1_2E0,V5ys2_2E0) )
          & p(c_2Elist_2ELIST__REL_2E3(A_27b,A_27a,V1P_2E0,V4ys1_2E0,V2xs1_2E0))
          & p(c_2Elist_2ELIST__REL_2E3(A_27b,A_27a,V1P_2E0,V5ys2_2E0,V0xs2_2E0)) ) ) ).

tff(thm_2Elist_2ELIST__REL__SPLIT1,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0xs2_2E0: tyop_2Elist_2Elist(A_27a),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2xs1_2E0: tyop_2Elist_2Elist(A_27a),V3zs_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V1P_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2xs1_2E0,V0xs2_2E0),V3zs_2E0))
    <=> ? [V4ys1_2E0: tyop_2Elist_2Elist(A_27b),V5ys2_2E0: tyop_2Elist_2Elist(A_27b)] :
          ( ( V3zs_2E0 = c_2Elist_2EAPPEND_2E2(A_27b,V4ys1_2E0,V5ys2_2E0) )
          & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V1P_2E0,V2xs1_2E0,V4ys1_2E0))
          & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V1P_2E0,V0xs2_2E0,V5ys2_2E0)) ) ) ).

tff(thm_2Elist_2ELIST__REL__LENGTH,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0P_2E0,V1l1_2E0,V2l2_2E0))
     => ( c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V2l2_2E0) ) ) ).

tff(thm_2Elist_2ELIST__REL__MAP2,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] :
      ( ! [V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V6a_2E0: A_27a,V7b_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,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_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),F1_2E0,V3R_2E0),V2f_2E0),V6a_2E0),V7b_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3R_2E0,V6a_2E0),app_2E2(A_27c,A_27b,V2f_2E0,V7b_2E0)) )
     => ( ! [V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4a_2E0: A_27a,V5b_2E0: A_27b] : ( 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_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F0_2E0,V3R_2E0),V4a_2E0),V5b_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3R_2E0,V4a_2E0),V5b_2E0) )
       => ! [V0l2_2E0: tyop_2Elist_2Elist(A_27c),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F0_2E0,V3R_2E0),V1l1_2E0,c_2Elist_2EMAP_2E2(A_27c,A_27b,V2f_2E0,V0l2_2E0)) = c_2Elist_2ELIST__REL_2E3(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,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_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),F1_2E0,V3R_2E0),V2f_2E0),V1l1_2E0,V0l2_2E0) ) ) ) ).

tff(thm_2Elist_2ELIST__REL__MAP1,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27c),V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V3R_2E0,c_2Elist_2EMAP_2E2(A_27c,A_27a,V2f_2E0,V1l1_2E0),V0l2_2E0) = c_2Elist_2ELIST__REL_2E3(A_27c,A_27b,c_2Ecombin_2Eo_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,V3R_2E0,V2f_2E0),V1l1_2E0,V0l2_2E0) ) ).

tff(thm_2Elist_2ELIST__REL__CONJ,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] :
      ( ! [V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4a_2E0: A_27a,V5b_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_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,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_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V3P_2E0),V2Q_2E0),V4a_2E0),V5b_2E0))
        <=> ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0,V4a_2E0),V5b_2E0))
            & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0,V4a_2E0),V5b_2E0)) ) )
     => ( ! [V2Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V8a_2E0: A_27a,V9b_2E0: A_27b] : ( 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_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F2_2E0,V2Q_2E0),V8a_2E0),V9b_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0,V8a_2E0),V9b_2E0) )
       => ( ! [V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V6a_2E0: A_27a,V7b_2E0: A_27b] : ( 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_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V3P_2E0),V6a_2E0),V7b_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0,V6a_2E0),V7b_2E0) )
         => ! [V0l2_2E0: tyop_2Elist_2Elist(A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
              ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_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_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V3P_2E0),V2Q_2E0),V1l1_2E0,V0l2_2E0))
            <=> ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V3P_2E0),V1l1_2E0,V0l2_2E0))
                & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F2_2E0,V2Q_2E0),V1l1_2E0,V0l2_2E0)) ) ) ) ) ) ).

tff(thm_2Elist_2ELIST__REL__CONS2,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27a),V1t_2E0: tyop_2Elist_2Elist(A_27b),V2h_2E0: A_27b,V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V3R_2E0,V0xs_2E0,c_2Elist_2ECONS_2E2(A_27b,V2h_2E0,V1t_2E0)))
    <=> ? [V4h_27_2E0: A_27a,V5t_27_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( V0xs_2E0 = c_2Elist_2ECONS_2E2(A_27a,V4h_27_2E0,V5t_27_2E0) )
          & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3R_2E0,V4h_27_2E0),V2h_2E0))
          & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V3R_2E0,V5t_27_2E0,V1t_2E0)) ) ) ).

tff(thm_2Elist_2ELIST__REL__CONS1,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27b),V1t_2E0: tyop_2Elist_2Elist(A_27a),V2h_2E0: A_27a,V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V3R_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V1t_2E0),V0xs_2E0))
    <=> ? [V4h_27_2E0: A_27b,V5t_27_2E0: tyop_2Elist_2Elist(A_27b)] :
          ( ( V0xs_2E0 = c_2Elist_2ECONS_2E2(A_27b,V4h_27_2E0,V5t_27_2E0) )
          & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3R_2E0,V2h_2E0),V4h_27_2E0))
          & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V3R_2E0,V1t_2E0,V5t_27_2E0)) ) ) ).

tff(thm_2Elist_2ELIST__REL__NIL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0y_2E0: tyop_2Elist_2Elist(A_27b),V1x_2E0: tyop_2Elist_2Elist(A_27a),V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V2R_2E0,c_2Elist_2ENIL_2E0(A_27a),V0y_2E0))
      <=> ( V0y_2E0 = c_2Elist_2ENIL_2E0(A_27b) ) )
      & ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V2R_2E0,V1x_2E0,c_2Elist_2ENIL_2E0(A_27b)))
      <=> ( V1x_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ) ).

tff(thm_2Elist_2ELIST__REL__mono,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( ! [V4x_2E0: A_27a,V5y_2E0: A_27b] :
          ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3R1_2E0,V4x_2E0),V5y_2E0))
         => p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2R2_2E0,V4x_2E0),V5y_2E0)) )
     => ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V3R1_2E0,V1l1_2E0,V0l2_2E0))
       => p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V2R2_2E0,V1l1_2E0,V0l2_2E0)) ) ) ).

tff(thm_2Elist_2ELIST__REL__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0bs_2E0: tyop_2Elist_2Elist(A_27b),V1b_2E0: A_27b,V2as_2E0: tyop_2Elist_2Elist(A_27a),V3a_2E0: A_27a,V4R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27b)) = c_2Ebool_2ET_2E0 )
      & ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,c_2Elist_2ECONS_2E2(A_27a,V3a_2E0,V2as_2E0),c_2Elist_2ENIL_2E0(A_27b)) = c_2Ebool_2EF_2E0 )
      & ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27b,V1b_2E0,V0bs_2E0)) = c_2Ebool_2EF_2E0 )
      & ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,c_2Elist_2ECONS_2E2(A_27a,V3a_2E0,V2as_2E0),c_2Elist_2ECONS_2E2(A_27b,V1b_2E0,V0bs_2E0)))
      <=> ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4R_2E0,V3a_2E0),V1b_2E0))
          & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,V2as_2E0,V0bs_2E0)) ) ) ) ).

tff(thm_2Elist_2EWF__LIST__PRED,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] :
      ( ! [V0L1_2E0: tyop_2Elist_2Elist(A_27a),V1L2_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0L1_2E0),V1L2_2E0))
        <=> ? [V2h_2E0: A_27a] : ( V1L2_2E0 = c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V0L1_2E0) ) )
     => p(c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(A_27a),F0_2E0)) ) ).

tff(thm_2Elist_2ENULL__FILTER,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ls_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2ENULL_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1ls_2E0)))
    <=> ! [V2x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1ls_2E0)))
         => ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) ) ) ).

tff(thm_2Elist_2ESUM__eq__0,axiom,
    ! [V0ls_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] :
      ( ( c_2Elist_2ESUM_2E1(V0ls_2E0) = c_2Enum_2E0_2E0 )
    <=> ! [V1x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,V0ls_2E0)))
         => ( V1x_2E0 = c_2Enum_2E0_2E0 ) ) ) ).

tff(thm_2Elist_2EEL__simp__restricted,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ls_2E0: tyop_2Elist_2Elist(A_27a),V2l_2E0: A_27a] :
      ( ( c_2Elist_2EEL_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)),c_2Elist_2ECONS_2E2(A_27a,V2l_2E0,V1ls_2E0)) = c_2Elist_2EEL_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0))),V1ls_2E0) )
      & ( c_2Elist_2EEL_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V0n_2E0)),c_2Elist_2ECONS_2E2(A_27a,V2l_2E0,V1ls_2E0)) = c_2Elist_2EEL_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)),V1ls_2E0) ) ) ).

tff(thm_2Elist_2EEL__restricted,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ls_2E0: tyop_2Elist_2Elist(A_27b),V2l_2E0: A_27b] :
      ( ( c_2Elist_2EEL_2E1(A_27a,c_2Enum_2E0_2E0) = c_2Elist_2EHD_2E0(A_27a) )
      & ( c_2Elist_2EEL_2E2(A_27b,c_2Enum_2ESUC_2E1(V0n_2E0),c_2Elist_2ECONS_2E2(A_27b,V2l_2E0,V1ls_2E0)) = c_2Elist_2EEL_2E2(A_27b,V0n_2E0,V1ls_2E0) ) ) ).

tff(thm_2Elist_2EEL__simp,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2EEL_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)),V1l_2E0) = c_2Elist_2EEL_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0))),c_2Elist_2ETL_2E1(A_27a,V1l_2E0)) )
      & ( c_2Elist_2EEL_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V0n_2E0)),V1l_2E0) = c_2Elist_2EEL_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)),c_2Elist_2ETL_2E1(A_27a,V1l_2E0)) ) ) ).

tff(thm_2Elist_2EEL__compute,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V1n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1n_2E0))
        <=> ( V1n_2E0 = c_2Enum_2E0_2E0 ) )
     => ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EEL_2E2(A_27a,V1n_2E0,V0l_2E0) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1n_2E0),c_2Elist_2EHD_2E1(A_27a,V0l_2E0),c_2Elist_2EEL_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(V1n_2E0),c_2Elist_2ETL_2E1(A_27a,V0l_2E0))) ) ) ).

tff(thm_2Elist_2ENOT__NULL__MEM,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ~ p(c_2Elist_2ENULL_2E1(A_27a,V0l_2E0))
    <=> ? [V1e_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V1e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0))) ) ).

tff(thm_2Elist_2EFILTER__COND__REWRITE,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V2h_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2h_2E0))
         => ( c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V0l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,V0l_2E0)) ) )
      & ! [V3h_2E0: A_27a] :
          ( ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3h_2E0))
         => ( c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,V0l_2E0)) = c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,V0l_2E0) ) ) ) ).

tff(thm_2Elist_2EEVERY__FILTER__IMP,axiom,
    ! [A_27a: $tType,V0P1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EEVERY_2E2(A_27a,V0P1_2E0,V2l_2E0))
     => p(c_2Elist_2EEVERY_2E2(A_27a,V0P1_2E0,c_2Elist_2EFILTER_2E2(A_27a,V1P2_2E0,V2l_2E0))) ) ).

tff(thm_2Elist_2EEVERY__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)))] :
      ( ! [V1P2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_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,V1P2_2E0),V0P1_2E0),V3x_2E0))
        <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P2_2E0,V3x_2E0))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P1_2E0,V3x_2E0)) ) )
     => ! [V0P1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEVERY_2E2(A_27a,V0P1_2E0,c_2Elist_2EFILTER_2E2(A_27a,V1P2_2E0,V2l_2E0)) = c_2Elist_2EEVERY_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,V1P2_2E0),V0P1_2E0),V2l_2E0) ) ) ).

tff(thm_2Elist_2EFILTER__EQ__APPEND,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a),V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V3l2_2E0) )
    <=> ? [V4l3_2E0: tyop_2Elist_2Elist(A_27a),V5l4_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( V1l_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V4l3_2E0,V5l4_2E0) )
          & ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V4l3_2E0) = V2l1_2E0 )
          & ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V5l4_2E0) = V3l2_2E0 ) ) ) ).

tff(thm_2Elist_2EMEM,axiom,
    ! [A_27a: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a))) = c_2Ebool_2EF_2E0 )
      & ! [V1x_2E0: A_27a,V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0))))
        <=> ( ( V1x_2E0 = V2h_2E0 )
            | p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V3t_2E0))) ) ) ) ).

tff(thm_2Elist_2EFILTER__APPEND__DISTRIB,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1L_2E0: tyop_2Elist_2Elist(A_27a),V2M_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1L_2E0,V2M_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1L_2E0),c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V2M_2E0)) ) ).

tff(thm_2Elist_2EFILTER__EQ__CONS,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a),V2h_2E0: A_27a,V3lr_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3lr_2E0) )
    <=> ? [V4l1_2E0: tyop_2Elist_2Elist(A_27a),V5l2_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( V1l_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V4l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,c_2Elist_2ENIL_2E0(A_27a))),V5l2_2E0) )
          & ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V4l1_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
          & ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V5l2_2E0) = V3lr_2E0 )
          & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2h_2E0)) ) ) ).

tff(thm_2Elist_2EFILTER__NEQ__ID,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l_2E0) != V1l_2E0 )
    <=> ? [V2x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)))
          & ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) ) ) ).

tff(thm_2Elist_2EFILTER__EQ__ID,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l_2E0) = V1l_2E0 )
    <=> p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0)) ) ).

tff(thm_2Elist_2EFILTER__NEQ__NIL,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l_2E0) != c_2Elist_2ENIL_2E0(A_27a) )
    <=> ? [V2x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)))
          & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) ) ) ).

tff(thm_2Elist_2EFILTER__EQ__NIL,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0P_2E0),V2x_2E0))
        <=> ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
     => ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
        <=> p(c_2Elist_2EEVERY_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0P_2E0),V1l_2E0)) ) ) ).

tff(thm_2Elist_2ELENGTH__TL,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)))
     => ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2ETL_2E1(A_27a,V0l_2E0)) = c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).

tff(thm_2Elist_2EFOLDR__CONS,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3x_2E0: A_27a,V4y_2E0: tyop_2Elist_2Elist(A_27b)] : ( app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),F0_2E0,V0f_2E0),V3x_2E0),V4y_2E0) = c_2Elist_2ECONS_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0),V4y_2E0) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1ls_2E0: tyop_2Elist_2Elist(A_27a),V2a_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),F0_2E0,V0f_2E0),V2a_2E0,V1ls_2E0) = c_2Elist_2EAPPEND_2E2(A_27b,c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V1ls_2E0),V2a_2E0) ) ) ).

tff(thm_2Elist_2EFOLDL__EQ__FOLDR,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V1l_2E0: tyop_2Elist_2Elist(A_27a),V2e_2E0: A_27a] :
      ( ( p(c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0))
        & p(c_2Ecombin_2ECOMM_2E1(A_27a,A_27a,V0f_2E0)) )
     => ( c_2Elist_2EFOLDL_2E3(A_27a,A_27a,V0f_2E0,V2e_2E0,V1l_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V2e_2E0,V1l_2E0) ) ) ).

tff(thm_2Elist_2ELIST__EQ,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V1l2_2E0) )
        & ! [V2x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Eprim__rec_2E_3C_2E2(V2x_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0)))
           => ( c_2Elist_2EEL_2E2(A_27a,V2x_2E0,V0l1_2E0) = c_2Elist_2EEL_2E2(A_27a,V2x_2E0,V1l2_2E0) ) ) )
     => ( V0l1_2E0 = V1l2_2E0 ) ) ).

tff(thm_2Elist_2ELIST__EQ__REWRITE,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( V0l1_2E0 = V1l2_2E0 )
    <=> ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V1l2_2E0) )
        & ! [V2x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Eprim__rec_2E_3C_2E2(V2x_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0)))
           => ( c_2Elist_2EEL_2E2(A_27a,V2x_2E0,V0l1_2E0) = c_2Elist_2EEL_2E2(A_27a,V2x_2E0,V1l2_2E0) ) ) ) ) ).

tff(thm_2Elist_2EMEM__SPLIT,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)))
    <=> ? [V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( V1l_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V3l2_2E0)) ) ) ).

tff(thm_2Elist_2EAPPEND__EQ__SELF,axiom,
    ! [A_27a: $tType] :
      ( ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0) = V0l1_2E0 )
        <=> ( V1l2_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
      & ! [V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V3l2_2E0) = V3l2_2E0 )
        <=> ( V2l1_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
      & ! [V4l1_2E0: tyop_2Elist_2Elist(A_27a),V5l2_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( V4l1_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V4l1_2E0,V5l2_2E0) )
        <=> ( V5l2_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
      & ! [V6l1_2E0: tyop_2Elist_2Elist(A_27a),V7l2_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( V7l2_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V6l1_2E0,V7l2_2E0) )
        <=> ( V6l1_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ) ).

tff(thm_2Elist_2EAPPEND__11__LENGTH,axiom,
    ! [A_27a: $tType] :
      ( ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2l1_27_2E0: tyop_2Elist_2Elist(A_27a),V3l2_27_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V2l1_27_2E0) )
         => ( ( c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,V2l1_27_2E0,V3l2_27_2E0) )
          <=> ( ( V0l1_2E0 = V2l1_27_2E0 )
              & ( V1l2_2E0 = V3l2_27_2E0 ) ) ) )
      & ! [V4l1_2E0: tyop_2Elist_2Elist(A_27a),V5l2_2E0: tyop_2Elist_2Elist(A_27a),V6l1_27_2E0: tyop_2Elist_2Elist(A_27a),V7l2_27_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V5l2_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V7l2_27_2E0) )
         => ( ( c_2Elist_2EAPPEND_2E2(A_27a,V4l1_2E0,V5l2_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,V6l1_27_2E0,V7l2_27_2E0) )
          <=> ( ( V4l1_2E0 = V6l1_27_2E0 )
              & ( V5l2_2E0 = V7l2_27_2E0 ) ) ) ) ) ).

tff(thm_2Elist_2EAPPEND__LENGTH__EQ,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l1_27_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V1l1_27_2E0) )
     => ! [V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3l2_27_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V2l2_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V3l2_27_2E0) )
         => ( ( c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V2l2_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,V1l1_27_2E0,V3l2_27_2E0) )
          <=> ( ( V0l1_2E0 = V1l1_27_2E0 )
              & ( V2l2_2E0 = V3l2_27_2E0 ) ) ) ) ) ).

tff(thm_2Elist_2EAPPEND__11,axiom,
    ! [A_27a: $tType] :
      ( ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2l3_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V2l3_2E0) )
        <=> ( V1l2_2E0 = V2l3_2E0 ) )
      & ! [V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4l2_2E0: tyop_2Elist_2Elist(A_27a),V5l3_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2EAPPEND_2E2(A_27a,V4l2_2E0,V3l1_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,V5l3_2E0,V3l1_2E0) )
        <=> ( V4l2_2E0 = V5l3_2E0 ) ) ) ).

tff(thm_2Elist_2EAPPEND__EQ__SING,axiom,
    ! [A_27a: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2e_2E0: A_27a] :
      ( ( c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V0l2_2E0) = c_2Elist_2ECONS_2E2(A_27a,V2e_2E0,c_2Elist_2ENIL_2E0(A_27a)) )
    <=> ( ( ( V1l1_2E0 = c_2Elist_2ECONS_2E2(A_27a,V2e_2E0,c_2Elist_2ENIL_2E0(A_27a)) )
          & ( V0l2_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
        | ( ( V1l1_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
          & ( V0l2_2E0 = c_2Elist_2ECONS_2E2(A_27a,V2e_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ) ) ) ).

tff(thm_2Elist_2EMAP__EQ__APPEND,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27b),V2l_2E0: tyop_2Elist_2Elist(A_27a),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V3f_2E0,V2l_2E0) = c_2Elist_2EAPPEND_2E2(A_27b,V1l1_2E0,V0l2_2E0) )
    <=> ? [V4l10_2E0: tyop_2Elist_2Elist(A_27a),V5l20_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( V2l_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V4l10_2E0,V5l20_2E0) )
          & ( V1l1_2E0 = c_2Elist_2EMAP_2E2(A_27a,A_27b,V3f_2E0,V4l10_2E0) )
          & ( V0l2_2E0 = c_2Elist_2EMAP_2E2(A_27a,A_27b,V3f_2E0,V5l20_2E0) ) ) ) ).

tff(thm_2Elist_2EAPPEND__eq__NIL,axiom,
    ! [A_27a: $tType] :
      ( ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2ENIL_2E0(A_27a) = c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0) )
        <=> ( ( V0l1_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
            & ( V1l2_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) )
      & ! [V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V3l2_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
        <=> ( ( V2l1_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
            & ( V3l2_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ) ) ).

tff(thm_2Elist_2ECONS__ACYCLIC,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a] :
      ( ( V0l_2E0 != c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V0l_2E0) )
      & ( c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V0l_2E0) != V0l_2E0 ) ) ).

tff(thm_2Elist_2ELENGTH__EQ__NIL,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
      ( ! [V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0) = c_2Enum_2E0_2E0 )
         => p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1l_2E0)) )
    <=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a))) ) ).

tff(thm_2Elist_2ELENGTH__EQ__NUM__compute,axiom,
    ! [A_27a: $tType] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) = c_2Enum_2E0_2E0 )
        <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
      & ! [V1l_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2n_2E0)) )
        <=> ? [V3h_2E0: A_27a,V4l_27_2E0: tyop_2Elist_2Elist(A_27a)] :
              ( ( c_2Elist_2ELENGTH_2E1(A_27a,V4l_27_2E0) = c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
              & ( V1l_2E0 = c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,V4l_27_2E0) ) ) )
      & ! [V5l_2E0: tyop_2Elist_2Elist(A_27a),V6n_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V5l_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V6n_2E0)) )
        <=> ? [V7h_2E0: A_27a,V8l_27_2E0: tyop_2Elist_2Elist(A_27a)] :
              ( ( c_2Elist_2ELENGTH_2E1(A_27a,V8l_27_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V6n_2E0)) )
              & ( V5l_2E0 = c_2Elist_2ECONS_2E2(A_27a,V7h_2E0,V8l_27_2E0) ) ) )
      & ! [V9l_2E0: tyop_2Elist_2Elist(A_27a),V10n1_2E0: tyop_2Enum_2Enum,V11n2_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V9l_2E0) = c_2Earithmetic_2E_2B_2E2(V10n1_2E0,V11n2_2E0) )
        <=> ? [V12l1_2E0: tyop_2Elist_2Elist(A_27a),V13l2_2E0: tyop_2Elist_2Elist(A_27a)] :
              ( ( c_2Elist_2ELENGTH_2E1(A_27a,V12l1_2E0) = V10n1_2E0 )
              & ( c_2Elist_2ELENGTH_2E1(A_27a,V13l2_2E0) = V11n2_2E0 )
              & ( V9l_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V12l1_2E0,V13l2_2E0) ) ) ) ) ).

tff(thm_2Elist_2ELENGTH__EQ__NUM,axiom,
    ! [A_27a: $tType] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) = c_2Enum_2E0_2E0 )
        <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
      & ! [V1l_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0) = c_2Enum_2ESUC_2E1(V2n_2E0) )
        <=> ? [V3h_2E0: A_27a,V4l_27_2E0: tyop_2Elist_2Elist(A_27a)] :
              ( ( c_2Elist_2ELENGTH_2E1(A_27a,V4l_27_2E0) = V2n_2E0 )
              & ( V1l_2E0 = c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,V4l_27_2E0) ) ) )
      & ! [V5l_2E0: tyop_2Elist_2Elist(A_27a),V6n1_2E0: tyop_2Enum_2Enum,V7n2_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V5l_2E0) = c_2Earithmetic_2E_2B_2E2(V6n1_2E0,V7n2_2E0) )
        <=> ? [V8l1_2E0: tyop_2Elist_2Elist(A_27a),V9l2_2E0: tyop_2Elist_2Elist(A_27a)] :
              ( ( c_2Elist_2ELENGTH_2E1(A_27a,V8l1_2E0) = V6n1_2E0 )
              & ( c_2Elist_2ELENGTH_2E1(A_27a,V9l2_2E0) = V7n2_2E0 )
              & ( V5l_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V8l1_2E0,V9l2_2E0) ) ) ) ) ).

tff(thm_2Elist_2ELENGTH__EQ__SUM,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1n1_2E0: tyop_2Enum_2Enum,V2n2_2E0: tyop_2Enum_2Enum] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) = c_2Earithmetic_2E_2B_2E2(V1n1_2E0,V2n2_2E0) )
    <=> ? [V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4l2_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V3l1_2E0) = V1n1_2E0 )
          & ( c_2Elist_2ELENGTH_2E1(A_27a,V4l2_2E0) = V2n2_2E0 )
          & ( V0l_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V3l1_2E0,V4l2_2E0) ) ) ) ).

tff(thm_2Elist_2ELENGTH__EQ__CONS,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] :
      ( ! [V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0) = c_2Enum_2ESUC_2E1(V1n_2E0) )
         => p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V2l_2E0)) )
    <=> ! [V3l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V3l_2E0) = V1n_2E0 )
         => ! [V4x_2E0: A_27a] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,V3l_2E0))) ) ) ).

tff(thm_2Elist_2ELENGTH__CONS,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) = c_2Enum_2ESUC_2E1(V1n_2E0) )
    <=> ? [V2h_2E0: A_27a,V3l_27_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V3l_27_2E0) = V1n_2E0 )
          & ( V0l_2E0 = c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3l_27_2E0) ) ) ) ).

tff(thm_2Elist_2ENULL__LENGTH,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2ENULL_2E1(A_27a,V0l_2E0))
    <=> ( c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) = c_2Enum_2E0_2E0 ) ) ).

tff(thm_2Elist_2ENULL__EQ,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2ENULL_2E1(A_27a,V0l_2E0))
    <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ).

tff(thm_2Elist_2ELENGTH__NIL__SYM,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Enum_2E0_2E0 = c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) )
    <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ).

tff(thm_2Elist_2ELENGTH__NIL,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) = c_2Enum_2E0_2E0 )
    <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ).

tff(thm_2Elist_2EMEM__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27b] :
      ( p(c_2Ebool_2EIN_2E2(A_27b,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27b,c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,V0l_2E0))))
    <=> ? [V3y_2E0: A_27a] :
          ( ( V2x_2E0 = app_2E2(A_27a,A_27b,V1f_2E0,V3y_2E0) )
          & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0))) ) ) ).

tff(thm_2Elist_2ENOT__EXISTS,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ~ p(c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,V1l_2E0))
    <=> p(c_2Elist_2EEVERY_2E2(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),V1l_2E0)) ) ).

tff(thm_2Elist_2ENOT__EVERY,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ~ p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0))
    <=> p(c_2Elist_2EEXISTS_2E2(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),V1l_2E0)) ) ).

tff(thm_2Elist_2EEXISTS__APPEND,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)))
    <=> ( p(c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,V1l1_2E0))
        | p(c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,V2l2_2E0)) ) ) ).

tff(thm_2Elist_2EEVERY__APPEND,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)))
    <=> ( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l1_2E0))
        & p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V2l2_2E0)) ) ) ).

tff(thm_2Elist_2EFLAT__compute,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0t2_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),V1t1_2E0: tyop_2Elist_2Elist(A_27c),V2t_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V3h_2E0: A_27c] :
      ( ( c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2ENIL_2E0(tyop_2Elist_2Elist(A_27a))) = c_2Elist_2ENIL_2E0(A_27a) )
      & ( c_2Elist_2EFLAT_2E1(A_27b,c_2Elist_2ECONS_2E2(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0(A_27b),V2t_2E0)) = c_2Elist_2EFLAT_2E1(A_27b,V2t_2E0) )
      & ( c_2Elist_2EFLAT_2E1(A_27c,c_2Elist_2ECONS_2E2(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(A_27c,V3h_2E0,V1t1_2E0),V0t2_2E0)) = c_2Elist_2ECONS_2E2(A_27c,V3h_2E0,c_2Elist_2EFLAT_2E1(A_27c,c_2Elist_2ECONS_2E2(tyop_2Elist_2Elist(A_27c),V1t1_2E0,V0t2_2E0))) ) ) ).

tff(thm_2Elist_2EFLAT__APPEND,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1l2_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2EAPPEND_2E2(tyop_2Elist_2Elist(A_27a),V0l1_2E0,V1l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EFLAT_2E1(A_27a,V0l1_2E0),c_2Elist_2EFLAT_2E1(A_27a,V1l2_2E0)) ) ).

tff(thm_2Elist_2EMEM__FLAT,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1L_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EFLAT_2E1(A_27a,V1L_2E0))))
    <=> ? [V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),V2l_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Elist_2Elist(A_27a),V1L_2E0)))
          & p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2l_2E0))) ) ) ).

tff(thm_2Elist_2EMEM__FILTER,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1L_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1L_2E0))))
    <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1L_2E0))) ) ) ).

tff(thm_2Elist_2EMEM__APPEND,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0))))
    <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l1_2E0)))
        | p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2l2_2E0))) ) ) ).

tff(thm_2Elist_2EEXISTS__NOT__EVERY,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0P_2E0),V2x_2E0))
        <=> ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
     => ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,V1l_2E0))
        <=> ~ p(c_2Elist_2EEVERY_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0P_2E0),V1l_2E0)) ) ) ).

tff(thm_2Elist_2EEVERY__NOT__EXISTS,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0P_2E0),V2x_2E0))
        <=> ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
     => ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0))
        <=> ~ p(c_2Elist_2EEXISTS_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0P_2E0),V1l_2E0)) ) ) ).

tff(thm_2Elist_2EMONO__EXISTS,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V3x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3x_2E0))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) )
     => ( p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,V0l_2E0))
       => p(c_2Elist_2EEXISTS_2E2(A_27a,V1Q_2E0,V0l_2E0)) ) ) ).

tff(thm_2Elist_2EEXISTS__SIMP,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V0c_2E0: tyop_2Emin_2Ebool,V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0c_2E0),V2x_2E0) = V0c_2E0 )
     => ! [V0c_2E0: tyop_2Emin_2Ebool,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Elist_2EEXISTS_2E2(A_27a,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0c_2E0),V1l_2E0))
        <=> ( ( V1l_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
            & p(V0c_2E0) ) ) ) ).

tff(thm_2Elist_2EEXISTS__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1f_2E0),V3x_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,V0P_2E0,app_2E2(A_27a,A_27b,V1f_2E0,V3x_2E0)) )
     => ! [V0P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEXISTS_2E2(A_27b,V0P_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,V2l_2E0)) = c_2Elist_2EEXISTS_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1f_2E0),V2l_2E0) ) ) ).

tff(thm_2Elist_2EEXISTS__MEM,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,V1l_2E0))
    <=> ? [V2e_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V2e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)))
          & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2e_2E0)) ) ) ).

tff(thm_2Elist_2EMONO__EVERY,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V3x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3x_2E0))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) )
     => ( p(c_2Elist_2EEVERY_2E2(A_27a,V2P_2E0,V0l_2E0))
       => p(c_2Elist_2EEVERY_2E2(A_27a,V1Q_2E0,V0l_2E0)) ) ) ).

tff(thm_2Elist_2EEVERY__SIMP,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V0c_2E0: tyop_2Emin_2Ebool,V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0c_2E0),V2x_2E0) = V0c_2E0 )
     => ! [V0c_2E0: tyop_2Emin_2Ebool,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Elist_2EEVERY_2E2(A_27a,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0c_2E0),V1l_2E0))
        <=> ( ( V1l_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
            | p(V0c_2E0) ) ) ) ).

tff(thm_2Elist_2EEVERY__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1f_2E0),V3x_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,V0P_2E0,app_2E2(A_27a,A_27b,V1f_2E0,V3x_2E0)) )
     => ! [V0P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEVERY_2E2(A_27b,V0P_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,V2l_2E0)) = c_2Elist_2EEVERY_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1f_2E0),V2l_2E0) ) ) ).

tff(thm_2Elist_2EEVERY__MEM,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0))
    <=> ! [V2e_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V2e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2e_2E0)) ) ) ).

tff(thm_2Elist_2EEVERY__CONJ,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)))] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_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,V0P_2E0),V1Q_2E0),V3x_2E0))
        <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
            & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) )
     => ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Elist_2EEVERY_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,V0P_2E0),V1Q_2E0),V2l_2E0))
        <=> ( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V2l_2E0))
            & p(c_2Elist_2EEVERY_2E2(A_27a,V1Q_2E0,V2l_2E0)) ) ) ) ).

tff(thm_2Elist_2EEVERY__EL,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Elist_2EEVERY_2E2(A_27a,V1P_2E0,V0l_2E0))
    <=> ! [V2n_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,c_2Elist_2EEL_2E2(A_27a,V2n_2E0,V0l_2E0))) ) ) ).

tff(thm_2Elist_2EMAP__TL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ~ p(c_2Elist_2ENULL_2E1(A_27a,V0l_2E0))
     => ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,c_2Elist_2ETL_2E1(A_27a,V0l_2E0)) = c_2Elist_2ETL_2E1(A_27b,c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,V0l_2E0)) ) ) ).

tff(thm_2Elist_2EEL__APPEND__EQN,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EEL_2E2(A_27a,V2n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = c_2Ebool_2ECOND_2E3(A_27a,c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0)),c_2Elist_2EEL_2E2(A_27a,V2n_2E0,V0l1_2E0),c_2Elist_2EEL_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V2n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0)),V1l2_2E0)) ) ).

tff(thm_2Elist_2EEL__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
     => ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Elist_2EEL_2E2(A_27b,V0n_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,V2f_2E0,V1l_2E0)) = app_2E2(A_27a,A_27b,V2f_2E0,c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ) ).

tff(thm_2Elist_2EMAP__MAP__o,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27b,A_27c,V0f_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,V1g_2E0,V2l_2E0)) = c_2Elist_2EMAP_2E2(A_27a,A_27c,c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,V0f_2E0,V1g_2E0),V2l_2E0) ) ).

tff(thm_2Elist_2EMAP__o,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Elist_2EMAP_2E1(A_27a,A_27c,c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,V0f_2E0,V1g_2E0)) = c_2Ecombin_2Eo_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E1(A_27b,A_27c,V0f_2E0),c_2Elist_2EMAP_2E1(A_27a,A_27b,V1g_2E0)) ) ).

tff(thm_2Elist_2EMAP__EQ__f,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f1_2E0,V2l_2E0) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f2_2E0,V2l_2E0) )
    <=> ! [V3e_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V3e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2l_2E0)))
         => ( app_2E2(A_27a,A_27b,V0f1_2E0,V3e_2E0) = app_2E2(A_27a,A_27b,V1f2_2E0,V3e_2E0) ) ) ) ).

tff(thm_2Elist_2EMAP__EQ__SING,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1l_2E0: tyop_2Elist_2Elist(A_27a),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V2f_2E0,V1l_2E0) = c_2Elist_2ECONS_2E2(A_27b,V0x_2E0,c_2Elist_2ENIL_2E0(A_27b)) )
    <=> ? [V3x0_2E0: A_27a] :
          ( ( V1l_2E0 = c_2Elist_2ECONS_2E2(A_27a,V3x0_2E0,c_2Elist_2ENIL_2E0(A_27a)) )
          & ( V0x_2E0 = app_2E2(A_27a,A_27b,V2f_2E0,V3x0_2E0) ) ) ) ).

tff(thm_2Elist_2EMAP__EQ__CONS,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Elist_2Elist(A_27b),V1l_2E0: tyop_2Elist_2Elist(A_27a),V2h_2E0: A_27b,V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V3f_2E0,V1l_2E0) = c_2Elist_2ECONS_2E2(A_27b,V2h_2E0,V0t_2E0) )
    <=> ? [V4x0_2E0: A_27a,V5t0_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( V1l_2E0 = c_2Elist_2ECONS_2E2(A_27a,V4x0_2E0,V5t0_2E0) )
          & ( V2h_2E0 = app_2E2(A_27a,A_27b,V3f_2E0,V4x0_2E0) )
          & ( V0t_2E0 = c_2Elist_2EMAP_2E2(A_27a,A_27b,V3f_2E0,V5t0_2E0) ) ) ) ).

tff(thm_2Elist_2EMAP__EQ__NIL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,V0l_2E0) = c_2Elist_2ENIL_2E0(A_27b) )
      <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
      & ( ( c_2Elist_2ENIL_2E0(A_27b) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,V0l_2E0) )
      <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ) ).

tff(thm_2Elist_2ELENGTH__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Elist_2ELENGTH_2E1(A_27b,c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,V0l_2E0)) = c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) ) ).

tff(thm_2Elist_2EMAP__ID,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
      ( ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,F0_2E0,V1x_2E0) = V1x_2E0 )
     => ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Elist_2EMAP_2E2(A_27a,A_27a,F0_2E0,V0l_2E0) = V0l_2E0 )
          & ( c_2Elist_2EMAP_2E2(A_27a,A_27a,c_2Ecombin_2EI_2E0(A_27a),V0l_2E0) = V0l_2E0 ) ) ) ).

tff(thm_2Elist_2EMAP__APPEND,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27b,c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V1l1_2E0),c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V2l2_2E0)) ) ).

tff(thm_2Elist_2ELENGTH__APPEND,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V1l2_2E0)) ) ).

tff(thm_2Elist_2EAPPEND__ASSOC,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2l3_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l2_2E0,V2l3_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0),V2l3_2E0) ) ).

tff(thm_2Elist_2EAPPEND__NIL,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,V0l_2E0,c_2Elist_2ENIL_2E0(A_27a)) = V0l_2E0 ) ).

tff(thm_2Elist_2ECONS,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ~ p(c_2Elist_2ENULL_2E1(A_27a,V0l_2E0))
     => ( c_2Elist_2ECONS_2E2(A_27a,c_2Elist_2EHD_2E1(A_27a,V0l_2E0),c_2Elist_2ETL_2E1(A_27a,V0l_2E0)) = V0l_2E0 ) ) ).

tff(thm_2Elist_2EEQ__LIST,axiom,
    ! [A_27a: $tType,V0h1_2E0: A_27a,V1h2_2E0: A_27a] :
      ( ( V0h1_2E0 = V1h2_2E0 )
     => ! [V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( V2l1_2E0 = V3l2_2E0 )
         => ( c_2Elist_2ECONS_2E2(A_27a,V0h1_2E0,V2l1_2E0) = c_2Elist_2ECONS_2E2(A_27a,V1h2_2E0,V3l2_2E0) ) ) ) ).

tff(thm_2Elist_2ENOT__EQ__LIST,axiom,
    ! [A_27a: $tType,V0h1_2E0: A_27a,V1h2_2E0: A_27a] :
      ( ( V0h1_2E0 != V1h2_2E0 )
     => ! [V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,V0h1_2E0,V2l1_2E0) != c_2Elist_2ECONS_2E2(A_27a,V1h2_2E0,V3l2_2E0) ) ) ).

tff(thm_2Elist_2ELIST__NOT__EQ,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( V0l1_2E0 != V1l2_2E0 )
     => ! [V2h1_2E0: A_27a,V3h2_2E0: A_27a] : ( c_2Elist_2ECONS_2E2(A_27a,V2h1_2E0,V0l1_2E0) != c_2Elist_2ECONS_2E2(A_27a,V3h2_2E0,V1l2_2E0) ) ) ).

tff(thm_2Elist_2ENOT__CONS__NIL,axiom,
    ! [A_27a: $tType,V0a1_2E0: tyop_2Elist_2Elist(A_27a),V1a0_2E0: A_27a] : ( c_2Elist_2ECONS_2E2(A_27a,V1a0_2E0,V0a1_2E0) != c_2Elist_2ENIL_2E0(A_27a) ) ).

tff(thm_2Elist_2ENOT__NIL__CONS,axiom,
    ! [A_27a: $tType,V0a1_2E0: tyop_2Elist_2Elist(A_27a),V1a0_2E0: A_27a] : ( c_2Elist_2ENIL_2E0(A_27a) != c_2Elist_2ECONS_2E2(A_27a,V1a0_2E0,V0a1_2E0) ) ).

tff(thm_2Elist_2ECONS__11,axiom,
    ! [A_27a: $tType,V0a0_2E0: A_27a,V1a1_2E0: tyop_2Elist_2Elist(A_27a),V2a0_27_2E0: A_27a,V3a1_27_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2ECONS_2E2(A_27a,V0a0_2E0,V1a1_2E0) = c_2Elist_2ECONS_2E2(A_27a,V2a0_27_2E0,V3a1_27_2E0) )
    <=> ( ( V0a0_2E0 = V2a0_27_2E0 )
        & ( V1a1_2E0 = V3a1_27_2E0 ) ) ) ).

tff(thm_2Elist_2Elist__case__compute,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V1b_2E0: A_27b,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2Elist__CASE_2E3(A_27a,A_27b,V2l_2E0,V1b_2E0,V0f_2E0) = c_2Ebool_2ECOND_2E3(A_27b,c_2Elist_2ENULL_2E1(A_27a,V2l_2E0),V1b_2E0,app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V0f_2E0,c_2Elist_2EHD_2E1(A_27a,V2l_2E0)),c_2Elist_2ETL_2E1(A_27a,V2l_2E0))) ) ).

tff(thm_2Elist_2Elist__nchotomy,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
      | ? [V1h_2E0: A_27a,V2t_2E0: tyop_2Elist_2Elist(A_27a)] : ( V0l_2E0 = c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V2t_2E0) ) ) ).

tff(thm_2Elist_2Elist__distinct,axiom,
    ! [A_27a: $tType,V0a1_2E0: tyop_2Elist_2Elist(A_27a),V1a0_2E0: A_27a] : ( c_2Elist_2ENIL_2E0(A_27a) != c_2Elist_2ECONS_2E2(A_27a,V1a0_2E0,V0a1_2E0) ) ).

tff(thm_2Elist_2Elist__11,axiom,
    ! [A_27a: $tType,V0a0_2E0: A_27a,V1a1_2E0: tyop_2Elist_2Elist(A_27a),V2a0_27_2E0: A_27a,V3a1_27_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2ECONS_2E2(A_27a,V0a0_2E0,V1a1_2E0) = c_2Elist_2ECONS_2E2(A_27a,V2a0_27_2E0,V3a1_27_2E0) )
    <=> ( ( V0a0_2E0 = V2a0_27_2E0 )
        & ( V1a1_2E0 = V3a1_27_2E0 ) ) ) ).

tff(thm_2Elist_2Edatatype__list,axiom,
    ! [A_27a: $tType,V0list_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool))] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),V0list_2E0,c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ECONS_2E0(A_27a)))) ).

tff(thm_2Elist_2Elist__case__cong,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0v_27_2E0: A_27b,V1f_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V2M_2E0: tyop_2Elist_2Elist(A_27a),V3M_27_2E0: tyop_2Elist_2Elist(A_27a),V4v_2E0: A_27b,V5f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))] :
      ( ( ( V2M_2E0 = V3M_27_2E0 )
        & ( ( V3M_27_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
         => ( V4v_2E0 = V0v_27_2E0 ) )
        & ! [V6a0_2E0: A_27a,V7a1_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( ( V3M_27_2E0 = c_2Elist_2ECONS_2E2(A_27a,V6a0_2E0,V7a1_2E0) )
           => ( app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V5f_2E0,V6a0_2E0),V7a1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V1f_27_2E0,V6a0_2E0),V7a1_2E0) ) ) )
     => ( c_2Elist_2Elist__CASE_2E3(A_27a,A_27b,V2M_2E0,V4v_2E0,V5f_2E0) = c_2Elist_2Elist__CASE_2E3(A_27a,A_27b,V3M_27_2E0,V0v_27_2E0,V1f_27_2E0) ) ) ).

tff(thm_2Elist_2Elist__case__eq,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1v_27_2E0: A_27b,V2v_2E0: A_27b,V3f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))] :
      ( ( c_2Elist_2Elist__CASE_2E3(A_27a,A_27b,V0x_2E0,V2v_2E0,V3f_2E0) = V1v_27_2E0 )
    <=> ( ( ( V0x_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
          & ( V2v_2E0 = V1v_27_2E0 ) )
        | ? [V4a_2E0: A_27a,V5l_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( ( V0x_2E0 = c_2Elist_2ECONS_2E2(A_27a,V4a_2E0,V5l_2E0) )
            & ( app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V3f_2E0,V4a_2E0),V5l_2E0) = V1v_27_2E0 ) ) ) ) ).

tff(thm_2Elist_2Elist__Axiom__old,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool)))] :
      ( ! [V0x_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),V2fn1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool)),F0_2E0,V0x_2E0),V1f_2E0),V2fn1_2E0))
        <=> ( ( app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V2fn1_2E0,c_2Elist_2ENIL_2E0(A_27a)) = V0x_2E0 )
            & ! [V3h_2E0: A_27a,V4t_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V2fn1_2E0,c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,V4t_2E0)) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V1f_2E0,app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V2fn1_2E0,V4t_2E0)),V3h_2E0),V4t_2E0) ) ) )
     => ! [V0x_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)))] : p(c_2Ebool_2E_3F_21_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool)),F0_2E0,V0x_2E0),V1f_2E0))) ) ).

tff(thm_2Elist_2ETL,axiom,
    ! [A_27a: $tType,V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETL_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0)) = V1t_2E0 ) ).

tff(thm_2Elist_2ELIST__TO__SET,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Elist_2Elist(A_27b),V1h_2E0: A_27b] :
      ( ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
      & ( c_2Elist_2ELIST__TO__SET_2E1(A_27b,c_2Elist_2ECONS_2E2(A_27b,V1h_2E0,V0t_2E0)) = c_2Epred__set_2EINSERT_2E2(A_27b,V1h_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27b,V0t_2E0)) ) ) ).

tff(thm_2Elist_2EMAP2__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))] :
      ( ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2h1_2E0: A_27b,V3t1_2E0: tyop_2Elist_2Elist(A_27b),V4h2_2E0: A_27c,V5t2_2E0: tyop_2Elist_2Elist(A_27c)] :
            ( p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V1f_2E0),V3t1_2E0),V5t2_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V1f_2E0),c_2Elist_2ECONS_2E2(A_27b,V2h1_2E0,V3t1_2E0)),c_2Elist_2ECONS_2E2(A_27c,V4h2_2E0,V5t2_2E0))) )
        & ! [V6f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V7y_2E0: tyop_2Elist_2Elist(A_27c)] : p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V6f_2E0),c_2Elist_2ENIL_2E0(A_27b)),V7y_2E0))
        & ! [V8f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V9v4_2E0: A_27b,V10v5_2E0: tyop_2Elist_2Elist(A_27b)] : p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V8f_2E0),c_2Elist_2ECONS_2E2(A_27b,V9v4_2E0,V10v5_2E0)),c_2Elist_2ENIL_2E0(A_27c))) )
     => ! [V11v_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V12v1_2E0: tyop_2Elist_2Elist(A_27b),V13v2_2E0: tyop_2Elist_2Elist(A_27c)] : p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V11v_2E0),V12v1_2E0),V13v2_2E0)) ) ).

tff(thm_2Elist_2EMAP2__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
      ( ! [V0t2_2E0: tyop_2Elist_2Elist(A_27c),V1t1_2E0: tyop_2Elist_2Elist(A_27b),V2h2_2E0: A_27c,V3h1_2E0: A_27b,V4f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))] : ( c_2Elist_2EMAP2_2E3(A_27a,A_27b,A_27c,V4f_2E0,c_2Elist_2ECONS_2E2(A_27b,V3h1_2E0,V1t1_2E0),c_2Elist_2ECONS_2E2(A_27c,V2h2_2E0,V0t2_2E0)) = c_2Elist_2ECONS_2E2(A_27a,app_2E2(A_27c,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),V4f_2E0,V3h1_2E0),V2h2_2E0),c_2Elist_2EMAP2_2E3(A_27a,A_27b,A_27c,V4f_2E0,V1t1_2E0,V0t2_2E0)) )
      & ! [V5y_2E0: tyop_2Elist_2Elist(A_27c),V6f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))] : ( c_2Elist_2EMAP2_2E3(A_27a,A_27b,A_27c,V6f_2E0,c_2Elist_2ENIL_2E0(A_27b),V5y_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V7v5_2E0: tyop_2Elist_2Elist(A_27b),V8v4_2E0: A_27b,V9f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))] : ( c_2Elist_2EMAP2_2E3(A_27a,A_27b,A_27c,V9f_2E0,c_2Elist_2ECONS_2E2(A_27b,V8v4_2E0,V7v5_2E0),c_2Elist_2ENIL_2E0(A_27c)) = c_2Elist_2ENIL_2E0(A_27a) ) ) ).

tff(thm_2Elist_2EMAP2,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2Elist_2EMAP2_2E3(A_27c,A_27a,A_27b,V0f_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27b)) = c_2Elist_2ENIL_2E0(A_27c) )
      & ! [V1f_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V2h1_2E0: A_27d,V3t1_2E0: tyop_2Elist_2Elist(A_27d),V4h2_2E0: A_27e,V5t2_2E0: tyop_2Elist_2Elist(A_27e)] : ( c_2Elist_2EMAP2_2E3(A_27f,A_27d,A_27e,V1f_2E0,c_2Elist_2ECONS_2E2(A_27d,V2h1_2E0,V3t1_2E0),c_2Elist_2ECONS_2E2(A_27e,V4h2_2E0,V5t2_2E0)) = c_2Elist_2ECONS_2E2(A_27f,app_2E2(A_27e,A_27f,app_2E2(A_27d,tyop_2Emin_2Efun(A_27e,A_27f),V1f_2E0,V2h1_2E0),V4h2_2E0),c_2Elist_2EMAP2_2E3(A_27f,A_27d,A_27e,V1f_2E0,V3t1_2E0,V5t2_2E0)) ) ) ).

tff(thm_2Elist_2EMAP2__NIL,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27b),V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))] : ( c_2Elist_2EMAP2_2E3(A_27a,A_27b,A_27c,V1f_2E0,V0x_2E0,c_2Elist_2ENIL_2E0(A_27c)) = c_2Elist_2ENIL_2E0(A_27a) ) ).

tff(thm_2Elist_2ELENGTH__MAP2,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1xs_2E0: tyop_2Elist_2Elist(A_27a),V2ys_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELENGTH_2E1(A_27c,c_2Elist_2EMAP2_2E3(A_27c,A_27a,A_27b,V0f_2E0,V1xs_2E0,V2ys_2E0)) = c_2Earithmetic_2EMIN_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1xs_2E0),c_2Elist_2ELENGTH_2E1(A_27b,V2ys_2E0)) ) ).

tff(thm_2Elist_2EEL__MAP2,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1ts_2E0: tyop_2Elist_2Elist(A_27a),V2tt_2E0: tyop_2Elist_2Elist(A_27b),V3n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V3n_2E0,c_2Earithmetic_2EMIN_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1ts_2E0),c_2Elist_2ELENGTH_2E1(A_27b,V2tt_2E0))))
     => ( c_2Elist_2EEL_2E2(A_27c,V3n_2E0,c_2Elist_2EMAP2_2E3(A_27c,A_27a,A_27b,V0f_2E0,V1ts_2E0,V2tt_2E0)) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,c_2Elist_2EEL_2E2(A_27a,V3n_2E0,V1ts_2E0)),c_2Elist_2EEL_2E2(A_27b,V3n_2E0,V2tt_2E0)) ) ) ).

tff(thm_2Elist_2ENULL,axiom,
    ! [A_27a: $tType] :
      ( p(c_2Elist_2ENULL_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)))
      & ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] : ~ p(c_2Elist_2ENULL_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0))) ) ).

tff(thm_2Elist_2Elist__INDUCT0,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)))
        & ! [V1t_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1t_2E0))
           => ! [V2h_2E0: A_27a] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V1t_2E0))) ) )
     => ! [V3l_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V3l_2E0)) ) ).

tff(thm_2Elist_2Elist__INDUCT,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)))
        & ! [V1t_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1t_2E0))
           => ! [V2h_2E0: A_27a] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V1t_2E0))) ) )
     => ! [V3l_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V3l_2E0)) ) ).

tff(thm_2Elist_2Elist__Axiom,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f0_2E0: A_27b,V1f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)))] :
    ? [V2fn_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)] :
      ( ( app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V2fn_2E0,c_2Elist_2ENIL_2E0(A_27a)) = V0f0_2E0 )
      & ! [V3a0_2E0: A_27a,V4a1_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V2fn_2E0,c_2Elist_2ECONS_2E2(A_27a,V3a0_2E0,V4a1_2E0)) = app_2E2(A_27b,A_27b,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),V1f1_2E0,V3a0_2E0),V4a1_2E0),app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V2fn_2E0,V4a1_2E0)) ) ) ).

tff(thm_2Elist_2Elist__induction,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)))
        & ! [V1t_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1t_2E0))
           => ! [V2h_2E0: A_27a] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V1t_2E0))) ) )
     => ! [V3l_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V3l_2E0)) ) ).

tff(thm_2Elist_2ELIST__REL__EL__EQN,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,V1l1_2E0,V2l2_2E0))
    <=> ( ( c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V2l2_2E0) )
        & ! [V3n_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Eprim__rec_2E_3C_2E2(V3n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
           => p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,c_2Elist_2EEL_2E2(A_27a,V3n_2E0,V1l1_2E0)),c_2Elist_2EEL_2E2(A_27b,V3n_2E0,V2l2_2E0))) ) ) ) ).

tff(thm_2Elist_2ELIST__REL__cases,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1a0_2E0: tyop_2Elist_2Elist(A_27a),V2a1_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,V1a0_2E0,V2a1_2E0))
    <=> ( ( ( V1a0_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
          & ( V2a1_2E0 = c_2Elist_2ENIL_2E0(A_27b) ) )
        | ? [V3h1_2E0: A_27a,V4h2_2E0: A_27b,V5t1_2E0: tyop_2Elist_2Elist(A_27a),V6t2_2E0: tyop_2Elist_2Elist(A_27b)] :
            ( ( V1a0_2E0 = c_2Elist_2ECONS_2E2(A_27a,V3h1_2E0,V5t1_2E0) )
            & ( V2a1_2E0 = c_2Elist_2ECONS_2E2(A_27b,V4h2_2E0,V6t2_2E0) )
            & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V3h1_2E0),V4h2_2E0))
            & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,V5t1_2E0,V6t2_2E0)) ) ) ) ).

tff(thm_2Elist_2ELIST__REL__strongind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))] :
      ( ( p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__REL_27_2E0,c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ENIL_2E0(A_27b)))
        & ! [V2h1_2E0: A_27a,V3h2_2E0: A_27b,V4t1_2E0: tyop_2Elist_2Elist(A_27a),V5t2_2E0: tyop_2Elist_2Elist(A_27b)] :
            ( ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V2h1_2E0),V3h2_2E0))
              & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,V4t1_2E0,V5t2_2E0))
              & p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__REL_27_2E0,V4t1_2E0),V5t2_2E0)) )
           => p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__REL_27_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h1_2E0,V4t1_2E0)),c_2Elist_2ECONS_2E2(A_27b,V3h2_2E0,V5t2_2E0))) ) )
     => ! [V6a0_2E0: tyop_2Elist_2Elist(A_27a),V7a1_2E0: tyop_2Elist_2Elist(A_27b)] :
          ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,V6a0_2E0,V7a1_2E0))
         => p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__REL_27_2E0,V6a0_2E0),V7a1_2E0)) ) ) ).

tff(thm_2Elist_2ELIST__REL__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))] :
      ( ( p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__REL_27_2E0,c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ENIL_2E0(A_27b)))
        & ! [V2h1_2E0: A_27a,V3h2_2E0: A_27b,V4t1_2E0: tyop_2Elist_2Elist(A_27a),V5t2_2E0: tyop_2Elist_2Elist(A_27b)] :
            ( ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V2h1_2E0),V3h2_2E0))
              & p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__REL_27_2E0,V4t1_2E0),V5t2_2E0)) )
           => p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__REL_27_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h1_2E0,V4t1_2E0)),c_2Elist_2ECONS_2E2(A_27b,V3h2_2E0,V5t2_2E0))) ) )
     => ! [V6a0_2E0: tyop_2Elist_2Elist(A_27a),V7a1_2E0: tyop_2Elist_2Elist(A_27b)] :
          ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,V6a0_2E0,V7a1_2E0))
         => p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__REL_27_2E0,V6a0_2E0),V7a1_2E0)) ) ) ).

tff(thm_2Elist_2ELIST__REL__rules,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27b)))
      & ! [V1h1_2E0: A_27a,V2h2_2E0: A_27b,V3t1_2E0: tyop_2Elist_2Elist(A_27a),V4t2_2E0: tyop_2Elist_2Elist(A_27b)] :
          ( ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V1h1_2E0),V2h2_2E0))
            & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,V3t1_2E0,V4t2_2E0)) )
         => p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,c_2Elist_2ECONS_2E2(A_27a,V1h1_2E0,V3t1_2E0),c_2Elist_2ECONS_2E2(A_27b,V2h2_2E0,V4t2_2E0))) ) ) ).

tff(thm_2Elist_2Elist__CASES,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
      | ? [V1h_2E0: A_27a,V2t_2E0: tyop_2Elist_2Elist(A_27a)] : ( V0l_2E0 = c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V2t_2E0) ) ) ).

tff(thm_2Elist_2EFORALL__LIST,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
      ( ! [V1l_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1l_2E0))
    <=> ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)))
        & ! [V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0))) ) ) ).

tff(thm_2Elist_2EMEM__SPLIT__APPEND__first,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1e_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V1e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0)))
    <=> ? [V2pfx_2E0: tyop_2Elist_2Elist(A_27a),V3sfx_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( V0l_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2pfx_2E0,c_2Elist_2ECONS_2E2(A_27a,V1e_2E0,c_2Elist_2ENIL_2E0(A_27a))),V3sfx_2E0) )
          & ~ p(c_2Ebool_2EIN_2E2(A_27a,V1e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2pfx_2E0))) ) ) ).

tff(thm_2Elist_2EMEM__SPLIT__APPEND__last,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1e_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V1e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0)))
    <=> ? [V2pfx_2E0: tyop_2Elist_2Elist(A_27a),V3sfx_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( V0l_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2pfx_2E0,c_2Elist_2ECONS_2E2(A_27a,V1e_2E0,c_2Elist_2ENIL_2E0(A_27a))),V3sfx_2E0) )
          & ~ p(c_2Ebool_2EIN_2E2(A_27a,V1e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V3sfx_2E0))) ) ) ).

tff(thm_2Elist_2EAPPEND__EQ__APPEND,axiom,
    ! [A_27a: $tType,V0m2_2E0: tyop_2Elist_2Elist(A_27a),V1m1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3l1_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2EAPPEND_2E2(A_27a,V3l1_2E0,V2l2_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,V1m1_2E0,V0m2_2E0) )
    <=> ( ? [V4l_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( ( V3l1_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V1m1_2E0,V4l_2E0) )
            & ( V0m2_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V4l_2E0,V2l2_2E0) ) )
        | ? [V5l_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( ( V1m1_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V3l1_2E0,V5l_2E0) )
            & ( V2l2_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V5l_2E0,V0m2_2E0) ) ) ) ) ).

tff(thm_2Elist_2EAPPEND__EQ__CONS,axiom,
    ! [A_27a: $tType,V0t_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3h_2E0: A_27a] :
      ( ( c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V1l2_2E0) = c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,V0t_2E0) )
    <=> ( ( ( V2l1_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
          & ( V1l2_2E0 = c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,V0t_2E0) ) )
        | ? [V4lt_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( ( V2l1_2E0 = c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,V4lt_2E0) )
            & ( V0t_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V4lt_2E0,V1l2_2E0) ) ) ) ) ).

tff(thm_2Elist_2EAPPEND__EQ__APPEND__MID,axiom,
    ! [A_27a: $tType,V0m2_2E0: tyop_2Elist_2Elist(A_27a),V1m1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4e_2E0: A_27a] :
      ( ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V3l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V4e_2E0,c_2Elist_2ENIL_2E0(A_27a))),V2l2_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,V1m1_2E0,V0m2_2E0) )
    <=> ( ? [V5l_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( ( V1m1_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V3l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V4e_2E0,c_2Elist_2ENIL_2E0(A_27a))),V5l_2E0) )
            & ( V2l2_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V5l_2E0,V0m2_2E0) ) )
        | ? [V6l_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( ( V3l1_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V1m1_2E0,V6l_2E0) )
            & ( V0m2_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V6l_2E0,c_2Elist_2ECONS_2E2(A_27a,V4e_2E0,c_2Elist_2ENIL_2E0(A_27a))),V2l2_2E0) ) ) ) ) ).

tff(thm_2Elist_2ELUPDATE__NIL,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a] :
      ( ( c_2Elist_2ELUPDATE_2E3(A_27a,V2x_2E0,V1n_2E0,V0xs_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
    <=> ( V0xs_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ).

tff(thm_2Elist_2ELUPDATE__SEM,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V6p_2E0: tyop_2Enum_2Enum,V4n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V6p_2E0),V4n_2E0))
        <=> ( V6p_2E0 = V4n_2E0 ) )
     => ( ! [V0e_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2ELUPDATE_2E3(A_27a,V0e_2E0,V1n_2E0,V2l_2E0)) = c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0) )
        & ! [V3e_2E0: A_27a,V4n_2E0: tyop_2Enum_2Enum,V5l_2E0: tyop_2Elist_2Elist(A_27a),V6p_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Eprim__rec_2E_3C_2E2(V6p_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V5l_2E0)))
           => ( c_2Elist_2EEL_2E2(A_27a,V6p_2E0,c_2Elist_2ELUPDATE_2E3(A_27a,V3e_2E0,V4n_2E0,V5l_2E0)) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V6p_2E0),V4n_2E0),V3e_2E0,c_2Elist_2EEL_2E2(A_27a,V6p_2E0,V5l_2E0)) ) ) ) ) ).

tff(thm_2Elist_2EEL__LUPDATE,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))] :
      ( ! [V2i_2E0: tyop_2Enum_2Enum,V3k_2E0: tyop_2Enum_2Enum,V0ys_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V2i_2E0),V3k_2E0),V0ys_2E0))
        <=> ( ( V2i_2E0 = V3k_2E0 )
            & p(c_2Eprim__rec_2E_3C_2E2(V3k_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0ys_2E0))) ) )
     => ! [V0ys_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a,V2i_2E0: tyop_2Enum_2Enum,V3k_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EEL_2E2(A_27a,V2i_2E0,c_2Elist_2ELUPDATE_2E3(A_27a,V1x_2E0,V3k_2E0,V0ys_2E0)) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V2i_2E0),V3k_2E0),V0ys_2E0),V1x_2E0,c_2Elist_2EEL_2E2(A_27a,V2i_2E0,V0ys_2E0)) ) ) ).

tff(thm_2Elist_2ELENGTH__LUPDATE,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum,V2ys_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2ELUPDATE_2E3(A_27a,V0x_2E0,V1n_2E0,V2ys_2E0)) = c_2Elist_2ELENGTH_2E1(A_27a,V2ys_2E0) ) ).

tff(thm_2Elist_2ELUPDATE__LENGTH,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a,V3ys_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELUPDATE_2E3(A_27a,V1x_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0xs_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V0xs_2E0,c_2Elist_2ECONS_2E2(A_27a,V2y_2E0,V3ys_2E0))) = c_2Elist_2EAPPEND_2E2(A_27a,V0xs_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V3ys_2E0)) ) ).

tff(thm_2Elist_2ELUPDATE__SNOC,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] :
      ( ! [V1k_2E0: tyop_2Enum_2Enum,V0ys_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V1k_2E0),V0ys_2E0))
        <=> ( V1k_2E0 = c_2Elist_2ELENGTH_2E1(A_27a,V0ys_2E0) ) )
     => ! [V0ys_2E0: tyop_2Elist_2Elist(A_27a),V1k_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a,V3y_2E0: A_27a] : ( c_2Elist_2ELUPDATE_2E3(A_27a,V2x_2E0,V1k_2E0,c_2Elist_2ESNOC_2E2(A_27a,V3y_2E0,V0ys_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V1k_2E0),V0ys_2E0),c_2Elist_2ESNOC_2E2(A_27a,V2x_2E0,V0ys_2E0),c_2Elist_2ESNOC_2E2(A_27a,V3y_2E0,c_2Elist_2ELUPDATE_2E3(A_27a,V2x_2E0,V1k_2E0,V0ys_2E0))) ) ) ).

tff(thm_2Elist_2EMEM__LUPDATE__E,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a,V3i_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ELUPDATE_2E3(A_27a,V2y_2E0,V3i_2E0,V0l_2E0))))
     => ( ( V1x_2E0 = V2y_2E0 )
        | p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0))) ) ) ).

tff(thm_2Elist_2EMEM__LUPDATE,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a,V3i_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ELUPDATE_2E3(A_27a,V2y_2E0,V3i_2E0,V0l_2E0))))
    <=> ( ( p(c_2Eprim__rec_2E_3C_2E2(V3i_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)))
          & ( V1x_2E0 = V2y_2E0 ) )
        | ? [V4j_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Eprim__rec_2E_3C_2E2(V4j_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)))
            & ( V3i_2E0 != V4j_2E0 )
            & ( c_2Elist_2EEL_2E2(A_27a,V4j_2E0,V0l_2E0) = V1x_2E0 ) ) ) ) ).

tff(thm_2Elist_2ELUPDATE__compute,axiom,
    ! [A_27a: $tType] :
      ( ! [V0e_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ELUPDATE_2E3(A_27a,V0e_2E0,V1n_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V2e_2E0: A_27a,V3x_2E0: A_27a,V4l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELUPDATE_2E3(A_27a,V2e_2E0,c_2Enum_2E0_2E0,c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V4l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V2e_2E0,V4l_2E0) )
      & ! [V5e_2E0: A_27a,V6n_2E0: tyop_2Enum_2Enum,V7x_2E0: A_27a,V8l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELUPDATE_2E3(A_27a,V5e_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V6n_2E0)),c_2Elist_2ECONS_2E2(A_27a,V7x_2E0,V8l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V7x_2E0,c_2Elist_2ELUPDATE_2E3(A_27a,V5e_2E0,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V6n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V8l_2E0)) )
      & ! [V9e_2E0: A_27a,V10n_2E0: tyop_2Enum_2Enum,V11x_2E0: A_27a,V12l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELUPDATE_2E3(A_27a,V9e_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V10n_2E0)),c_2Elist_2ECONS_2E2(A_27a,V11x_2E0,V12l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V11x_2E0,c_2Elist_2ELUPDATE_2E3(A_27a,V9e_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V10n_2E0)),V12l_2E0)) ) ) ).

tff(thm_2Elist_2ELUPDATE__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V3f_2E0,c_2Elist_2ELUPDATE_2E3(A_27a,V0x_2E0,V1n_2E0,V2l_2E0)) = c_2Elist_2ELUPDATE_2E3(A_27b,app_2E2(A_27a,A_27b,V3f_2E0,V0x_2E0),V1n_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,V3f_2E0,V2l_2E0)) ) ).

tff(thm_2Elist_2EsplitAtPki__APPEND,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V2P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2P_2E0),V4i_2E0) = c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0,V4i_2E0)) )
     => ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3k_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))] :
          ( ( p(c_2Elist_2EEVERYi_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2P_2E0),V0l1_2E0))
            & ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l2_2E0)))
             => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0)),c_2Elist_2EHD_2E1(A_27a,V1l2_2E0))) ) )
         => ( c_2Elist_2EsplitAtPki_2E3(A_27b,A_27a,V2P_2E0,V3k_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V3k_2E0,V0l1_2E0),V1l2_2E0) ) ) ) ).

tff(thm_2Elist_2EsplitAtPki__EQN,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27b),V2P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3i_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0l_2E0),V2P_2E0),V3i_2E0))
        <=> ( p(c_2Eprim__rec_2E_3C_2E2(V3i_2E0,c_2Elist_2ELENGTH_2E1(A_27b,V0l_2E0)))
            & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0,V3i_2E0),c_2Elist_2EEL_2E2(A_27b,V3i_2E0,V0l_2E0))) ) )
     => ( ! [V1k_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V0l_2E0: tyop_2Elist_2Elist(A_27b),V4i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F1_2E0,V1k_2E0),V0l_2E0),V4i_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27a,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),V1k_2E0,c_2Elist_2ETAKE_2E2(A_27b,V4i_2E0,V0l_2E0)),c_2Elist_2EDROP_2E2(A_27b,V4i_2E0,V0l_2E0)) )
       => ! [V0l_2E0: tyop_2Elist_2Elist(A_27b),V1k_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V2P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Elist_2EsplitAtPki_2E3(A_27a,A_27b,V2P_2E0,V1k_2E0,V0l_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Enum_2Enum,A_27a,c_2Ewhile_2EOLEAST_2E1(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0l_2E0),V2P_2E0)),app_2E2(tyop_2Elist_2Elist(A_27b),A_27a,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),V1k_2E0,V0l_2E0),c_2Elist_2ENIL_2E0(A_27b)),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F1_2E0,V1k_2E0),V0l_2E0)) ) ) ) ).

tff(thm_2Elist_2ETAKE__LENGTH__TOO__LONG,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),V1n_2E0))
     => ( c_2Elist_2ETAKE_2E2(A_27a,V1n_2E0,V0l_2E0) = V0l_2E0 ) ) ).

tff(thm_2Elist_2EDROP__LENGTH__TOO__LONG,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),V1n_2E0))
     => ( c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,V0l_2E0) = c_2Elist_2ENIL_2E0(A_27a) ) ) ).

tff(thm_2Elist_2ETAKE__splitAtPki,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Elist_2EsplitAtPki_2E3(tyop_2Elist_2Elist(A_27a),A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ecombin_2EK_2E0(tyop_2Emin_2Ebool,A_27a),c_2Emin_2E_3D_2E1(tyop_2Enum_2Enum,V0n_2E0)),c_2Ecombin_2EK_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),V1l_2E0) ) ).

tff(thm_2Elist_2EDROP__splitAtPki,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Elist_2EsplitAtPki_2E3(tyop_2Elist_2Elist(A_27a),A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ecombin_2EK_2E0(tyop_2Emin_2Ebool,A_27a),c_2Emin_2E_3D_2E1(tyop_2Enum_2Enum,V0n_2E0)),c_2Ecombin_2EK_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(A_27a))),V1l_2E0) ) ).

tff(thm_2Elist_2ELIST__BIND__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Elist_2Elist(A_27b),V1h_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a))] :
      ( ( c_2Elist_2ELIST__BIND_2E2(A_27a,A_27b,c_2Elist_2ENIL_2E0(A_27b),V2f_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
      & ( c_2Elist_2ELIST__BIND_2E2(A_27a,A_27b,c_2Elist_2ECONS_2E2(A_27b,V1h_2E0,V0t_2E0),V2f_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,app_2E2(A_27b,tyop_2Elist_2Elist(A_27a),V2f_2E0,V1h_2E0),c_2Elist_2ELIST__BIND_2E2(A_27a,A_27b,V0t_2E0,V2f_2E0)) ) ) ).

tff(thm_2Elist_2ELIST__BIND__ID,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))] :
      ( ! [V1x_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),F0_2E0,V1x_2E0) = V1x_2E0 )
     => ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] :
          ( ( c_2Elist_2ELIST__BIND_2E2(A_27a,tyop_2Elist_2Elist(A_27a),V0l_2E0,F0_2E0) = c_2Elist_2EFLAT_2E1(A_27a,V0l_2E0) )
          & ( c_2Elist_2ELIST__BIND_2E2(A_27a,tyop_2Elist_2Elist(A_27a),V0l_2E0,c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(A_27a))) = c_2Elist_2EFLAT_2E1(A_27a,V0l_2E0) ) ) ) ).

tff(thm_2Elist_2ELIST__BIND__APPEND,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27b),V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELIST__BIND_2E2(A_27a,A_27b,c_2Elist_2EAPPEND_2E2(A_27b,V1l1_2E0,V0l2_2E0),V2f_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ELIST__BIND_2E2(A_27a,A_27b,V1l1_2E0,V2f_2E0),c_2Elist_2ELIST__BIND_2E2(A_27a,A_27b,V0l2_2E0,V2f_2E0)) ) ).

tff(thm_2Elist_2ELIST__BIND__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2Elist_2ELIST__BIND_2E2(A_27a,A_27b,c_2Elist_2EMAP_2E2(A_27c,A_27b,V2f_2E0,V0l_2E0),V1g_2E0) = c_2Elist_2ELIST__BIND_2E2(A_27a,A_27c,V0l_2E0,c_2Ecombin_2Eo_2E2(A_27c,tyop_2Elist_2Elist(A_27a),A_27b,V1g_2E0,V2f_2E0)) ) ).

tff(thm_2Elist_2EMAP__LIST__BIND,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V2f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Elist_2EMAP_2E2(A_27b,A_27a,V2f_2E0,c_2Elist_2ELIST__BIND_2E2(A_27b,A_27c,V0l_2E0,V1g_2E0)) = c_2Elist_2ELIST__BIND_2E2(A_27a,A_27c,V0l_2E0,c_2Ecombin_2Eo_2E2(A_27c,tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E1(A_27b,A_27a,V2f_2E0),V1g_2E0)) ) ).

tff(thm_2Elist_2ELIST__BIND__LIST__BIND,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELIST__BIND_2E2(A_27a,A_27b,c_2Elist_2ELIST__BIND_2E2(A_27b,A_27c,V0l_2E0,V1g_2E0),V2f_2E0) = c_2Elist_2ELIST__BIND_2E2(A_27a,A_27c,V0l_2E0,c_2Ecombin_2Eo_2E2(A_27c,tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Ecombin_2EC_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E0(A_27a,A_27b),V2f_2E0),V1g_2E0)) ) ).

tff(thm_2Elist_2ESINGL__LIST__APPLY__L,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELIST__BIND_2E2(A_27a,A_27b,c_2Elist_2ECONS_2E2(A_27b,V0x_2E0,c_2Elist_2ENIL_2E0(A_27b)),V1f_2E0) = app_2E2(A_27b,tyop_2Elist_2Elist(A_27a),V1f_2E0,V0x_2E0) ) ).

tff(thm_2Elist_2ESINGL__LIST__APPLY__R,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))] :
      ( ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Elist_2Elist(A_27a),F0_2E0,V1x_2E0) = c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ENIL_2E0(A_27a)) )
     => ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__BIND_2E2(A_27a,A_27a,V0l_2E0,F0_2E0) = V0l_2E0 ) ) ).

tff(thm_2Elist_2ESINGL__APPLY__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27b),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Elist_2ELIST__APPLY_2E2(A_27a,A_27b,c_2Elist_2ECONS_2E2(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0,c_2Elist_2ENIL_2E0(tyop_2Emin_2Efun(A_27b,A_27a))),V0l_2E0) = c_2Elist_2EMAP_2E2(A_27b,A_27a,V1f_2E0,V0l_2E0) ) ).

tff(thm_2Elist_2ESINGL__SINGL__APPLY,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Elist_2ELIST__APPLY_2E2(A_27a,A_27b,c_2Elist_2ECONS_2E2(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0,c_2Elist_2ENIL_2E0(tyop_2Emin_2Efun(A_27b,A_27a))),c_2Elist_2ECONS_2E2(A_27b,V0x_2E0,c_2Elist_2ENIL_2E0(A_27b))) = c_2Elist_2ECONS_2E2(A_27a,app_2E2(A_27b,A_27a,V1f_2E0,V0x_2E0),c_2Elist_2ENIL_2E0(A_27a)) ) ).

tff(thm_2Elist_2ESINGL__APPLY__PERMUTE,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a))] :
      ( ! [V0x_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),F0_2E0,V0x_2E0),V2f_2E0) = app_2E2(A_27b,A_27a,V2f_2E0,V0x_2E0) )
     => ! [V0x_2E0: A_27b,V1fs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a))] : ( c_2Elist_2ELIST__APPLY_2E2(A_27a,A_27b,V1fs_2E0,c_2Elist_2ECONS_2E2(A_27b,V0x_2E0,c_2Elist_2ENIL_2E0(A_27b))) = c_2Elist_2ELIST__APPLY_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),c_2Elist_2ECONS_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),F0_2E0,V0x_2E0),c_2Elist_2ENIL_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a))),V1fs_2E0) ) ) ).

tff(thm_2Elist_2EMAP__FLAT,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Elist_2EMAP_2E2(A_27b,A_27a,V1f_2E0,c_2Elist_2EFLAT_2E1(A_27b,V0l_2E0)) = c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E1(A_27b,A_27a,V1f_2E0),V0l_2E0)) ) ).

tff(thm_2Elist_2ELIST__APPLY__o,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27b),V1gs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),V2fs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a))] : ( c_2Elist_2ELIST__APPLY_2E2(A_27a,A_27b,c_2Elist_2ELIST__APPLY_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c),c_2Elist_2ELIST__APPLY_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27c,A_27a),c_2Elist_2ECONS_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Ecombin_2Eo_2E0(A_27b,A_27a,A_27c),c_2Elist_2ENIL_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))))),V2fs_2E0),V1gs_2E0),V0xs_2E0) = c_2Elist_2ELIST__APPLY_2E2(A_27a,A_27c,V2fs_2E0,c_2Elist_2ELIST__APPLY_2E2(A_27c,A_27b,V1gs_2E0,V0xs_2E0)) ) ).

tff(thm_2Elist_2ESHORTLEX__THM,axiom,
    ! [A_27a: $tType,V0t2_2E0: tyop_2Elist_2Elist(A_27a),V1t1_2E0: tyop_2Elist_2Elist(A_27a),V2h2_2E0: A_27a,V3h1_2E0: A_27a,V4R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ~ p(c_2Elist_2ESHORTLEX_2E3(A_27a,V4R_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a)))
      & ~ p(c_2Elist_2ESHORTLEX_2E3(A_27a,V4R_2E0,c_2Elist_2ECONS_2E2(A_27a,V3h1_2E0,V1t1_2E0),c_2Elist_2ENIL_2E0(A_27a)))
      & p(c_2Elist_2ESHORTLEX_2E3(A_27a,V4R_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V2h2_2E0,V0t2_2E0)))
      & ( p(c_2Elist_2ESHORTLEX_2E3(A_27a,V4R_2E0,c_2Elist_2ECONS_2E2(A_27a,V3h1_2E0,V1t1_2E0),c_2Elist_2ECONS_2E2(A_27a,V2h2_2E0,V0t2_2E0)))
      <=> ( p(c_2Eprim__rec_2E_3C_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1t1_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V0t2_2E0)))
          | ( ( c_2Elist_2ELENGTH_2E1(A_27a,V1t1_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V0t2_2E0) )
            & ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4R_2E0,V3h1_2E0),V2h2_2E0))
              | ( ( V3h1_2E0 = V2h2_2E0 )
                & p(c_2Elist_2ESHORTLEX_2E3(A_27a,V4R_2E0,V1t1_2E0,V0t2_2E0)) ) ) ) ) ) ) ).

tff(thm_2Elist_2ESHORTLEX__MONO,axiom,
    ! [A_27a: $tType,V0y_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: tyop_2Elist_2Elist(A_27a),V2R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3R1_2E0,V4x_2E0),V5y_2E0))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R2_2E0,V4x_2E0),V5y_2E0)) )
     => ( p(c_2Elist_2ESHORTLEX_2E3(A_27a,V3R1_2E0,V1x_2E0,V0y_2E0))
       => p(c_2Elist_2ESHORTLEX_2E3(A_27a,V2R2_2E0,V1x_2E0,V0y_2E0)) ) ) ).

tff(thm_2Elist_2ESHORTLEX__NIL2,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ~ p(c_2Elist_2ESHORTLEX_2E3(A_27a,V1R_2E0,V0l_2E0,c_2Elist_2ENIL_2E0(A_27a))) ).

tff(thm_2Elist_2ESHORTLEX__transitive,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))
     => p(c_2Erelation_2Etransitive_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESHORTLEX_2E1(A_27a,V0R_2E0))) ) ).

tff(thm_2Elist_2ELENGTH__LT__SHORTLEX,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Eprim__rec_2E_3C_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l2_2E0)))
     => p(c_2Elist_2ESHORTLEX_2E3(A_27a,V0R_2E0,V1l1_2E0,V2l2_2E0)) ) ).

tff(thm_2Elist_2ESHORTLEX__LENGTH__LE,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2ESHORTLEX_2E3(A_27a,V0R_2E0,V1l1_2E0,V2l2_2E0))
     => p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l2_2E0))) ) ).

tff(thm_2Elist_2ESHORTLEX__total,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2Etotal_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)))
     => p(c_2Erelation_2Etotal_2E1(tyop_2Elist_2Elist(A_27a),c_2Erelation_2ERC_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESHORTLEX_2E1(A_27a,V0R_2E0)))) ) ).

tff(thm_2Elist_2EWF__SHORTLEX__same__lengths,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))
     => ! [V1l_2E0: tyop_2Enum_2Enum,V2s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
          ( ( ! [V3d_2E0: tyop_2Elist_2Elist(A_27a)] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),V3d_2E0,V2s_2E0))
               => ( c_2Elist_2ELENGTH_2E1(A_27a,V3d_2E0) = V1l_2E0 ) )
            & ? [V4a_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),V4a_2E0,V2s_2E0)) )
         => ? [V5b_2E0: tyop_2Elist_2Elist(A_27a)] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),V5b_2E0,V2s_2E0))
              & ! [V6c_2E0: tyop_2Elist_2Elist(A_27a)] :
                  ( p(c_2Elist_2ESHORTLEX_2E3(A_27a,V0R_2E0,V6c_2E0,V5b_2E0))
                 => ~ p(c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),V6c_2E0,V2s_2E0)) ) ) ) ) ).

tff(thm_2Elist_2EWF__SHORTLEX,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_2Elist_2Elist(A_27a),c_2Elist_2ESHORTLEX_2E1(A_27a,V0R_2E0))) ) ).

tff(thm_2Elist_2ELLEX__THM,axiom,
    ! [A_27a: $tType,V0t2_2E0: tyop_2Elist_2Elist(A_27a),V1t1_2E0: tyop_2Elist_2Elist(A_27a),V2h2_2E0: A_27a,V3h1_2E0: A_27a,V4R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ~ p(c_2Elist_2ELLEX_2E3(A_27a,V4R_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a)))
      & ~ p(c_2Elist_2ELLEX_2E3(A_27a,V4R_2E0,c_2Elist_2ECONS_2E2(A_27a,V3h1_2E0,V1t1_2E0),c_2Elist_2ENIL_2E0(A_27a)))
      & p(c_2Elist_2ELLEX_2E3(A_27a,V4R_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V2h2_2E0,V0t2_2E0)))
      & ( p(c_2Elist_2ELLEX_2E3(A_27a,V4R_2E0,c_2Elist_2ECONS_2E2(A_27a,V3h1_2E0,V1t1_2E0),c_2Elist_2ECONS_2E2(A_27a,V2h2_2E0,V0t2_2E0)))
      <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4R_2E0,V3h1_2E0),V2h2_2E0))
          | ( ( V3h1_2E0 = V2h2_2E0 )
            & p(c_2Elist_2ELLEX_2E3(A_27a,V4R_2E0,V1t1_2E0,V0t2_2E0)) ) ) ) ) ).

tff(thm_2Elist_2ELLEX__MONO,axiom,
    ! [A_27a: $tType,V0y_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: tyop_2Elist_2Elist(A_27a),V2R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3R1_2E0,V4x_2E0),V5y_2E0))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R2_2E0,V4x_2E0),V5y_2E0)) )
     => ( p(c_2Elist_2ELLEX_2E3(A_27a,V3R1_2E0,V1x_2E0,V0y_2E0))
       => p(c_2Elist_2ELLEX_2E3(A_27a,V2R2_2E0,V1x_2E0,V0y_2E0)) ) ) ).

tff(thm_2Elist_2ELLEX__CONG,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3R_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4l1_27_2E0: tyop_2Elist_2Elist(A_27a),V5l2_27_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( ( V1l1_2E0 = V4l1_27_2E0 )
        & ( V2l2_2E0 = V5l2_27_2E0 )
        & ! [V6a_2E0: A_27a,V7b_2E0: A_27a] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V6a_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V4l1_27_2E0)))
              & p(c_2Ebool_2EIN_2E2(A_27a,V7b_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V5l2_27_2E0))) )
           => ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V6a_2E0),V7b_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3R_27_2E0,V6a_2E0),V7b_2E0) ) ) )
     => ( c_2Elist_2ELLEX_2E3(A_27a,V0R_2E0,V1l1_2E0,V2l2_2E0) = c_2Elist_2ELLEX_2E3(A_27a,V3R_27_2E0,V4l1_27_2E0,V5l2_27_2E0) ) ) ).

tff(thm_2Elist_2ELLEX__NIL2,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ~ p(c_2Elist_2ELLEX_2E3(A_27a,V1R_2E0,V0l_2E0,c_2Elist_2ENIL_2E0(A_27a))) ).

tff(thm_2Elist_2ELLEX__transitive,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))
     => p(c_2Erelation_2Etransitive_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELLEX_2E1(A_27a,V0R_2E0))) ) ).

tff(thm_2Elist_2ELLEX__total,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Erelation_2Etotal_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)))
     => p(c_2Erelation_2Etotal_2E1(tyop_2Elist_2Elist(A_27a),c_2Erelation_2ERC_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELLEX_2E1(A_27a,V0R_2E0)))) ) ).

tff(thm_2Elist_2ELLEX__not__WF,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ? [V1a_2E0: A_27a,V2b_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1a_2E0),V2b_2E0))
     => ~ p(c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELLEX_2E1(A_27a,V0R_2E0))) ) ).

tff(thm_2Elist_2ELLEX__EL__THM,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2ELLEX_2E3(A_27a,V0R_2E0,V1l1_2E0,V2l2_2E0))
    <=> ? [V3n_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Earithmetic_2E_3C_3D_2E2(V3n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
          & p(c_2Eprim__rec_2E_3C_2E2(V3n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V2l2_2E0)))
          & ( c_2Elist_2ETAKE_2E2(A_27a,V3n_2E0,V1l1_2E0) = c_2Elist_2ETAKE_2E2(A_27a,V3n_2E0,V2l2_2E0) )
          & ( p(c_2Eprim__rec_2E_3C_2E2(V3n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,c_2Elist_2EEL_2E2(A_27a,V3n_2E0,V1l1_2E0)),c_2Elist_2EEL_2E2(A_27a,V3n_2E0,V2l2_2E0))) ) ) ) ).

tff(thm_2Elist_2Enub__set,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2Enub_2E1(A_27a,V0l_2E0)) = c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0) ) ).

tff(thm_2Elist_2Eall__distinct__nub,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2Enub_2E1(A_27a,V0l_2E0))) ).

tff(thm_2Elist_2Enub__append,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1l2_2E0),V2x_2E0))
        <=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0))) )
     => ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2Enub_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2Enub_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1l2_2E0),V0l1_2E0)),c_2Elist_2Enub_2E1(A_27a,V1l2_2E0)) ) ) ).

tff(thm_2Elist_2Elist__to__set__diff,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0l1_2E0),V2x_2E0))
        <=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l1_2E0))) )
     => ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l1_2E0)) = c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0l1_2E0),V1l2_2E0)) ) ) ).

tff(thm_2Elist_2Elength__nub__append,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0l1_2E0),V2x_2E0))
        <=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l1_2E0))) )
     => ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2Enub_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0))) = c_2Earithmetic_2E_2B_2E2(c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2Enub_2E1(A_27a,V0l1_2E0)),c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2Enub_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0l1_2E0),V1l2_2E0)))) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT__DROP,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0ls_2E0))
     => p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,V0ls_2E0))) ) ).

tff(thm_2Elist_2EEXISTS__LIST__EQ__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1f_2E0),V2x_2E0))
        <=> ? [V3y_2E0: A_27b] : ( V2x_2E0 = app_2E2(A_27b,A_27a,V1f_2E0,V3y_2E0) ) )
     => ! [V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
          ( p(c_2Elist_2EEVERY_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1f_2E0),V0ls_2E0))
         => ? [V4l_2E0: tyop_2Elist_2Elist(A_27b)] : ( V0ls_2E0 = c_2Elist_2EMAP_2E2(A_27b,A_27a,V1f_2E0,V4l_2E0) ) ) ) ).

tff(thm_2Elist_2ELIST__TO__SET__FLAT,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EFLAT_2E1(A_27a,V0ls_2E0)) = c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),V0ls_2E0))) ) ).

tff(thm_2Elist_2EMEM__APPEND__lemma,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Elist_2Elist(A_27a),V1b_2E0: tyop_2Elist_2Elist(A_27a),V2c_2E0: tyop_2Elist_2Elist(A_27a),V3d_2E0: tyop_2Elist_2Elist(A_27a),V4x_2E0: A_27a] :
      ( ( ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0a_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,c_2Elist_2ENIL_2E0(A_27a))),V1b_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2c_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,c_2Elist_2ENIL_2E0(A_27a))),V3d_2E0) )
        & ~ p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1b_2E0)))
        & ~ p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0a_2E0))) )
     => ( ( V0a_2E0 = V2c_2E0 )
        & ( V1b_2E0 = V3d_2E0 ) ) ) ).

tff(thm_2Elist_2EEVERY2__REVERSE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,V1l1_2E0,V2l2_2E0))
     => p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l1_2E0),c_2Elist_2EREVERSE_2E1(A_27b,V2l2_2E0))) ) ).

tff(thm_2Elist_2ESUM__MAP__PLUS,axiom,
    ! [A_27a: $tType,F0_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)))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3x_2E0: A_27a] : ( 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)),F0_2E0,V0f_2E0),V1g_2E0),V3x_2E0) = c_2Earithmetic_2E_2B_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V1g_2E0,V3x_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2ls_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ESUM_2E1(c_2Elist_2EMAP_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)),F0_2E0,V0f_2E0),V1g_2E0),V2ls_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Elist_2ESUM_2E1(c_2Elist_2EMAP_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2ls_2E0)),c_2Elist_2ESUM_2E1(c_2Elist_2EMAP_2E2(A_27a,tyop_2Enum_2Enum,V1g_2E0,V2ls_2E0))) ) ) ).

tff(thm_2Elist_2ETAKE__LENGTH__ID__rwt,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1m_2E0: tyop_2Enum_2Enum] :
      ( ( V1m_2E0 = c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) )
     => ( c_2Elist_2ETAKE_2E2(A_27a,V1m_2E0,V0l_2E0) = V0l_2E0 ) ) ).

tff(thm_2Elist_2EZIP__DROP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Elist_2Elist(A_27a),V1b_2E0: tyop_2Elist_2Elist(A_27b),V2n_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0a_2E0)))
        & ( c_2Elist_2ELENGTH_2E1(A_27a,V0a_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1b_2E0) ) )
     => ( c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(A_27a,V2n_2E0,V0a_2E0),c_2Elist_2EDROP_2E2(A_27b,V2n_2E0,V1b_2E0))) = c_2Elist_2EDROP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V2n_2E0,c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0a_2E0,V1b_2E0))) ) ) ).

tff(thm_2Elist_2EGENLIST__EL,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2n_2E0: tyop_2Enum_2Enum] :
      ( ( ( V2n_2E0 = c_2Elist_2ELENGTH_2E1(A_27a,V0ls_2E0) )
        & ! [V3i_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Eprim__rec_2E_3C_2E2(V3i_2E0,V2n_2E0))
           => ( app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V3i_2E0) = c_2Elist_2EEL_2E2(A_27a,V3i_2E0,V0ls_2E0) ) ) )
     => ( c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,V2n_2E0) = V0ls_2E0 ) ) ).

tff(thm_2Elist_2EEVERY2__trans,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
          ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
            & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V3z_2E0)) )
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V3z_2E0)) )
     => ! [V4x_2E0: tyop_2Elist_2Elist(A_27a),V5y_2E0: tyop_2Elist_2Elist(A_27a),V6z_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V4x_2E0,V5y_2E0))
            & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V5y_2E0,V6z_2E0)) )
         => p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V4x_2E0,V6z_2E0)) ) ) ).

tff(thm_2Elist_2EEVERY2__sym,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
      ( ! [V2x_2E0: A_27a,V3y_2E0: A_27b] :
          ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1R1_2E0,V2x_2E0),V3y_2E0))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R2_2E0,V3y_2E0),V2x_2E0)) )
     => ! [V4x_2E0: tyop_2Elist_2Elist(A_27a),V5y_2E0: tyop_2Elist_2Elist(A_27b)] :
          ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V1R1_2E0,V4x_2E0,V5y_2E0))
         => p(c_2Elist_2ELIST__REL_2E3(A_27b,A_27a,V0R2_2E0,V5y_2E0,V4x_2E0)) ) ) ).

tff(thm_2Elist_2EEVERY2__LUPDATE__same,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3v1_2E0: A_27a,V4v2_2E0: A_27b,V5n_2E0: tyop_2Enum_2Enum] :
      ( ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V3v1_2E0),V4v2_2E0))
        & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0P_2E0,V1l1_2E0,V2l2_2E0)) )
     => p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0P_2E0,c_2Elist_2ELUPDATE_2E3(A_27a,V3v1_2E0,V5n_2E0,V1l1_2E0),c_2Elist_2ELUPDATE_2E3(A_27b,V4v2_2E0,V5n_2E0,V2l2_2E0))) ) ).

tff(thm_2Elist_2EEVERY2__refl,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V2x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0ls_2E0)))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V2x_2E0),V2x_2E0)) )
     => p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V1R_2E0,V0ls_2E0,V0ls_2E0)) ) ).

tff(thm_2Elist_2EEVERY2__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,A_27g: $tType,A_27h: $tType] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1ys_2E0: tyop_2Elist_2Elist(A_27b)] :
          ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a),V1ys_2E0))
        <=> ( V1ys_2E0 = c_2Elist_2ENIL_2E0(A_27b) ) )
      & ! [V2P_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V3yys_2E0: tyop_2Elist_2Elist(A_27d),V4x_2E0: A_27c,V5xs_2E0: tyop_2Elist_2Elist(A_27c)] :
          ( p(c_2Elist_2ELIST__REL_2E3(A_27c,A_27d,V2P_2E0,c_2Elist_2ECONS_2E2(A_27c,V4x_2E0,V5xs_2E0),V3yys_2E0))
        <=> ? [V6y_2E0: A_27d,V7ys_2E0: tyop_2Elist_2Elist(A_27d)] :
              ( ( V3yys_2E0 = c_2Elist_2ECONS_2E2(A_27d,V6y_2E0,V7ys_2E0) )
              & p(app_2E2(A_27d,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V2P_2E0,V4x_2E0),V6y_2E0))
              & p(c_2Elist_2ELIST__REL_2E3(A_27c,A_27d,V2P_2E0,V5xs_2E0,V7ys_2E0)) ) )
      & ! [V8P_2E0: tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),V9xs_2E0: tyop_2Elist_2Elist(A_27e)] :
          ( p(c_2Elist_2ELIST__REL_2E3(A_27e,A_27f,V8P_2E0,V9xs_2E0,c_2Elist_2ENIL_2E0(A_27f)))
        <=> ( V9xs_2E0 = c_2Elist_2ENIL_2E0(A_27e) ) )
      & ! [V10P_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V11xxs_2E0: tyop_2Elist_2Elist(A_27g),V12y_2E0: A_27h,V13ys_2E0: tyop_2Elist_2Elist(A_27h)] :
          ( p(c_2Elist_2ELIST__REL_2E3(A_27g,A_27h,V10P_2E0,V11xxs_2E0,c_2Elist_2ECONS_2E2(A_27h,V12y_2E0,V13ys_2E0)))
        <=> ? [V14x_2E0: A_27g,V15xs_2E0: tyop_2Elist_2Elist(A_27g)] :
              ( ( V11xxs_2E0 = c_2Elist_2ECONS_2E2(A_27g,V14x_2E0,V15xs_2E0) )
              & p(app_2E2(A_27h,tyop_2Emin_2Ebool,app_2E2(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool),V10P_2E0,V14x_2E0),V12y_2E0))
              & p(c_2Elist_2ELIST__REL_2E3(A_27g,A_27h,V10P_2E0,V15xs_2E0,V13ys_2E0)) ) ) ) ).

tff(thm_2Elist_2ELIST__REL__trans,axiom,
    ! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3l3_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( ! [V4n_2E0: tyop_2Enum_2Enum] :
            ( ( p(c_2Eprim__rec_2E_3C_2E2(V4n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
              & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,c_2Elist_2EEL_2E2(A_27a,V4n_2E0,V1l1_2E0)),c_2Elist_2EEL_2E2(A_27a,V4n_2E0,V2l2_2E0)))
              & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,c_2Elist_2EEL_2E2(A_27a,V4n_2E0,V2l2_2E0)),c_2Elist_2EEL_2E2(A_27a,V4n_2E0,V3l3_2E0))) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,c_2Elist_2EEL_2E2(A_27a,V4n_2E0,V1l1_2E0)),c_2Elist_2EEL_2E2(A_27a,V4n_2E0,V3l3_2E0))) )
        & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V1l1_2E0,V2l2_2E0))
        & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V2l2_2E0,V3l3_2E0)) )
     => p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V1l1_2E0,V3l3_2E0)) ) ).

tff(thm_2Elist_2ESWAP__REVERSE,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( V0l1_2E0 = c_2Elist_2EREVERSE_2E1(A_27a,V1l2_2E0) )
    <=> ( V1l2_2E0 = c_2Elist_2EREVERSE_2E1(A_27a,V0l1_2E0) ) ) ).

tff(thm_2Elist_2ESWAP__REVERSE__SYM,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2EREVERSE_2E1(A_27a,V0l1_2E0) = V1l2_2E0 )
    <=> ( V0l1_2E0 = c_2Elist_2EREVERSE_2E1(A_27a,V1l2_2E0) ) ) ).

tff(thm_2Elist_2EBIGUNION__IMAGE__set__SUBSET,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ls_2E0: tyop_2Elist_2Elist(A_27b),V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27b,V1ls_2E0))),V0s_2E0))
    <=> ! [V3x_2E0: A_27b] :
          ( p(c_2Ebool_2EIN_2E2(A_27b,V3x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27b,V1ls_2E0)))
         => p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0,V3x_2E0),V0s_2E0)) ) ) ).

tff(thm_2Elist_2EIMAGE__EL__count__LENGTH,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1ls_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27b,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),F0_2E0,V0f_2E0),V1ls_2E0),V2n_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2EEL_2E2(A_27a,V2n_2E0,V1ls_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1ls_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27b,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),F0_2E0,V0f_2E0),V1ls_2E0),c_2Epred__set_2Ecount_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V1ls_2E0))) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1ls_2E0)) ) ) ).

tff(thm_2Elist_2EGENLIST__EL__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1ls_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27b,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),F0_2E0,V0f_2E0),V1ls_2E0),V2n_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2EEL_2E2(A_27a,V2n_2E0,V1ls_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1ls_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EGENLIST_2E2(A_27b,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),F0_2E0,V0f_2E0),V1ls_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V1ls_2E0)) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V1ls_2E0) ) ) ).

tff(thm_2Elist_2ELENGTH__FILTER__LEQ__MONO,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
     => ! [V3ls_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V3ls_2E0)),c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V1Q_2E0,V3ls_2E0)))) ) ).

tff(thm_2Elist_2ELIST__EQ__MAP__PAIR,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
      ( ( ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0l1_2E0) = c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V1l2_2E0) )
        & ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),V0l1_2E0) = c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),V1l2_2E0) ) )
     => ( V0l1_2E0 = V1l2_2E0 ) ) ).

tff(thm_2Elist_2ETAKE__SUM,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),V2l_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V2l_2E0),c_2Elist_2ETAKE_2E2(A_27a,V1m_2E0,c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,V2l_2E0))) ) ).

tff(thm_2Elist_2EALL__DISTINCT__FILTER__EL__IMP,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a),V2n1_2E0: tyop_2Enum_2Enum,V3n2_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l_2E0)))
        & p(c_2Eprim__rec_2E_3C_2E2(V2n1_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
        & p(c_2Eprim__rec_2E_3C_2E2(V3n2_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
        & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2EEL_2E2(A_27a,V2n1_2E0,V1l_2E0)))
        & ( c_2Elist_2EEL_2E2(A_27a,V2n1_2E0,V1l_2E0) = c_2Elist_2EEL_2E2(A_27a,V3n2_2E0,V1l_2E0) ) )
     => ( V2n1_2E0 = V3n2_2E0 ) ) ).

tff(thm_2Elist_2EFLAT__EQ__NIL,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] :
      ( ( c_2Elist_2EFLAT_2E1(A_27a,V0ls_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
    <=> p(c_2Elist_2EEVERY_2E2(tyop_2Elist_2Elist(A_27a),c_2Emin_2E_3D_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a)),V0ls_2E0)) ) ).

tff(thm_2Elist_2EALL__DISTINCT__MAP__INJ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0ls_2E0)))
              & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0ls_2E0)))
              & ( app_2E2(A_27a,A_27b,V1f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1f_2E0,V3y_2E0) ) )
           => ( V2x_2E0 = V3y_2E0 ) )
        & p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0ls_2E0)) )
     => p(c_2Elist_2EALL__DISTINCT_2E1(A_27b,c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,V0ls_2E0))) ) ).

tff(thm_2Elist_2ELENGTH__o__REVERSE,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c))] :
      ( ( c_2Ecombin_2Eo_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),c_2Elist_2ELENGTH_2E0(A_27a),c_2Elist_2EREVERSE_2E0(A_27a)) = c_2Elist_2ELENGTH_2E0(A_27a) )
      & ( c_2Ecombin_2Eo_2E2(A_27b,tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27c),c_2Elist_2ELENGTH_2E0(A_27c),c_2Ecombin_2Eo_2E2(A_27b,tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c),c_2Elist_2EREVERSE_2E0(A_27c),V0f_2E0)) = c_2Ecombin_2Eo_2E2(A_27b,tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27c),c_2Elist_2ELENGTH_2E0(A_27c),V0f_2E0) ) ) ).

tff(thm_2Elist_2EREVERSE__o__REVERSE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b))] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E0(A_27b),c_2Ecombin_2Eo_2E2(A_27a,tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E0(A_27b),V0f_2E0)) = V0f_2E0 ) ).

tff(thm_2Elist_2EGENLIST__PLUS__APPEND,axiom,
    ! [V0n2_2E0: tyop_2Enum_2Enum,V1n1_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EAPPEND_2E2(tyop_2Enum_2Enum,c_2Elist_2EGENLIST_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E1(V2a_2E0),V1n1_2E0),c_2Elist_2EGENLIST_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E1(c_2Earithmetic_2E_2B_2E2(V1n1_2E0,V2a_2E0)),V0n2_2E0)) = c_2Elist_2EGENLIST_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E1(V2a_2E0),c_2Earithmetic_2E_2B_2E2(V1n1_2E0,V0n2_2E0)) ) ).

tff(thm_2Elist_2ELIST__TO__SET__GENLIST,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EGENLIST_2E2(A_27a,V0f_2E0,V1n_2E0)) = c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,c_2Epred__set_2Ecount_2E1(V1n_2E0)) ) ).

tff(thm_2Elist_2EMEM__ZIP__MEM__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0ps_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V1p_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] :
      ( ( ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0ps_2E0)) = c_2Elist_2ELENGTH_2E1(A_27b,c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0ps_2E0)) )
        & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EZIP_2E1(A_27a,A_27b,V0ps_2E0)))) )
     => ( p(c_2Ebool_2EIN_2E2(A_27a,c_2Epair_2EFST_2E1(A_27a,A_27b,V1p_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0ps_2E0))))
        & p(c_2Ebool_2EIN_2E2(A_27b,c_2Epair_2ESND_2E1(A_27a,A_27b,V1p_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27b,c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0ps_2E0)))) ) ) ).

tff(thm_2Elist_2EDISJOINT__GENLIST__PLUS,axiom,
    ! [V0x_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Enum_2Enum,V3a_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Epred__set_2EDISJOINT_2E2(tyop_2Enum_2Enum,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,c_2Elist_2EGENLIST_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E1(V1n_2E0),c_2Earithmetic_2E_2B_2E2(V3a_2E0,V2b_2E0)))))
     => ( p(c_2Epred__set_2EDISJOINT_2E2(tyop_2Enum_2Enum,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,c_2Elist_2EGENLIST_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E1(V1n_2E0),V3a_2E0))))
        & p(c_2Epred__set_2EDISJOINT_2E2(tyop_2Enum_2Enum,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,c_2Elist_2EGENLIST_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E1(c_2Earithmetic_2E_2B_2E2(V1n_2E0,V3a_2E0)),V2b_2E0)))) ) ) ).

tff(thm_2Elist_2EEVERY2__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))] :
      ( ! [V4Q_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V2g_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V8x_2E0: A_27c,V9y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F1_2E0,V4Q_2E0),V2g_2E0),V8x_2E0),V9y_2E0) = app_2E2(A_27d,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4Q_2E0,V8x_2E0),app_2E2(A_27b,A_27d,V2g_2E0,V9y_2E0)) )
     => ( ! [V5P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3f_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V6x_2E0: A_27c,V7y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,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_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V5P_2E0),V3f_2E0),V6x_2E0),V7y_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0,app_2E2(A_27c,A_27a,V3f_2E0,V6x_2E0)),V7y_2E0) )
       => ! [V0l2_2E0: tyop_2Elist_2Elist(A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27c),V2g_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V3f_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V4Q_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V5P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
            ( ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V5P_2E0,c_2Elist_2EMAP_2E2(A_27c,A_27a,V3f_2E0,V1l1_2E0),V0l2_2E0) = c_2Elist_2ELIST__REL_2E3(A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,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_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V5P_2E0),V3f_2E0),V1l1_2E0,V0l2_2E0) )
            & ( c_2Elist_2ELIST__REL_2E3(A_27c,A_27d,V4Q_2E0,V1l1_2E0,c_2Elist_2EMAP_2E2(A_27b,A_27d,V2g_2E0,V0l2_2E0)) = c_2Elist_2ELIST__REL_2E3(A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F1_2E0,V4Q_2E0),V2g_2E0),V1l1_2E0,V0l2_2E0) ) ) ) ) ).

tff(thm_2Elist_2Eexists__list__GENLIST,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
      ( ? [V1ls_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1ls_2E0))
    <=> ? [V2n_2E0: tyop_2Enum_2Enum,V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2EGENLIST_2E2(A_27a,V3f_2E0,V2n_2E0))) ) ).

tff(thm_2Elist_2EEVERY__MEM__MONO,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( ! [V3x_2E0: A_27a] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2l_2E0)))
              & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0)) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) )
        & p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V2l_2E0)) )
     => p(c_2Elist_2EEVERY_2E2(A_27a,V1Q_2E0,V2l_2E0)) ) ).

tff(thm_2Elist_2EEVERY2__MEM__MONO,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( ( ! [V4x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] :
            ( ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V4x_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V2l1_2E0,V3l2_2E0)))))
              & p(c_2Epair_2EUNCURRY_2E2(A_27a,A_27b,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0)) )
           => p(c_2Epair_2EUNCURRY_2E2(A_27a,A_27b,tyop_2Emin_2Ebool,V1Q_2E0,V4x_2E0)) )
        & p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0P_2E0,V2l1_2E0,V3l2_2E0)) )
     => p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V1Q_2E0,V2l1_2E0,V3l2_2E0)) ) ).

tff(thm_2Elist_2Emem__exists__set,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b,V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V2l_2E0)))
     => ? [V3z_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] :
          ( ( V0x_2E0 = c_2Epair_2EFST_2E1(A_27a,A_27b,V3z_2E0) )
          & p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V3z_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V2l_2E0))) ) ) ).

tff(thm_2Elist_2Eevery__zip__snd,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))] :
      ( ! [V2P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),F0_2E0,V2P_2E0),V3x_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,V2P_2E0,c_2Epair_2ESND_2E1(A_27a,A_27b,V3x_2E0)) )
     => ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b),V2P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
         => ( c_2Elist_2EEVERY_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),F0_2E0,V2P_2E0),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) = c_2Elist_2EEVERY_2E2(A_27b,V2P_2E0,V1l2_2E0) ) ) ) ).

tff(thm_2Elist_2Eevery__zip__fst,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))] :
      ( ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),F0_2E0,V2P_2E0),V3x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,c_2Epair_2EFST_2E1(A_27a,A_27b,V3x_2E0)) )
     => ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
         => ( c_2Elist_2EEVERY_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),F0_2E0,V2P_2E0),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) = c_2Elist_2EEVERY_2E2(A_27a,V2P_2E0,V0l1_2E0) ) ) ) ).

tff(thm_2Elist_2Eel__append3,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a,V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEL_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0),c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ENIL_2E0(A_27a))),V2l2_2E0)) = V1x_2E0 ) ).

tff(thm_2Elist_2Elupdate__append,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum,V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V2l1_2E0)))
     => ( c_2Elist_2ELUPDATE_2E3(A_27a,V0x_2E0,V1n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V3l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ELUPDATE_2E3(A_27a,V0x_2E0,V1n_2E0,V2l1_2E0),V3l2_2E0) ) ) ).

tff(thm_2Elist_2Elupdate__append2,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0v_2E0: A_27a,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a,V3l2_2E0: tyop_2Elist_2Elist(A_27a),V4l3_2E0: A_27b] : ( c_2Elist_2ELUPDATE_2E3(A_27a,V0v_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0),c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Elist_2ENIL_2E0(A_27a))),V3l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V0v_2E0,c_2Elist_2ENIL_2E0(A_27a))),V3l2_2E0) ) ).

tff(thm_2Elist_2EHD__REVERSE,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( V0x_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
     => ( c_2Elist_2EHD_2E1(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V0x_2E0)) = c_2Elist_2ELAST_2E1(A_27a,V0x_2E0) ) ) ).

tff(thm_2Elist_2ELAST__REVERSE,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( V0ls_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
     => ( c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V0ls_2E0)) = c_2Elist_2EHD_2E1(A_27a,V0ls_2E0) ) ) ).

tff(thm_2Elist_2ENOT__NIL__EQ__LENGTH__NOT__0,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( V0x_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
    <=> p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0x_2E0))) ) ).

tff(thm_2Elist_2Elast__drop,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)))
     => ( c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,V0l_2E0)) = c_2Elist_2ELAST_2E1(A_27a,V0l_2E0) ) ) ).

tff(thm_2Elist_2EdropWhile__splitAtPki,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EdropWhile_2E1(A_27a,V0P_2E0) = c_2Elist_2EsplitAtPki_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Ecombin_2EC_2E1(A_27a,tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ecombin_2EK_2E0(tyop_2Emin_2Ebool,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0))),c_2Ecombin_2EK_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(A_27a)))) ) ).

tff(thm_2Elist_2EdropWhile__eq__nil,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ls_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Elist_2EdropWhile_2E2(A_27a,V0P_2E0,V1ls_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
    <=> p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1ls_2E0)) ) ).

tff(thm_2Elist_2EMEM__dropWhile__IMP,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ls_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a] :
      ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EdropWhile_2E2(A_27a,V0P_2E0,V1ls_2E0))))
     => p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1ls_2E0))) ) ).

tff(thm_2Elist_2EHD__dropWhile,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ls_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EEXISTS_2E2(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),V1ls_2E0))
     => ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2EHD_2E1(A_27a,c_2Elist_2EdropWhile_2E2(A_27a,V0P_2E0,V1ls_2E0)))) ) ).

tff(thm_2Elist_2ELENGTH__dropWhile__LESS__EQ,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ls_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EdropWhile_2E2(A_27a,V0P_2E0,V1ls_2E0)),c_2Elist_2ELENGTH_2E1(A_27a,V1ls_2E0))) ).

tff(thm_2Elist_2EdropWhile__APPEND__EVERY,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l1_2E0))
     => ( c_2Elist_2EdropWhile_2E2(A_27a,V0P_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)) = c_2Elist_2EdropWhile_2E2(A_27a,V0P_2E0,V2l2_2E0) ) ) ).

tff(thm_2Elist_2EdropWhile__APPEND__EXISTS,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EEXISTS_2E2(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),V1l1_2E0))
     => ( c_2Elist_2EdropWhile_2E2(A_27a,V0P_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EdropWhile_2E2(A_27a,V0P_2E0,V1l1_2E0),V2l2_2E0) ) ) ).

tff(thm_2Elist_2EEL__LENGTH__dropWhile__REVERSE,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ls_2E0: tyop_2Elist_2Elist(A_27a),V2k_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EdropWhile_2E2(A_27a,V0P_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1ls_2E0))),V2k_2E0))
        & p(c_2Eprim__rec_2E_3C_2E2(V2k_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1ls_2E0))) )
     => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2EEL_2E2(A_27a,V2k_2E0,V1ls_2E0))) ) ).

tff(thm_2Elist_2ELENGTH__TAKE__EQ,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2ETAKE_2E2(A_27a,V1n_2E0,V0xs_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0xs_2E0)),V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0xs_2E0)) ) ).

tff(thm_2Elist_2EIMP__EVERY__LUPDATE,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1xs_2E0: tyop_2Elist_2Elist(A_27a),V2h_2E0: A_27a,V3i_2E0: tyop_2Enum_2Enum] :
      ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2h_2E0))
        & p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1xs_2E0)) )
     => p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,c_2Elist_2ELUPDATE_2E3(A_27a,V2h_2E0,V3i_2E0,V1xs_2E0))) ) ).

tff(thm_2Elist_2EMAP__APPEND__MAP__EQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0g2_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1g1_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V2f2_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V3f1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V4xs_2E0: tyop_2Elist_2Elist(A_27a),V5ys_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( ( c_2Elist_2EAPPEND_2E2(A_27c,c_2Elist_2EMAP_2E2(A_27a,A_27c,V3f1_2E0,V4xs_2E0),c_2Elist_2EMAP_2E2(A_27b,A_27c,V1g1_2E0,V5ys_2E0)) = c_2Elist_2EAPPEND_2E2(A_27c,c_2Elist_2EMAP_2E2(A_27a,A_27c,V2f2_2E0,V4xs_2E0),c_2Elist_2EMAP_2E2(A_27b,A_27c,V0g2_2E0,V5ys_2E0)) )
    <=> ( ( c_2Elist_2EMAP_2E2(A_27a,A_27c,V3f1_2E0,V4xs_2E0) = c_2Elist_2EMAP_2E2(A_27a,A_27c,V2f2_2E0,V4xs_2E0) )
        & ( c_2Elist_2EMAP_2E2(A_27b,A_27c,V1g1_2E0,V5ys_2E0) = c_2Elist_2EMAP_2E2(A_27b,A_27c,V0g2_2E0,V5ys_2E0) ) ) ) ).

tff(thm_2Elist_2ELUPDATE__SOME__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0xs_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),V1n_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3h_2E0: A_27a] : ( c_2Elist_2ELUPDATE_2E3(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V3h_2E0)),V1n_2E0,c_2Elist_2EMAP_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E1(A_27a,A_27b,V2f_2E0),V0xs_2E0)) = c_2Elist_2EMAP_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E1(A_27a,A_27b,V2f_2E0),c_2Elist_2ELUPDATE_2E3(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(A_27a,V3h_2E0),V1n_2E0,V0xs_2E0)) ) ).

tff(thm_2Elist_2EZIP__EQ__NIL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
     => ( ( c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0)) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
      <=> ( ( V0l1_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
          & ( V1l2_2E0 = c_2Elist_2ENIL_2E0(A_27b) ) ) ) ) ).

tff(thm_2Elist_2ELUPDATE__SAME,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ls_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1ls_2E0)))
     => ( c_2Elist_2ELUPDATE_2E3(A_27a,c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1ls_2E0),V0n_2E0,V1ls_2E0) = V1ls_2E0 ) ) ).

tff(thm_2Elist_2EUNIQUE__FILTER,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1L_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EUNIQUE_2E2(A_27a,V0e_2E0,V1L_2E0))
    <=> ( c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V0e_2E0),V1L_2E0) = c_2Elist_2ECONS_2E2(A_27a,V0e_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ) ).

tff(thm_2Elist_2EUNIQUE__LENGTH__FILTER,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a,V1L_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Elist_2EUNIQUE_2E2(A_27a,V0e_2E0,V1L_2E0))
    <=> ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V0e_2E0),V1L_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).

tff(thm_2Elist_2EOPT__MMAP__cong,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2x1_2E0: tyop_2Elist_2Elist(A_27a),V3x2_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( ( V2x1_2E0 = V3x2_2E0 )
        & ! [V4a_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V4a_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V3x2_2E0)))
           => ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),V0f1_2E0,V4a_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),V1f2_2E0,V4a_2E0) ) ) )
     => ( c_2Elist_2EOPT__MMAP_2E2(A_27b,A_27a,V0f1_2E0,V2x1_2E0) = c_2Elist_2EOPT__MMAP_2E2(A_27b,A_27a,V1f2_2E0,V3x2_2E0) ) ) ).

tff(thm_2Elist_2ELAST__compute,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a))) = V0x_2E0 )
      & ! [V1h1_2E0: A_27b,V2h2_2E0: A_27b,V3t_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELAST_2E1(A_27b,c_2Elist_2ECONS_2E2(A_27b,V1h1_2E0,c_2Elist_2ECONS_2E2(A_27b,V2h2_2E0,V3t_2E0))) = c_2Elist_2ELAST_2E1(A_27b,c_2Elist_2ECONS_2E2(A_27b,V2h2_2E0,V3t_2E0)) ) ) ).

tff(thm_2Elist_2ETAKE__compute,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ETAKE_2E2(A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),c_2Elist_2ENIL_2E0(A_27b)) = c_2Elist_2ENIL_2E0(A_27b) )
      & ! [V2n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ETAKE_2E2(A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V2n_2E0)),c_2Elist_2ENIL_2E0(A_27b)) = c_2Elist_2ENIL_2E0(A_27b) )
      & ! [V3n_2E0: tyop_2Enum_2Enum,V4h_2E0: A_27c,V5t_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ETAKE_2E2(A_27c,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),c_2Elist_2ECONS_2E2(A_27c,V4h_2E0,V5t_2E0)) = c_2Elist_2ECONS_2E2(A_27c,V4h_2E0,c_2Elist_2ETAKE_2E2(A_27c,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V5t_2E0)) )
      & ! [V6n_2E0: tyop_2Enum_2Enum,V7h_2E0: A_27c,V8t_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ETAKE_2E2(A_27c,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V6n_2E0)),c_2Elist_2ECONS_2E2(A_27c,V7h_2E0,V8t_2E0)) = c_2Elist_2ECONS_2E2(A_27c,V7h_2E0,c_2Elist_2ETAKE_2E2(A_27c,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V6n_2E0)),V8t_2E0)) ) ) ).

tff(thm_2Elist_2EDROP__compute,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = V0l_2E0 )
      & ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EDROP_2E2(A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),c_2Elist_2ENIL_2E0(A_27b)) = c_2Elist_2ENIL_2E0(A_27b) )
      & ! [V2n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EDROP_2E2(A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V2n_2E0)),c_2Elist_2ENIL_2E0(A_27b)) = c_2Elist_2ENIL_2E0(A_27b) )
      & ! [V3n_2E0: tyop_2Enum_2Enum,V4h_2E0: A_27c,V5t_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EDROP_2E2(A_27c,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),c_2Elist_2ECONS_2E2(A_27c,V4h_2E0,V5t_2E0)) = c_2Elist_2EDROP_2E2(A_27c,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V5t_2E0) )
      & ! [V6n_2E0: tyop_2Enum_2Enum,V7h_2E0: A_27c,V8t_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EDROP_2E2(A_27c,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V6n_2E0)),c_2Elist_2ECONS_2E2(A_27c,V7h_2E0,V8t_2E0)) = c_2Elist_2EDROP_2E2(A_27c,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V6n_2E0)),V8t_2E0) ) ) ).

tff(thm_2Elist_2EoHD__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Elist_2Elist(A_27b),V1h_2E0: A_27b] :
      ( ( c_2Elist_2EoHD_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(A_27a) )
      & ( c_2Elist_2EoHD_2E1(A_27b,c_2Elist_2ECONS_2E2(A_27b,V1h_2E0,V0t_2E0)) = c_2Eoption_2ESOME_2E1(A_27b,V1h_2E0) ) ) ).

tff(thm_2Elist_2EoEL__THM,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EoEL_2E2(A_27a,V1n_2E0,V0xs_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0xs_2E0)),c_2Eoption_2ESOME_2E1(A_27a,c_2Elist_2EEL_2E2(A_27a,V1n_2E0,V0xs_2E0)),c_2Eoption_2ENONE_2E0(A_27a)) ) ).

tff(thm_2Elist_2EoEL__EQ__EL,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum,V2y_2E0: A_27a] :
      ( ( c_2Elist_2EoEL_2E2(A_27a,V1n_2E0,V0xs_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V2y_2E0) )
    <=> ( p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0xs_2E0)))
        & ( V2y_2E0 = c_2Elist_2EEL_2E2(A_27a,V1n_2E0,V0xs_2E0) ) ) ) ).

tff(thm_2Elist_2EoEL__DROP,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum,V2m_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EoEL_2E2(A_27a,V1n_2E0,c_2Elist_2EDROP_2E2(A_27a,V2m_2E0,V0xs_2E0)) = c_2Elist_2EoEL_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V2m_2E0,V1n_2E0),V0xs_2E0) ) ).

tff(thm_2Elist_2EoEL__TAKE__E,axiom,
    ! [A_27a: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a,V2n_2E0: tyop_2Enum_2Enum,V3m_2E0: tyop_2Enum_2Enum] :
      ( ( c_2Elist_2EoEL_2E2(A_27a,V2n_2E0,c_2Elist_2ETAKE_2E2(A_27a,V3m_2E0,V0xs_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,V1x_2E0) )
     => ( c_2Elist_2EoEL_2E2(A_27a,V2n_2E0,V0xs_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V1x_2E0) ) ) ).

tff(thm_2Elist_2EoEL__LUPDATE,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1i_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1i_2E0),V2n_2E0))
        <=> ( V1i_2E0 != V2n_2E0 ) )
     => ! [V0xs_2E0: tyop_2Elist_2Elist(A_27a),V1i_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum,V3x_2E0: A_27a] : ( c_2Elist_2EoEL_2E2(A_27a,V2n_2E0,c_2Elist_2ELUPDATE_2E3(A_27a,V3x_2E0,V1i_2E0,V0xs_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1i_2E0),V2n_2E0),c_2Elist_2EoEL_2E2(A_27a,V2n_2E0,V0xs_2E0),c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),c_2Eprim__rec_2E_3C_2E2(V1i_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0xs_2E0)),c_2Eoption_2ESOME_2E1(A_27a,V3x_2E0),c_2Eoption_2ENONE_2E0(A_27a))) ) ) ).

tff(thm_2Elist_2Elazy__list__case__compute,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1x_27_2E0: A_27b,V2x_27_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))] : ( c_2Elist_2Elist__CASE_2E3(A_27a,A_27b,V0x_2E0,V1x_27_2E0,V2x_27_27_2E0) = c_2Ebool_2ECOND_2E3(A_27b,c_2Elist_2ENULL_2E1(A_27a,V0x_2E0),V1x_27_2E0,app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2x_27_27_2E0,c_2Elist_2EHD_2E1(A_27a,V0x_2E0)),c_2Elist_2ETL_2E1(A_27a,V0x_2E0))) ) ).

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