%------------------------------------------------------------------------------
% File     : ITP043_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    : Encode.ax [Gau19]
%          : HL4043_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  352 ( 117 unt; 174 typ;   0 def)
%            Number of atoms       :  323 ( 182 equ)
%            Maximal formula atoms :   14 (   0 avg)
%            Number of connectives :  157 (  12   ~;   5   |;  51   &)
%                                         (  33 <=>;  56  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   5 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  154 (  91   >;  63   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  170 ( 170 usr;  25 con; 0-6 aty)
%            Number of variables   :  754 ( 582   !;  13   ?; 754   :)
%                                         ( 159  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2EEncode_2Etree,type,
    tyop_2EEncode_2Etree: $tType > $tType ).

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(tyop_2Esum_2Esum,type,
    tyop_2Esum_2Esum: ( $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_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_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

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

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

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

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

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

tff(c_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_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_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_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_2Earithmetic_2EDIV_2E0,type,
    c_2Earithmetic_2EDIV_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2EDIV_2E2,type,
    c_2Earithmetic_2EDIV_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Earithmetic_2EEVEN_2E0,type,
    c_2Earithmetic_2EEVEN_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2Earithmetic_2EEVEN_2E1,type,
    c_2Earithmetic_2EEVEN_2E1: tyop_2Enum_2Enum > 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_2E1,type,
    c_2Elist_2EEVERY_2E1: 
      !>[A_27a: $tType] : ( 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_2Earithmetic_2EEXP_2E0,type,
    c_2Earithmetic_2EEXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2EEXP_2E2,type,
    c_2Earithmetic_2EEXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

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_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_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_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_2Esum_2EINL_2E0,type,
    c_2Esum_2EINL_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)) ).

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

tff(c_2Esum_2EINR_2E0,type,
    c_2Esum_2EINR_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)) ).

tff(c_2Esum_2EINR_2E1,type,
    c_2Esum_2EINR_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27b > tyop_2Esum_2Esum(A_27a,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_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_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_2Earithmetic_2EMOD_2E0,type,
    c_2Earithmetic_2EMOD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2EMOD_2E2,type,
    c_2Earithmetic_2EMOD_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_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_2EEncode_2ENode_2E0,type,
    c_2EEncode_2ENode_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2EEncode_2Etree(A_27a))) ).

tff(c_2EEncode_2ENode_2E2,type,
    c_2EEncode_2ENode_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)) ) > tyop_2EEncode_2Etree(A_27a) ) ).

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_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_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

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

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(c_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_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_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_2EEncode_2Ebiprefix_2E0,type,
    c_2EEncode_2Ebiprefix_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_2EEncode_2Ebiprefix_2E2,type,
    c_2EEncode_2Ebiprefix_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2EEncode_2Ecollision__free_2E0,type,
    c_2EEncode_2Ecollision__free_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2EEncode_2Ecollision__free_2E2,type,
    c_2EEncode_2Ecollision__free_2E2: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ).

tff(c_2EEncode_2Eencode__blist_2E0,type,
    c_2EEncode_2Eencode__blist_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,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)))) ).

tff(c_2EEncode_2Eencode__blist_2E2,type,
    c_2EEncode_2Eencode__blist_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)) ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)) ) ).

tff(c_2EEncode_2Eencode__blist_2E3,type,
    c_2EEncode_2Eencode__blist_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)) * tyop_2Elist_2Elist(A_27b) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2EEncode_2Eencode__bnum_2E0,type,
    c_2EEncode_2Eencode__bnum_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ).

tff(c_2EEncode_2Eencode__bnum_2E1,type,
    c_2EEncode_2Eencode__bnum_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ).

tff(c_2EEncode_2Eencode__bnum_2E2,type,
    c_2EEncode_2Eencode__bnum_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ).

tff(c_2EEncode_2Eencode__bool_2E0,type,
    c_2EEncode_2Eencode__bool_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ).

tff(c_2EEncode_2Eencode__bool_2E1,type,
    c_2EEncode_2Eencode__bool_2E1: tyop_2Emin_2Ebool > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ).

tff(c_2EEncode_2Eencode__list_2E0,type,
    c_2EEncode_2Eencode__list_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ).

tff(c_2EEncode_2Eencode__list_2E1,type,
    c_2EEncode_2Eencode__list_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ) ).

tff(c_2EEncode_2Eencode__list_2E2,type,
    c_2EEncode_2Eencode__list_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) ).

tff(c_2EEncode_2Eencode__num_2E0,type,
    c_2EEncode_2Eencode__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ).

tff(c_2EEncode_2Eencode__num_2E1,type,
    c_2EEncode_2Eencode__num_2E1: tyop_2Enum_2Enum > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ).

tff(c_2EEncode_2Eencode__option_2E0,type,
    c_2EEncode_2Eencode__option_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ).

tff(c_2EEncode_2Eencode__option_2E1,type,
    c_2EEncode_2Eencode__option_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ) ).

tff(c_2EEncode_2Eencode__option_2E2,type,
    c_2EEncode_2Eencode__option_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) * tyop_2Eoption_2Eoption(A_27a) ) > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) ).

tff(c_2EEncode_2Eencode__prod_2E0,type,
    c_2EEncode_2Eencode__prod_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ).

tff(c_2EEncode_2Eencode__prod_2E2,type,
    c_2EEncode_2Eencode__prod_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ) ).

tff(c_2EEncode_2Eencode__prod_2E3,type,
    c_2EEncode_2Eencode__prod_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) * tyop_2Epair_2Eprod(A_27a,A_27b) ) > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) ).

tff(c_2EEncode_2Eencode__sum_2E0,type,
    c_2EEncode_2Eencode__sum_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ).

tff(c_2EEncode_2Eencode__sum_2E2,type,
    c_2EEncode_2Eencode__sum_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ) ).

tff(c_2EEncode_2Eencode__sum_2E3,type,
    c_2EEncode_2Eencode__sum_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) * tyop_2Esum_2Esum(A_27a,A_27b) ) > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) ).

tff(c_2EEncode_2Eencode__tree_2E0,type,
    c_2EEncode_2Eencode__tree_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ).

tff(c_2EEncode_2Eencode__tree_2E1,type,
    c_2EEncode_2Eencode__tree_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ) ).

tff(c_2EEncode_2Eencode__tree_2E2,type,
    c_2EEncode_2Eencode__tree_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) * tyop_2EEncode_2Etree(A_27a) ) > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) ).

tff(c_2EEncode_2Eencode__unit_2E0,type,
    c_2EEncode_2Eencode__unit_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ).

tff(c_2EEncode_2Eencode__unit_2E1,type,
    c_2EEncode_2Eencode__unit_2E1: tyop_2Eone_2Eone > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ).

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_2EEncode_2Elift__blist_2E0,type,
    c_2EEncode_2Elift__blist_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_2Emin_2Ebool))) ).

tff(c_2EEncode_2Elift__blist_2E2,type,
    c_2EEncode_2Elift__blist_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ) ).

tff(c_2EEncode_2Elift__blist_2E3,type,
    c_2EEncode_2Elift__blist_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2EEncode_2Elift__option_2E0,type,
    c_2EEncode_2Elift__option_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2EEncode_2Elift__option_2E1,type,
    c_2EEncode_2Elift__option_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool) ) ).

tff(c_2EEncode_2Elift__option_2E2,type,
    c_2EEncode_2Elift__option_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Eoption_2Eoption(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2EEncode_2Elift__prod_2E0,type,
    c_2EEncode_2Elift__prod_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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))) ).

tff(c_2EEncode_2Elift__prod_2E2,type,
    c_2EEncode_2Elift__prod_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).

tff(c_2EEncode_2Elift__prod_2E3,type,
    c_2EEncode_2Elift__prod_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * tyop_2Epair_2Eprod(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).

tff(c_2EEncode_2Elift__sum_2E0,type,
    c_2EEncode_2Elift__sum_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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))) ).

tff(c_2EEncode_2Elift__sum_2E2,type,
    c_2EEncode_2Elift__sum_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).

tff(c_2EEncode_2Elift__sum_2E3,type,
    c_2EEncode_2Elift__sum_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * tyop_2Esum_2Esum(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).

tff(c_2EEncode_2Elift__tree_2E0,type,
    c_2EEncode_2Elift__tree_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2EEncode_2Elift__tree_2E1,type,
    c_2EEncode_2Elift__tree_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool) ) ).

tff(c_2EEncode_2Elift__tree_2E2,type,
    c_2EEncode_2Elift__tree_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2EEncode_2Etree(A_27a) ) > tyop_2Emin_2Ebool ) ).

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_2Esum_2Esum__CASE_2E0,type,
    c_2Esum_2Esum__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),A_27c))) ).

tff(c_2Esum_2Esum__CASE_2E3,type,
    c_2Esum_2Esum__CASE_2E3: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Esum_2Esum(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) * tyop_2Emin_2Efun(A_27b,A_27c) ) > A_27c ) ).

tff(c_2EEncode_2Etree1__size_2E0,type,
    c_2EEncode_2Etree1__size_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Enum_2Enum)) ).

tff(c_2EEncode_2Etree1__size_2E2,type,
    c_2EEncode_2Etree1__size_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)) ) > tyop_2Enum_2Enum ) ).

tff(c_2EEncode_2Etree__CASE_2E0,type,
    c_2EEncode_2Etree__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b)),A_27b)) ).

tff(c_2EEncode_2Etree__CASE_2E2,type,
    c_2EEncode_2Etree__CASE_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2EEncode_2Etree(A_27a) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b)) ) > A_27b ) ).

tff(c_2EEncode_2Etree__size_2E0,type,
    c_2EEncode_2Etree__size_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Enum_2Enum)) ).

tff(c_2EEncode_2Etree__size_2E2,type,
    c_2EEncode_2Etree__size_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2EEncode_2Etree(A_27a) ) > tyop_2Enum_2Enum ) ).

tff(c_2EEncode_2Ewf__encoder_2E0,type,
    c_2EEncode_2Ewf__encoder_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)) ).

tff(c_2EEncode_2Ewf__encoder_2E2,type,
    c_2EEncode_2Ewf__encoder_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Ebool ) ).

tff(c_2EEncode_2Ewf__pred_2E0,type,
    c_2EEncode_2Ewf__pred_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2EEncode_2Ewf__pred_2E1,type,
    c_2EEncode_2Ewf__pred_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2EEncode_2Ewf__pred__bnum_2E0,type,
    c_2EEncode_2Ewf__pred__bnum_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2EEncode_2Ewf__pred__bnum_2E2,type,
    c_2EEncode_2Ewf__pred__bnum_2E2: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(arityeq2_2Ec_2Earithmetic_2E_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_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_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_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
      ( ( X0_2E0 = X1_2E0 )
    <=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).

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

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

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),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_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Elist_2EAPPEND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

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

tff(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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X2_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),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_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Elist_2ECONS_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2EEncode_2Etree_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2EEncode_2Etree(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] : ( c_2Elist_2ECONS_2E2(tyop_2EEncode_2Etree(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))),c_2Elist_2ECONS_2E0(tyop_2EEncode_2Etree(A_27a)),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_2Earithmetic_2EDIV_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV_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_2EDIV_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EEVERY_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EEVERY_2E1(A_27a,X0_2E0) = 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) ) ).

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_2Etyop_2EEncode_2Etree_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] : ( c_2Elist_2EEVERY_2E2(tyop_2EEncode_2Etree(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(tyop_2EEncode_2Etree(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_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_2EEXP_2E0,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(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_2Elist_2EHD_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EHD_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2EHD_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2EEncode_2Etree_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2EEncode_2Etree(A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2EEncode_2Etree(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2EEncode_2Etree(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a] : ( c_2Esum_2EINL_2E1(A_27a,A_27b,X0_2E0) = app_2E2(A_27a,tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b] : ( c_2Esum_2EINR_2E1(A_27a,A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E0(tyop_2Emin_2Ebool,A_27a),X0_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_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Elist_2ELENGTH_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Emin_2Ebool),X0_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(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2EEncode_2Etree_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2EEncode_2Etree(A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2EEncode_2Etree(A_27a)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2EMOD_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_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_2EMOD_2E0,X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2EEncode_2ENode_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] : ( c_2EEncode_2ENode_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2EEncode_2Etree(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2EEncode_2Etree(A_27a)),c_2EEncode_2ENode_2E0(A_27a),X0_2E0),X1_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_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_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_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_2EEncode_2Etree_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_2EEncode_2Etree(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2EEncode_2Etree(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(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_2EEncode_2Etree(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Eind__type_2Erecspace(A_27a),tyop_2EEncode_2Etree(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Erelation_2EWFREC_2E0(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2EEncode_2Ebiprefix_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EEncode_2Ebiprefix_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_2EEncode_2Ebiprefix_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ebiprefix_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EEncode_2Ebiprefix_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2EEncode_2Ebiprefix_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ecollision__free_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Ecollision__free_2E2(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_2EEncode_2Ecollision__free_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Eencode__blist_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__blist_2E2(tyop_2Emin_2Ebool,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EEncode_2Eencode__blist_2E0(tyop_2Emin_2Ebool,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EEncode_2Eencode__blist_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EEncode_2Eencode__blist_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),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(A_27a)),app_2E2(tyop_2Enum_2Enum,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_2EEncode_2Eencode__blist_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Eencode__bnum_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2EEncode_2Eencode__bnum_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__bnum_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Eencode__bnum_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2EEncode_2Eencode__bnum_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__bnum_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Eencode__bool_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2EEncode_2Eencode__bool_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EEncode_2Eencode__bool_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Eencode__list_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__list_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__list_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Eencode__list_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EEncode_2Eencode__list_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__list_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Eencode__list_2E2_2Emono_2Etyop_2EEncode_2Etree_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] : ( c_2EEncode_2Eencode__list_2E2(tyop_2EEncode_2Etree(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__list_2E0(tyop_2EEncode_2Etree(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Eencode__num_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2EEncode_2Eencode__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EEncode_2Eencode__num_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Eencode__option_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__option_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__option_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Eencode__option_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2EEncode_2Eencode__option_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__option_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Eencode__prod_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__prod_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EEncode_2Eencode__prod_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EEncode_2Eencode__prod_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X2_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2EEncode_2Eencode__prod_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EEncode_2Eencode__prod_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Eencode__sum_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__sum_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EEncode_2Eencode__sum_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EEncode_2Eencode__sum_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X2_2E0: tyop_2Esum_2Esum(A_27a,A_27b)] : ( c_2EEncode_2Eencode__sum_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EEncode_2Eencode__sum_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Eencode__tree_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__tree_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__tree_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Eencode__tree_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2EEncode_2Etree(A_27a)] : ( c_2EEncode_2Eencode__tree_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__tree_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Eencode__unit_2E1,axiom,
    ! [X0_2E0: tyop_2Eone_2Eone] : ( c_2EEncode_2Eencode__unit_2E1(X0_2E0) = app_2E2(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EEncode_2Eencode__unit_2E0,X0_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(arityeq2_2Ec_2Elist_2EisPREFIX_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Elist_2EisPREFIX_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Elist_2EisPREFIX_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Elift__blist_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Elift__blist_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_2Emin_2Ebool),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_2Emin_2Ebool)),c_2EEncode_2Elift__blist_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EEncode_2Elift__blist_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_2EEncode_2Elift__blist_2E3(A_27a,X0_2E0,X1_2E0,X2_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),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_2Emin_2Ebool)),c_2EEncode_2Elift__blist_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Elift__option_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Elift__option_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2EEncode_2Elift__option_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Elift__option_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2EEncode_2Elift__option_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2EEncode_2Elift__option_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Elift__prod_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Elift__prod_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),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_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2EEncode_2Elift__prod_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EEncode_2Elift__prod_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2EEncode_2Elift__prod_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = 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),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2EEncode_2Elift__prod_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Elift__sum_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Elift__sum_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),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_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2EEncode_2Elift__sum_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EEncode_2Elift__sum_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: tyop_2Esum_2Esum(A_27a,A_27b)] : ( c_2EEncode_2Elift__sum_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),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_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2EEncode_2Elift__sum_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Elift__tree_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Elift__tree_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),c_2EEncode_2Elift__tree_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Elift__tree_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2EEncode_2Etree(A_27a)] : ( c_2EEncode_2Elift__tree_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),c_2EEncode_2Elift__tree_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eoption_2Eoption__CASE_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Esum_2Esum__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Esum_2Esum(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_2Esum_2Esum__CASE_2E3(A_27a,A_27b,tyop_2Emin_2Ebool,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_2Esum_2Esum(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_2Esum_2Esum__CASE_2E0(A_27a,A_27b,tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Etree1__size_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] : ( c_2EEncode_2Etree1__size_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Enum_2Enum),c_2EEncode_2Etree1__size_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Etree__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2EEncode_2Etree(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b))] : ( c_2EEncode_2Etree__CASE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b)),A_27b,app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b)),A_27b),c_2EEncode_2Etree__CASE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Etree__size_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2EEncode_2Etree(A_27a)] : ( c_2EEncode_2Etree__size_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Enum_2Enum),c_2EEncode_2Etree__size_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ewf__encoder_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_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Ewf__encoder_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(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_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EEncode_2Ewf__encoder_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ewf__encoder_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_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Ewf__encoder_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EEncode_2Ewf__encoder_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ewf__encoder_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Ewf__encoder_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EEncode_2Ewf__encoder_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ewf__encoder_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_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Ewf__encoder_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EEncode_2Ewf__encoder_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ewf__encoder_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_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Ewf__encoder_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(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_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EEncode_2Ewf__encoder_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ewf__encoder_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Ewf__encoder_2E2(tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EEncode_2Ewf__encoder_2E0(tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ewf__encoder_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Ewf__encoder_2E2(tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EEncode_2Ewf__encoder_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ewf__encoder_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_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Ewf__encoder_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_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EEncode_2Ewf__encoder_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ewf__encoder_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Ewf__encoder_2E2(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EEncode_2Ewf__encoder_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ewf__encoder_2E2_2Emono_2Etyop_2EEncode_2Etree_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Ewf__encoder_2E2(tyop_2EEncode_2Etree(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EEncode_2Ewf__encoder_2E0(tyop_2EEncode_2Etree(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Ewf__pred_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Ewf__pred_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2EEncode_2Ewf__pred_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Ewf__pred_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Ewf__pred_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2EEncode_2Ewf__pred_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ewf__pred__bnum_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Ewf__pred__bnum_2E2(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_2EEncode_2Ewf__pred__bnum_2E0,X0_2E0),X1_2E0) ) ).

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

tff(thm_2EEncode_2Ebiprefix__def,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Elist_2Elist(A_27a),V1b_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2EEncode_2Ebiprefix_2E2(A_27a,V0a_2E0,V1b_2E0))
    <=> ( p(c_2Elist_2EisPREFIX_2E2(A_27a,V1b_2E0,V0a_2E0))
        | p(c_2Elist_2EisPREFIX_2E2(A_27a,V0a_2E0,V1b_2E0)) ) ) ).

tff(thm_2EEncode_2Ewf__pred__def,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2EEncode_2Ewf__pred_2E1(A_27a,V0p_2E0))
    <=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V1x_2E0)) ) ).

tff(thm_2EEncode_2Ewf__encoder__def,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
      ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
    <=> ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
          ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V2x_2E0))
            & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V3y_2E0))
            & p(c_2Elist_2EisPREFIX_2E2(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V3y_2E0),app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V2x_2E0))) )
         => ( V2x_2E0 = V3y_2E0 ) ) ) ).

tff(thm_2EEncode_2Eencode__unit__def,axiom,
    ! [V0v0_2E0: tyop_2Eone_2Eone] : ( c_2EEncode_2Eencode__unit_2E1(V0v0_2E0) = c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool) ) ).

tff(thm_2EEncode_2Eencode__bool__def,axiom,
    ! [V0x_2E0: tyop_2Emin_2Ebool] : ( c_2EEncode_2Eencode__bool_2E1(V0x_2E0) = c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,V0x_2E0,c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool)) ) ).

tff(thm_2EEncode_2Eencode__prod__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0xb_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V1yb_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V2x_2E0: A_27a,V3y_2E0: A_27b] : ( c_2EEncode_2Eencode__prod_2E3(A_27a,A_27b,V0xb_2E0,V1yb_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)) = c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0xb_2E0,V2x_2E0),app_2E2(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1yb_2E0,V3y_2E0)) ) ).

tff(thm_2EEncode_2Elift__prod__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] :
      ( p(c_2EEncode_2Elift__prod_2E3(A_27a,A_27b,V0p1_2E0,V1p2_2E0,V2x_2E0))
    <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p1_2E0,c_2Epair_2EFST_2E1(A_27a,A_27b,V2x_2E0)))
        & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V1p2_2E0,c_2Epair_2ESND_2E1(A_27a,A_27b,V2x_2E0))) ) ) ).

tff(thm_2EEncode_2Eencode__sum__def,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0xb_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V1yb_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V2x_2E0: A_27a] : ( c_2EEncode_2Eencode__sum_2E3(A_27a,A_27b,V0xb_2E0,V1yb_2E0,c_2Esum_2EINL_2E1(A_27a,A_27b,V2x_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0xb_2E0,V2x_2E0)) )
      & ! [V3xb_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V4yb_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V5y_2E0: A_27b] : ( c_2EEncode_2Eencode__sum_2E3(A_27a,A_27b,V3xb_2E0,V4yb_2E0,c_2Esum_2EINR_2E1(A_27a,A_27b,V5y_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0,app_2E2(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V4yb_2E0,V5y_2E0)) ) ) ).

tff(thm_2EEncode_2Elift__sum__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F0_2E0: 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_27b,tyop_2Emin_2Ebool),V4x2_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F1_2E0,V1p2_2E0),V4x2_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,V1p2_2E0,V4x2_2E0) )
     => ( ! [V0p1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x1_2E0: A_27a] : ( 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,V0p1_2E0),V3x1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0p1_2E0,V3x1_2E0) )
       => ! [V0p1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Esum_2Esum(A_27a,A_27b)] : ( c_2EEncode_2Elift__sum_2E3(A_27a,A_27b,V0p1_2E0,V1p2_2E0,V2x_2E0) = c_2Esum_2Esum__CASE_2E3(A_27a,A_27b,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0p1_2E0),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F1_2E0,V1p2_2E0)) ) ) ) ).

tff(thm_2EEncode_2Eencode__option__def,axiom,
    ! [A_27a: $tType] :
      ( ! [V0xb_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__option_2E2(A_27a,V0xb_2E0,c_2Eoption_2ENONE_2E0(A_27a)) = c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0,c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool)) )
      & ! [V1xb_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V2x_2E0: A_27a] : ( c_2EEncode_2Eencode__option_2E2(A_27a,V1xb_2E0,c_2Eoption_2ESOME_2E1(A_27a,V2x_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1xb_2E0,V2x_2E0)) ) ) ).

tff(thm_2EEncode_2Elift__option__def,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),V2y_2E0: A_27a] : ( 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),V2y_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V2y_2E0) )
     => ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2EEncode_2Elift__option_2E2(A_27a,V0p_2E0,V1x_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Emin_2Ebool,V1x_2E0,c_2Ebool_2ET_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0p_2E0)) ) ) ).

tff(thm_2EEncode_2Eencode__list__def,axiom,
    ! [A_27a: $tType] :
      ( ! [V0xb_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__list_2E2(A_27a,V0xb_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0,c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool)) )
      & ! [V1xb_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V2x_2E0: A_27a,V3xs_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EEncode_2Eencode__list_2E2(A_27a,V1xb_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3xs_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1xb_2E0,V2x_2E0),c_2EEncode_2Eencode__list_2E2(A_27a,V1xb_2E0,V3xs_2E0))) ) ) ).

tff(thm_2EEncode_2Eencode__blist__def,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0e_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EEncode_2Eencode__blist_2E3(A_27a,A_27b,c_2Enum_2E0_2E0,V0e_2E0,V1l_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V2m_2E0: tyop_2Enum_2Enum,V3e_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V4l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EEncode_2Eencode__blist_2E3(A_27a,A_27b,c_2Enum_2ESUC_2E1(V2m_2E0),V3e_2E0,V4l_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,app_2E2(A_27b,tyop_2Elist_2Elist(A_27a),V3e_2E0,c_2Elist_2EHD_2E1(A_27b,V4l_2E0)),c_2EEncode_2Eencode__blist_2E3(A_27a,A_27b,V2m_2E0,V3e_2E0,c_2Elist_2ETL_2E1(A_27b,V4l_2E0))) ) ) ).

tff(thm_2EEncode_2Elift__blist__def,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2EEncode_2Elift__blist_2E3(A_27a,V0m_2E0,V1p_2E0,V2x_2E0))
    <=> ( p(c_2Elist_2EEVERY_2E2(A_27a,V1p_2E0,V2x_2E0))
        & ( c_2Elist_2ELENGTH_2E1(A_27a,V2x_2E0) = V0m_2E0 ) ) ) ).

tff(thm_2EEncode_2Eencode__num__primitive__def,axiom,
    ! [F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
      ( ! [V4a_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V4a_2E0))
        <=> ( V4a_2E0 = c_2Enum_2E0_2E0 ) )
     => ( ! [V3encode__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V4a_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),F1_2E0,V3encode__num_2E0),V4a_2E0) = c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V4a_2E0),c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Earithmetic_2EEVEN_2E1(V4a_2E0),c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3encode__num_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V4a_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3encode__num_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V4a_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))) )
       => ( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
              ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0))
            <=> ( p(c_2Erelation_2EWF_2E1(tyop_2Enum_2Enum,V0R_2E0))
                & ! [V1n_2E0: tyop_2Enum_2Enum] :
                    ( ( ( V1n_2E0 != c_2Enum_2E0_2E0 )
                      & p(c_2Earithmetic_2EEVEN_2E1(V1n_2E0)) )
                   => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0R_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),V1n_2E0)) )
                & ! [V2n_2E0: tyop_2Enum_2Enum] :
                    ( ( ( V2n_2E0 != c_2Enum_2E0_2E0 )
                      & ~ p(c_2Earithmetic_2EEVEN_2E1(V2n_2E0)) )
                   => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0R_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),V2n_2E0)) ) ) )
         => ( c_2EEncode_2Eencode__num_2E0 = c_2Erelation_2EWFREC_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ).

tff(thm_2EEncode_2Eencode__bnum__def,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V2n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2n_2E0))
        <=> ~ p(c_2Earithmetic_2EEVEN_2E1(V2n_2E0)) )
     => ( ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2EEncode_2Eencode__bnum_2E2(c_2Enum_2E0_2E0,V0n_2E0) = c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool) )
        & ! [V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2EEncode_2Eencode__bnum_2E2(c_2Enum_2ESUC_2E1(V1m_2E0),V2n_2E0) = c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2n_2E0),c_2EEncode_2Eencode__bnum_2E2(V1m_2E0,c_2Earithmetic_2EDIV_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) ) ).

tff(thm_2EEncode_2Ecollision__free__def,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2EEncode_2Ecollision__free_2E2(V0m_2E0,V1p_2E0))
    <=> ! [V2x_2E0: tyop_2Enum_2Enum,V3y_2E0: tyop_2Enum_2Enum] :
          ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1p_2E0,V2x_2E0))
            & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1p_2E0,V3y_2E0))
            & ( c_2Earithmetic_2EMOD_2E2(V2x_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0m_2E0)) = c_2Earithmetic_2EMOD_2E2(V3y_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0m_2E0)) ) )
         => ( V2x_2E0 = V3y_2E0 ) ) ) ).

tff(thm_2EEncode_2Ewf__pred__bnum__def,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2EEncode_2Ewf__pred__bnum_2E2(V0m_2E0,V1p_2E0))
    <=> ( p(c_2EEncode_2Ewf__pred_2E1(tyop_2Enum_2Enum,V1p_2E0))
        & ! [V2x_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1p_2E0,V2x_2E0))
           => p(c_2Eprim__rec_2E_3C_2E2(V2x_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0m_2E0))) ) ) ) ).

tff(thm_2EEncode_2Etree__TY__DEF,axiom,
    ! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),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)] :
      ( ! [V12n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F3_2E0,V12n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
     => ( ! [V9n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F2_2E0,V9n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
       => ( ! [V7n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F1_2E0,V7n_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_27tree_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V3_27_40temp_20_40ind__typeEncode0list_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
                    ( ( ! [V4a0_27_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
                          ( ? [V5a0_2E0: A_27a,V6a1_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
                              ( ( V4a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2E0_2E0,V5a0_2E0,c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),V6a1_2E0,F1_2E0)) )
                              & p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V3_27_40temp_20_40ind__typeEncode0list_27_2E0,V6a1_2E0)) )
                         => p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27tree_27_2E0,V4a0_27_2E0)) )
                      & ! [V8a1_27_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
                          ( ( ( V8a1_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0),c_2Ebool_2EARB_2E0(A_27a),F2_2E0) )
                            | ? [V10a0_2E0: tyop_2Eind__type_2Erecspace(A_27a),V11a1_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
                                ( ( V8a1_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0)),c_2Ebool_2EARB_2E0(A_27a),c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),V10a0_2E0,c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),V11a1_2E0,F3_2E0))) )
                                & p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27tree_27_2E0,V10a0_2E0))
                                & p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V3_27_40temp_20_40ind__typeEncode0list_27_2E0,V11a1_2E0)) ) )
                         => p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V3_27_40temp_20_40ind__typeEncode0list_27_2E0,V8a1_27_2E0)) ) )
                   => p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27tree_27_2E0,V1a0_27_2E0)) ) )
           => ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2EEncode_2Etree(A_27a),F0_2E0,V0rep_2E0)) ) ) ) ) ).

tff(thm_2EEncode_2Etree__case__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a0_2E0: A_27a,V1a1_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b))] : ( c_2EEncode_2Etree__CASE_2E2(A_27a,A_27b,c_2EEncode_2ENode_2E2(A_27a,V0a0_2E0,V1a1_2E0),V2f_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b),V2f_2E0,V0a0_2E0),V1a1_2E0) ) ).

tff(thm_2EEncode_2Etree__size__def,axiom,
    ! [A_27a: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1a0_2E0: A_27a,V2a1_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] : ( c_2EEncode_2Etree__size_2E2(A_27a,V0f_2E0,c_2EEncode_2ENode_2E2(A_27a,V1a0_2E0,V2a1_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,V0f_2E0,V1a0_2E0),c_2EEncode_2Etree1__size_2E2(A_27a,V0f_2E0,V2a1_2E0))) )
      & ! [V3f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2EEncode_2Etree1__size_2E2(A_27a,V3f_2E0,c_2Elist_2ENIL_2E0(tyop_2EEncode_2Etree(A_27a))) = c_2Enum_2E0_2E0 )
      & ! [V4f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5a0_2E0: tyop_2EEncode_2Etree(A_27a),V6a1_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] : ( c_2EEncode_2Etree1__size_2E2(A_27a,V4f_2E0,c_2Elist_2ECONS_2E2(tyop_2EEncode_2Etree(A_27a),V5a0_2E0,V6a1_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E2(c_2EEncode_2Etree__size_2E2(A_27a,V4f_2E0,V5a0_2E0),c_2EEncode_2Etree1__size_2E2(A_27a,V4f_2E0,V6a1_2E0))) ) ) ).

tff(thm_2EEncode_2Ebiprefix__refl,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2EEncode_2Ebiprefix_2E2(A_27a,V0x_2E0,V0x_2E0)) ).

tff(thm_2EEncode_2Ebiprefix__sym,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1y_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2EEncode_2Ebiprefix_2E2(A_27a,V0x_2E0,V1y_2E0))
     => p(c_2EEncode_2Ebiprefix_2E2(A_27a,V1y_2E0,V0x_2E0)) ) ).

tff(thm_2EEncode_2Ebiprefix__append,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)] :
      ( p(c_2EEncode_2Ebiprefix_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0a_2E0,V1b_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V2c_2E0,V3d_2E0)))
     => p(c_2EEncode_2Ebiprefix_2E2(A_27a,V0a_2E0,V2c_2E0)) ) ).

tff(thm_2EEncode_2Ebiprefix__cons,axiom,
    ! [A_27a: $tType,V0a_2E0: A_27a,V1b_2E0: tyop_2Elist_2Elist(A_27a),V2c_2E0: A_27a,V3d_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2EEncode_2Ebiprefix_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0a_2E0,V1b_2E0),c_2Elist_2ECONS_2E2(A_27a,V2c_2E0,V3d_2E0)))
    <=> ( ( V0a_2E0 = V2c_2E0 )
        & p(c_2EEncode_2Ebiprefix_2E2(A_27a,V1b_2E0,V3d_2E0)) ) ) ).

tff(thm_2EEncode_2Ebiprefix__appends,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)] : ( c_2EEncode_2Ebiprefix_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0a_2E0,V1b_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V0a_2E0,V2c_2E0)) = c_2EEncode_2Ebiprefix_2E2(A_27a,V1b_2E0,V2c_2E0) ) ).

tff(thm_2EEncode_2Ewf__encoder__alt,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
      ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
    <=> ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
          ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V2x_2E0))
            & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V3y_2E0))
            & p(c_2EEncode_2Ebiprefix_2E2(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V3y_2E0))) )
         => ( V2x_2E0 = V3y_2E0 ) ) ) ).

tff(thm_2EEncode_2Ewf__encoder__eq,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
      ( ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
        & ! [V3x_2E0: A_27a] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V3x_2E0))
           => ( app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V3x_2E0) = app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2f_2E0,V3x_2E0) ) ) )
     => p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V2f_2E0)) ) ).

tff(thm_2EEncode_2Ewf__encoder__total,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
      ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,A_27a,c_2Ebool_2ET_2E0),V1e_2E0))
     => p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0)) ) ).

tff(thm_2EEncode_2Ewf__encode__unit,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool)] : p(c_2EEncode_2Ewf__encoder_2E2(tyop_2Eone_2Eone,V0p_2E0,c_2EEncode_2Eencode__unit_2E0)) ).

tff(thm_2EEncode_2Ewf__encode__bool,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : p(c_2EEncode_2Ewf__encoder_2E2(tyop_2Emin_2Ebool,V0p_2E0,c_2EEncode_2Eencode__bool_2E0)) ).

tff(thm_2EEncode_2Eencode__prod__alt,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0xb_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V1yb_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V2p_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2EEncode_2Eencode__prod_2E3(A_27a,A_27b,V0xb_2E0,V1yb_2E0,V2p_2E0) = c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0xb_2E0,c_2Epair_2EFST_2E1(A_27a,A_27b,V2p_2E0)),app_2E2(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1yb_2E0,c_2Epair_2ESND_2E1(A_27a,A_27b,V2p_2E0))) ) ).

tff(thm_2EEncode_2Ewf__encode__prod,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2e1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V3e2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
      ( ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p1_2E0,V2e1_2E0))
        & p(c_2EEncode_2Ewf__encoder_2E2(A_27b,V1p2_2E0,V3e2_2E0)) )
     => p(c_2EEncode_2Ewf__encoder_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2EEncode_2Elift__prod_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0),c_2EEncode_2Eencode__prod_2E2(A_27a,A_27b,V2e1_2E0,V3e2_2E0))) ) ).

tff(thm_2EEncode_2Ewf__encode__sum,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2e1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V3e2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
      ( ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p1_2E0,V2e1_2E0))
        & p(c_2EEncode_2Ewf__encoder_2E2(A_27b,V1p2_2E0,V3e2_2E0)) )
     => p(c_2EEncode_2Ewf__encoder_2E2(tyop_2Esum_2Esum(A_27a,A_27b),c_2EEncode_2Elift__sum_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0),c_2EEncode_2Eencode__sum_2E2(A_27a,A_27b,V2e1_2E0,V3e2_2E0))) ) ).

tff(thm_2EEncode_2Ewf__encode__option,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
      ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
     => p(c_2EEncode_2Ewf__encoder_2E2(tyop_2Eoption_2Eoption(A_27a),c_2EEncode_2Elift__option_2E1(A_27a,V0p_2E0),c_2EEncode_2Eencode__option_2E1(A_27a,V1e_2E0))) ) ).

tff(thm_2EEncode_2Ewf__encode__list,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
      ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
     => p(c_2EEncode_2Ewf__encoder_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2EEVERY_2E1(A_27a,V0p_2E0),c_2EEncode_2Eencode__list_2E1(A_27a,V1e_2E0))) ) ).

tff(thm_2EEncode_2Eencode__list__cong,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V3f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(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_2Elist_2Elist(tyop_2Emin_2Ebool),V2f1_2E0,V4x_2E0) = app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3f2_2E0,V4x_2E0) ) ) )
     => ( c_2EEncode_2Eencode__list_2E2(A_27a,V2f1_2E0,V0l1_2E0) = c_2EEncode_2Eencode__list_2E2(A_27a,V3f2_2E0,V1l2_2E0) ) ) ).

tff(thm_2EEncode_2Eencode__blist__def__compute,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0e_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EEncode_2Eencode__blist_2E3(A_27a,A_27b,c_2Enum_2E0_2E0,V0e_2E0,V1l_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
      & ! [V2m_2E0: tyop_2Enum_2Enum,V3e_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V4l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EEncode_2Eencode__blist_2E3(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2m_2E0)),V3e_2E0,V4l_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,app_2E2(A_27b,tyop_2Elist_2Elist(A_27a),V3e_2E0,c_2Elist_2EHD_2E1(A_27b,V4l_2E0)),c_2EEncode_2Eencode__blist_2E3(A_27a,A_27b,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2m_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V3e_2E0,c_2Elist_2ETL_2E1(A_27b,V4l_2E0))) )
      & ! [V5m_2E0: tyop_2Enum_2Enum,V6e_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V7l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EEncode_2Eencode__blist_2E3(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V5m_2E0)),V6e_2E0,V7l_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,app_2E2(A_27b,tyop_2Elist_2Elist(A_27a),V6e_2E0,c_2Elist_2EHD_2E1(A_27b,V7l_2E0)),c_2EEncode_2Eencode__blist_2E3(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V5m_2E0)),V6e_2E0,c_2Elist_2ETL_2E1(A_27b,V7l_2E0))) ) ) ).

tff(thm_2EEncode_2Elift__blist__suc,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2EEncode_2Elift__blist_2E3(A_27a,c_2Enum_2ESUC_2E1(V0n_2E0),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_2EEncode_2Elift__blist_2E3(A_27a,V0n_2E0,V1p_2E0,V3t_2E0)) ) ) ).

tff(thm_2EEncode_2Ewf__encode__blist,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
      ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V1p_2E0,V2e_2E0))
     => p(c_2EEncode_2Ewf__encoder_2E2(tyop_2Elist_2Elist(A_27a),c_2EEncode_2Elift__blist_2E2(A_27a,V0m_2E0,V1p_2E0),c_2EEncode_2Eencode__blist_2E2(tyop_2Emin_2Ebool,A_27a,V0m_2E0,V2e_2E0))) ) ).

tff(thm_2EEncode_2Eencode__num__def,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0n_2E0))
        <=> ( V0n_2E0 = c_2Enum_2E0_2E0 ) )
     => ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2EEncode_2Eencode__num_2E1(V0n_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0n_2E0),c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Earithmetic_2EEVEN_2E1(V0n_2E0),c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0,c_2EEncode_2Eencode__num_2E1(c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0,c_2EEncode_2Eencode__num_2E1(c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) ) ).

tff(thm_2EEncode_2Eencode__num__ind,axiom,
    ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V1n_2E0: tyop_2Enum_2Enum] :
          ( ( ( ( ( V1n_2E0 != c_2Enum_2E0_2E0 )
                & p(c_2Earithmetic_2EEVEN_2E1(V1n_2E0)) )
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))) )
            & ( ( ( V1n_2E0 != c_2Enum_2E0_2E0 )
                & ~ p(c_2Earithmetic_2EEVEN_2E1(V1n_2E0)) )
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))) ) )
         => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V1n_2E0)) )
     => ! [V2v_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V2v_2E0)) ) ).

tff(thm_2EEncode_2Ewf__encode__num,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : p(c_2EEncode_2Ewf__encoder_2E2(tyop_2Enum_2Enum,V0p_2E0,c_2EEncode_2Eencode__num_2E0)) ).

tff(thm_2EEncode_2Eencode__bnum__def__compute,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V4n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V4n_2E0))
        <=> ~ p(c_2Earithmetic_2EEVEN_2E1(V4n_2E0)) )
     => ( ! [V2n_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2n_2E0))
          <=> ~ p(c_2Earithmetic_2EEVEN_2E1(V2n_2E0)) )
       => ( ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2EEncode_2Eencode__bnum_2E2(c_2Enum_2E0_2E0,V0n_2E0) = c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool) )
          & ! [V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2EEncode_2Eencode__bnum_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1m_2E0)),V2n_2E0) = c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2n_2E0),c_2EEncode_2Eencode__bnum_2E2(c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1m_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2EDIV_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))) )
          & ! [V3m_2E0: tyop_2Enum_2Enum,V4n_2E0: tyop_2Enum_2Enum] : ( c_2EEncode_2Eencode__bnum_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V3m_2E0)),V4n_2E0) = c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V4n_2E0),c_2EEncode_2Eencode__bnum_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3m_2E0)),c_2Earithmetic_2EDIV_2E2(V4n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) ) ) ).

tff(thm_2EEncode_2Ewf__pred__bnum__total,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V0m_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0m_2E0),V1x_2E0) = c_2Eprim__rec_2E_3C_2E2(V1x_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0m_2E0)) )
     => ! [V0m_2E0: tyop_2Enum_2Enum] : p(c_2EEncode_2Ewf__pred__bnum_2E2(V0m_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0m_2E0))) ) ).

tff(thm_2EEncode_2Ewf__pred__bnum,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2EEncode_2Ewf__pred__bnum_2E2(V0m_2E0,V1p_2E0))
     => p(c_2EEncode_2Ecollision__free_2E2(V0m_2E0,V1p_2E0)) ) ).

tff(thm_2EEncode_2Eencode__bnum__length,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ELENGTH_2E1(tyop_2Emin_2Ebool,c_2EEncode_2Eencode__bnum_2E2(V0m_2E0,V1n_2E0)) = V0m_2E0 ) ).

tff(thm_2EEncode_2Eencode__bnum__inj,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Enum_2Enum,V2y_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Eprim__rec_2E_3C_2E2(V1x_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0m_2E0)))
        & p(c_2Eprim__rec_2E_3C_2E2(V2y_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0m_2E0)))
        & ( c_2EEncode_2Eencode__bnum_2E2(V0m_2E0,V1x_2E0) = c_2EEncode_2Eencode__bnum_2E2(V0m_2E0,V2y_2E0) ) )
     => ( V1x_2E0 = V2y_2E0 ) ) ).

tff(thm_2EEncode_2Ewf__encode__bnum__collision__free,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Ewf__encoder_2E2(tyop_2Enum_2Enum,V1p_2E0,c_2EEncode_2Eencode__bnum_2E1(V0m_2E0)) = c_2EEncode_2Ecollision__free_2E2(V0m_2E0,V1p_2E0) ) ).

tff(thm_2EEncode_2Ewf__encode__bnum,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2EEncode_2Ewf__pred__bnum_2E2(V0m_2E0,V1p_2E0))
     => p(c_2EEncode_2Ewf__encoder_2E2(tyop_2Enum_2Enum,V1p_2E0,c_2EEncode_2Eencode__bnum_2E1(V0m_2E0))) ) ).

tff(thm_2EEncode_2Edatatype__tree,axiom,
    ! [A_27a: $tType,V0tree_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2EEncode_2Etree(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(tyop_2EEncode_2Etree(A_27a)),tyop_2EEncode_2Etree(A_27a))),tyop_2Emin_2Ebool,V0tree_2E0,c_2EEncode_2ENode_2E0(A_27a)))) ).

tff(thm_2EEncode_2Etree__11,axiom,
    ! [A_27a: $tType,V0a0_2E0: A_27a,V1a1_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),V2a0_27_2E0: A_27a,V3a1_27_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] :
      ( ( c_2EEncode_2ENode_2E2(A_27a,V0a0_2E0,V1a1_2E0) = c_2EEncode_2ENode_2E2(A_27a,V2a0_27_2E0,V3a1_27_2E0) )
    <=> ( ( V0a0_2E0 = V2a0_27_2E0 )
        & ( V1a1_2E0 = V3a1_27_2E0 ) ) ) ).

tff(thm_2EEncode_2Etree__nchotomy,axiom,
    ! [A_27a: $tType,V0tt_2E0: tyop_2EEncode_2Etree(A_27a)] :
    ? [V1a_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] : ( V0tt_2E0 = c_2EEncode_2ENode_2E2(A_27a,V1a_2E0,V2l_2E0) ) ).

tff(thm_2EEncode_2Etree__Axiom,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(A_27c,A_27b))),V1f1_2E0: A_27c,V2f2_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27c))))] :
    ? [V3fn0_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),A_27b),V4fn1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27c)] :
      ( ! [V5a0_2E0: A_27a,V6a1_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] : ( app_2E2(tyop_2EEncode_2Etree(A_27a),A_27b,V3fn0_2E0,c_2EEncode_2ENode_2E2(A_27a,V5a0_2E0,V6a1_2E0)) = app_2E2(A_27c,A_27b,app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(A_27c,A_27b)),V0f0_2E0,V5a0_2E0),V6a1_2E0),app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27c,V4fn1_2E0,V6a1_2E0)) )
      & ( app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27c,V4fn1_2E0,c_2Elist_2ENIL_2E0(tyop_2EEncode_2Etree(A_27a))) = V1f1_2E0 )
      & ! [V7a0_2E0: tyop_2EEncode_2Etree(A_27a),V8a1_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27c,V4fn1_2E0,c_2Elist_2ECONS_2E2(tyop_2EEncode_2Etree(A_27a),V7a0_2E0,V8a1_2E0)) = app_2E2(A_27c,A_27c,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27c),app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27c)),app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27c))),V2f2_2E0,V7a0_2E0),V8a1_2E0),app_2E2(tyop_2EEncode_2Etree(A_27a),A_27b,V3fn0_2E0,V7a0_2E0)),app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27c,V4fn1_2E0,V8a1_2E0)) ) ) ).

tff(thm_2EEncode_2Etree__induction,axiom,
    ! [A_27a: $tType,V0P0_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),V1P1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Ebool)] :
      ( ( ! [V2l_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Ebool,V1P1_2E0,V2l_2E0))
           => ! [V3a_2E0: A_27a] : p(app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool,V0P0_2E0,c_2EEncode_2ENode_2E2(A_27a,V3a_2E0,V2l_2E0))) )
        & p(app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Ebool,V1P1_2E0,c_2Elist_2ENIL_2E0(tyop_2EEncode_2Etree(A_27a))))
        & ! [V4t_2E0: tyop_2EEncode_2Etree(A_27a),V5l_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] :
            ( ( p(app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool,V0P0_2E0,V4t_2E0))
              & p(app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Ebool,V1P1_2E0,V5l_2E0)) )
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Ebool,V1P1_2E0,c_2Elist_2ECONS_2E2(tyop_2EEncode_2Etree(A_27a),V4t_2E0,V5l_2E0))) ) )
     => ( ! [V6t_2E0: tyop_2EEncode_2Etree(A_27a)] : p(app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool,V0P0_2E0,V6t_2E0))
        & ! [V7l_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Ebool,V1P1_2E0,V7l_2E0)) ) ) ).

tff(thm_2EEncode_2Etree__case__cong,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b)),V1M_2E0: tyop_2EEncode_2Etree(A_27a),V2M_27_2E0: tyop_2EEncode_2Etree(A_27a),V3f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b))] :
      ( ( ( V1M_2E0 = V2M_27_2E0 )
        & ! [V4a0_2E0: A_27a,V5a1_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] :
            ( ( V2M_27_2E0 = c_2EEncode_2ENode_2E2(A_27a,V4a0_2E0,V5a1_2E0) )
           => ( app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b),V3f_2E0,V4a0_2E0),V5a1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b),V0f_27_2E0,V4a0_2E0),V5a1_2E0) ) ) )
     => ( c_2EEncode_2Etree__CASE_2E2(A_27a,A_27b,V1M_2E0,V3f_2E0) = c_2EEncode_2Etree__CASE_2E2(A_27a,A_27b,V2M_27_2E0,V0f_27_2E0) ) ) ).

tff(thm_2EEncode_2Etree__case__eq,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2EEncode_2Etree(A_27a),V1v_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b))] :
      ( ( c_2EEncode_2Etree__CASE_2E2(A_27a,A_27b,V0x_2E0,V2f_2E0) = V1v_2E0 )
    <=> ? [V3a_2E0: A_27a,V4l_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] :
          ( ( V0x_2E0 = c_2EEncode_2ENode_2E2(A_27a,V3a_2E0,V4l_2E0) )
          & ( app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),A_27b),V2f_2E0,V3a_2E0),V4l_2E0) = V1v_2E0 ) ) ) ).

tff(thm_2EEncode_2Etree__ind,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool)] :
      ( ! [V1a_2E0: A_27a,V2ts_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a))] :
          ( ! [V3t_2E0: tyop_2EEncode_2Etree(A_27a)] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2EEncode_2Etree(A_27a),V3t_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2EEncode_2Etree(A_27a),V2ts_2E0)))
             => p(app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool,V0p_2E0,V3t_2E0)) )
         => p(app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool,V0p_2E0,c_2EEncode_2ENode_2E2(A_27a,V1a_2E0,V2ts_2E0))) )
     => ! [V4t_2E0: tyop_2EEncode_2Etree(A_27a)] : p(app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool,V0p_2E0,V4t_2E0)) ) ).

tff(thm_2EEncode_2Eencode__tree__def,axiom,
    ! [A_27a: $tType,V0ts_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V2a_2E0: A_27a] : ( c_2EEncode_2Eencode__tree_2E2(A_27a,V1e_2E0,c_2EEncode_2ENode_2E2(A_27a,V2a_2E0,V0ts_2E0)) = c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V2a_2E0),c_2EEncode_2Eencode__list_2E2(tyop_2EEncode_2Etree(A_27a),c_2EEncode_2Eencode__tree_2E1(A_27a,V1e_2E0),V0ts_2E0)) ) ).

tff(thm_2EEncode_2Elift__tree__def,axiom,
    ! [A_27a: $tType,V0ts_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0: A_27a] :
      ( p(c_2EEncode_2Elift__tree_2E2(A_27a,V1p_2E0,c_2EEncode_2ENode_2E2(A_27a,V2a_2E0,V0ts_2E0)))
    <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1p_2E0,V2a_2E0))
        & p(c_2Elist_2EEVERY_2E2(tyop_2EEncode_2Etree(A_27a),c_2EEncode_2Elift__tree_2E1(A_27a,V1p_2E0),V0ts_2E0)) ) ) ).

tff(thm_2EEncode_2Ewf__encode__tree,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
      ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
     => p(c_2EEncode_2Ewf__encoder_2E2(tyop_2EEncode_2Etree(A_27a),c_2EEncode_2Elift__tree_2E1(A_27a,V0p_2E0),c_2EEncode_2Eencode__tree_2E1(A_27a,V1e_2E0))) ) ).

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