ITP001 Axioms: ITP060_7.ax


%------------------------------------------------------------------------------
% File     : ITP060_7 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : Decode.ax [Gau19]
%          : HL4060_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  417 ( 180 unt; 174 typ;   0 def)
%            Number of atoms       :  401 ( 284 equ)
%            Maximal formula atoms :    9 (   0 avg)
%            Number of connectives :  163 (   5   ~;   3   |;  32   &)
%                                         (  24 <=>;  99  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Maximal term depth    :   13 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  183 (  96   >;  87   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  170 ( 170 usr;  28 con; 0-6 aty)
%            Number of variables   : 1121 ( 960   !;   4   ?;1121   :)
%                                         ( 157  !>;   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_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_2A_2E0,type,
    c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

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

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

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

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

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

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

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

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

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

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).

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

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

tff(c_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_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_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_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_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_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_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_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).

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

tff(c_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_2EDecode_2Edec2enc_2E0,type,
    c_2EDecode_2Edec2enc_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ).

tff(c_2EDecode_2Edec2enc_2E1,type,
    c_2EDecode_2Edec2enc_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) > tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ) ).

tff(c_2EDecode_2Edec2enc_2E2,type,
    c_2EDecode_2Edec2enc_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) * A_27a ) > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) ).

tff(c_2EDecode_2Edec__bnum_2E0,type,
    c_2EDecode_2Edec__bnum_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))) ).

tff(c_2EDecode_2Edec__bnum_2E2,type,
    c_2EDecode_2Edec__bnum_2E2: ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ).

tff(c_2EDecode_2Edecode__blist_2E0,type,
    c_2EDecode_2Edecode__blist_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))) ).

tff(c_2EDecode_2Edecode__blist_2E3,type,
    c_2EDecode_2Edecode__blist_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) * tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) ).

tff(c_2EDecode_2Edecode__blist_2E4,type,
    c_2EDecode_2Edecode__blist_2E4: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) * tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ) ).

tff(c_2EDecode_2Edecode__bnum_2E0,type,
    c_2EDecode_2Edecode__bnum_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))) ).

tff(c_2EDecode_2Edecode__bnum_2E2,type,
    c_2EDecode_2Edecode__bnum_2E2: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ).

tff(c_2EDecode_2Edecode__bnum_2E3,type,
    c_2EDecode_2Edecode__bnum_2E3: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ).

tff(c_2EDecode_2Edecode__bool_2E0,type,
    c_2EDecode_2Edecode__bool_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))) ).

tff(c_2EDecode_2Edecode__bool_2E1,type,
    c_2EDecode_2Edecode__bool_2E1: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ).

tff(c_2EDecode_2Edecode__bool_2E2,type,
    c_2EDecode_2Edecode__bool_2E2: ( tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ).

tff(c_2EDecode_2Edecode__list_2E0,type,
    c_2EDecode_2Edecode__list_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))) ).

tff(c_2EDecode_2Edecode__list_2E2,type,
    c_2EDecode_2Edecode__list_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) ).

tff(c_2EDecode_2Edecode__list_2E3,type,
    c_2EDecode_2Edecode__list_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ) ).

tff(c_2EDecode_2Edecode__num_2E0,type,
    c_2EDecode_2Edecode__num_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))) ).

tff(c_2EDecode_2Edecode__num_2E1,type,
    c_2EDecode_2Edecode__num_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ).

tff(c_2EDecode_2Edecode__num_2E2,type,
    c_2EDecode_2Edecode__num_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ).

tff(c_2EDecode_2Edecode__option_2E0,type,
    c_2EDecode_2Edecode__option_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))) ).

tff(c_2EDecode_2Edecode__option_2E2,type,
    c_2EDecode_2Edecode__option_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) ).

tff(c_2EDecode_2Edecode__option_2E3,type,
    c_2EDecode_2Edecode__option_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ) ).

tff(c_2EDecode_2Edecode__prod_2E0,type,
    c_2EDecode_2Edecode__prod_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))) ).

tff(c_2EDecode_2Edecode__prod_2E3,type,
    c_2EDecode_2Edecode__prod_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) ).

tff(c_2EDecode_2Edecode__prod_2E4,type,
    c_2EDecode_2Edecode__prod_2E4: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ) ).

tff(c_2EDecode_2Edecode__sum_2E0,type,
    c_2EDecode_2Edecode__sum_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))) ).

tff(c_2EDecode_2Edecode__sum_2E3,type,
    c_2EDecode_2Edecode__sum_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) ).

tff(c_2EDecode_2Edecode__sum_2E4,type,
    c_2EDecode_2Edecode__sum_2E4: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ) ).

tff(c_2EDecode_2Edecode__tree_2E0,type,
    c_2EDecode_2Edecode__tree_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))) ).

tff(c_2EDecode_2Edecode__tree_2E2,type,
    c_2EDecode_2Edecode__tree_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) ).

tff(c_2EDecode_2Edecode__tree_2E3,type,
    c_2EDecode_2Edecode__tree_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ) ).

tff(c_2EDecode_2Edecode__unit_2E0,type,
    c_2EDecode_2Edecode__unit_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))) ).

tff(c_2EDecode_2Edecode__unit_2E1,type,
    c_2EDecode_2Edecode__unit_2E1: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ).

tff(c_2EDecode_2Edecode__unit_2E2,type,
    c_2EDecode_2Edecode__unit_2E2: ( tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ).

tff(c_2EDecode_2Eenc2dec_2E0,type,
    c_2EDecode_2Eenc2dec_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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))) ).

tff(c_2EDecode_2Eenc2dec_2E2,type,
    c_2EDecode_2Eenc2dec_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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) ).

tff(c_2EDecode_2Eenc2dec_2E3,type,
    c_2EDecode_2Eenc2dec_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(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__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_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_2Elist_2Elist__CASE_2E0,type,
    c_2Elist_2Elist__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b))) ).

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

tff(c_2Earithmetic_2Enum__CASE_2E0,type,
    c_2Earithmetic_2Enum__CASE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a))) ).

tff(c_2Earithmetic_2Enum__CASE_2E3,type,
    c_2Earithmetic_2Enum__CASE_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) > A_27a ) ).

tff(c_2Eone_2Eone_2E0,type,
    c_2Eone_2Eone_2E0: tyop_2Eone_2Eone ).

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

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

tff(c_2Epair_2Epair__CASE_2E0,type,
    c_2Epair_2Epair__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),A_27a)) ).

tff(c_2Epair_2Epair__CASE_2E2,type,
    c_2Epair_2Epair__CASE_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epair_2Eprod(A_27b,A_27c) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)) ) > A_27a ) ).

tff(c_2EDecode_2Ewf__decoder_2E0,type,
    c_2EDecode_2Ewf__decoder_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool)) ).

tff(c_2EDecode_2Ewf__decoder_2E2,type,
    c_2EDecode_2Ewf__decoder_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) > tyop_2Emin_2Ebool ) ).

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__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_2A_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ) ).

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

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

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Eone_2Eone,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Esum_2Esum(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2EEncode_2Etree_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2EEncode_2Etree(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

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

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

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

tff(arityeq2_2Ec_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_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Emin_2E_40_2E0(tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_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_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).

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

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),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(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(arityeq1_2Ec_2Elist_2EEVERY_2E1_2Emono_2Etyop_2EEncode_2Etree_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool)] : ( c_2Elist_2EEVERY_2E1(tyop_2EEncode_2Etree(A_27a),X0_2E0) = 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) ) ).

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(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2Epair_2EFST_2E1(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),A_27a,c_2Epair_2EFST_2E0(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_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_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E0(tyop_2Emin_2Ebool,tyop_2Enum_2Enum),X0_2E0) ) ).

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

tff(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_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2Epair_2ESND_2E1(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Epair_2ESND_2E0(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),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_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2EEncode_2Etree_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),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_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E0(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0) ) ).

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

tff(arityeq1_2Ec_2EDecode_2Edec2enc_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edec2enc_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EDecode_2Edec2enc_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edec2enc_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X1_2E0: A_27a] : ( c_2EDecode_2Edec2enc_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EDecode_2Edec2enc_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2EDecode_2Edec2enc_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edec2enc_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EDecode_2Edec2enc_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edec2enc_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X1_2E0: tyop_2Emin_2Ebool] : ( c_2EDecode_2Edec2enc_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EDecode_2Edec2enc_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edec2enc_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EDecode_2Edec2enc_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EDecode_2Edec2enc_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edec2enc_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X1_2E0: tyop_2Enum_2Enum] : ( c_2EDecode_2Edec2enc_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EDecode_2Edec2enc_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edec2enc_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X1_2E0: tyop_2Eone_2Eone] : ( c_2EDecode_2Edec2enc_2E2(tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EDecode_2Edec2enc_2E0(tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edec2enc_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X1_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2EDecode_2Edec2enc_2E2(tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EDecode_2Edec2enc_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edec2enc_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X1_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2EDecode_2Edec2enc_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,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_2EDecode_2Edec2enc_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edec2enc_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X1_2E0: tyop_2Esum_2Esum(A_27a,A_27b)] : ( c_2EDecode_2Edec2enc_2E2(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,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_2EDecode_2Edec2enc_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edec__bnum_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edec__bnum_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2EDecode_2Edec__bnum_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EDecode_2Edecode__blist_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edecode__blist_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2EDecode_2Edecode__blist_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq4_2Ec_2EDecode_2Edecode__blist_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X3_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__blist_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2EDecode_2Edecode__blist_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edecode__bnum_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__bnum_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Edecode__bnum_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EDecode_2Edecode__bnum_2E3,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__bnum_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Edecode__bnum_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2EDecode_2Edecode__bool_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__bool_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2EDecode_2Edecode__bool_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edecode__bool_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__bool_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2EDecode_2Edecode__bool_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edecode__list_2E2_2Emono_2EA_27a,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(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edecode__list_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(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(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Edecode__list_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EDecode_2Edecode__list_2E3_2Emono_2EA_27a,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(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X2_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__list_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(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(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Edecode__list_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2EDecode_2Edecode__list_2E3_2Emono_2Etyop_2EEncode_2Etree_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X2_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__list_2E3(tyop_2EEncode_2Etree(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Edecode__list_2E0(tyop_2EEncode_2Etree(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2EDecode_2Edecode__num_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__num_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2EDecode_2Edecode__num_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edecode__num_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__num_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2EDecode_2Edecode__num_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edecode__option_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edecode__option_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Edecode__option_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EDecode_2Edecode__option_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X2_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__option_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Edecode__option_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2EDecode_2Edecode__prod_2E3_2Emono_2EA_27a_20mono_2EA_27b,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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edecode__prod_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2EDecode_2Edecode__prod_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq4_2Ec_2EDecode_2Edecode__prod_2E4_2Emono_2EA_27a_20mono_2EA_27b,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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X3_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__prod_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2EDecode_2Edecode__prod_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq3_2Ec_2EDecode_2Edecode__sum_2E3_2Emono_2EA_27a_20mono_2EA_27b,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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edecode__sum_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2EDecode_2Edecode__sum_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq4_2Ec_2EDecode_2Edecode__sum_2E4_2Emono_2EA_27a_20mono_2EA_27b,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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X3_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__sum_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2EDecode_2Edecode__sum_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edecode__tree_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edecode__tree_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Edecode__tree_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EDecode_2Edecode__tree_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X2_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__tree_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Edecode__tree_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2EDecode_2Edecode__unit_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__unit_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2EDecode_2Edecode__unit_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Edecode__unit_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__unit_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2EDecode_2Edecode__unit_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Eenc2dec_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_2EDecode_2Eenc2dec_2E2(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(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Eenc2dec_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EDecode_2Eenc2dec_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X2_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Eenc2dec_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Eenc2dec_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Eenc2dec_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_2EDecode_2Eenc2dec_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Eenc2dec_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Eenc2dec_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_2EDecode_2Eenc2dec_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Eenc2dec_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Eenc2dec_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_2EDecode_2Eenc2dec_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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Eenc2dec_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Eenc2dec_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_2EDecode_2Eenc2dec_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Eenc2dec_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Eenc2dec_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_2EDecode_2Eenc2dec_2E2(tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Eenc2dec_2E0(tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Eenc2dec_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_2EDecode_2Eenc2dec_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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Eenc2dec_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Eenc2dec_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_2EDecode_2Eenc2dec_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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Eenc2dec_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Eenc2dec_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_2EDecode_2Eenc2dec_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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Eenc2dec_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Eenc2dec_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_2EDecode_2Eenc2dec_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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2EDecode_2Eenc2dec_2E0(tyop_2EEncode_2Etree(A_27a)),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_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)),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EEncode_2Eencode__blist_2E3(tyop_2Emin_2Ebool,A_27a,X0_2E0,X1_2E0,X2_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)),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),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(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(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_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(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Elist_2Elist__CASE_2E0(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Elist_2Elist__CASE_2E0(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Elist_2Elist__CASE_2E0(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Elist_2Elist__CASE_2E0(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Elist_2Elist__CASE_2E0(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Earithmetic_2Enum__CASE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2Earithmetic_2Enum__CASE_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Earithmetic_2Enum__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2EEncode_2Etree_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2EEncode_2Etree_28A_27a_29_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2EEncode_2Etree_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2EEncode_2Etree_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2EEncode_2Etree_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2EEncode_2Etree_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Ewf__decoder_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Ewf__decoder_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),c_2EDecode_2Ewf__decoder_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Ewf__decoder_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Ewf__decoder_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),c_2EDecode_2Ewf__decoder_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Ewf__decoder_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Ewf__decoder_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),c_2EDecode_2Ewf__decoder_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Ewf__decoder_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(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Ewf__decoder_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),c_2EDecode_2Ewf__decoder_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Ewf__decoder_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Ewf__decoder_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),c_2EDecode_2Ewf__decoder_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Ewf__decoder_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Ewf__decoder_2E2(tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),c_2EDecode_2Ewf__decoder_2E0(tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Ewf__decoder_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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Ewf__decoder_2E2(tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),c_2EDecode_2Ewf__decoder_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Ewf__decoder_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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Ewf__decoder_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),c_2EDecode_2Ewf__decoder_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Ewf__decoder_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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Ewf__decoder_2E2(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),c_2EDecode_2Ewf__decoder_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EDecode_2Ewf__decoder_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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Ewf__decoder_2E2(tyop_2EEncode_2Etree(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),c_2EDecode_2Ewf__decoder_2E0(tyop_2EEncode_2Etree(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__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_2EDecode_2Ewf__decoder__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1d_2E0),V2x_2E0))
        <=> ? [V3a_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
            ! [V4b_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5c_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
              ( ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V1d_2E0,V4b_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2x_2E0,V5c_2E0)) )
            <=> ( V4b_2E0 = c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,V3a_2E0,V5c_2E0) ) ) )
     => ( ! [V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2x_2E0: A_27a] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V1d_2E0),V2x_2E0))
          <=> ! [V6a_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V7b_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V1d_2E0,V6a_2E0) != c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2x_2E0,V7b_2E0)) ) )
       => ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
            ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V1d_2E0))
          <=> ! [V2x_2E0: A_27a] : p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1d_2E0),V2x_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V1d_2E0),V2x_2E0))) ) ) ) ).

tff(thm_2EDecode_2Eenc2dec__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))))] :
      ( ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),F0_2E0,V0p_2E0),V2l_2E0),V1e_2E0))
        <=> ? [V3x_2E0: A_27a,V4t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
              ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V3x_2E0))
              & ( V2l_2E0 = c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V3x_2E0),V4t_2E0) ) ) )
     => ( ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V5x_2E0: A_27a,V6t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F1_2E0,V0p_2E0),V2l_2E0),V1e_2E0),V5x_2E0),V6t_2E0))
          <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V5x_2E0))
              & ( V2l_2E0 = c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V5x_2E0),V6t_2E0) ) ) )
       => ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Eenc2dec_2E3(A_27a,V0p_2E0,V1e_2E0,V2l_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),F0_2E0,V0p_2E0),V2l_2E0),V1e_2E0),c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F1_2E0,V0p_2E0),V2l_2E0),V1e_2E0)))),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) ) ) ).

tff(thm_2EDecode_2Edec2enc__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
      ( ! [V0d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0d_2E0),V1x_2E0),V2l_2E0))
        <=> ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V0d_2E0,V2l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1x_2E0,c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool))) ) )
     => ! [V0d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V1x_2E0: A_27a] : ( c_2EDecode_2Edec2enc_2E2(A_27a,V0d_2E0,V1x_2E0) = c_2Emin_2E_40_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0d_2E0),V1x_2E0)) ) ) ).

tff(thm_2EDecode_2Edecode__unit__def,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__unit_2E1(V0p_2E0) = c_2EDecode_2Eenc2dec_2E2(tyop_2Eone_2Eone,V0p_2E0,c_2EEncode_2Eencode__unit_2E0) ) ).

tff(thm_2EDecode_2Edecode__bool__def,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__bool_2E1(V0p_2E0) = c_2EDecode_2Eenc2dec_2E2(tyop_2Emin_2Ebool,V0p_2E0,c_2EEncode_2Eencode__bool_2E0) ) ).

tff(thm_2EDecode_2Edecode__prod__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1d1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2d2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edecode__prod_2E3(A_27a,A_27b,V0p_2E0,V1d1_2E0,V2d2_2E0) = c_2EDecode_2Eenc2dec_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0,c_2EEncode_2Eencode__prod_2E2(A_27a,A_27b,c_2EDecode_2Edec2enc_2E1(A_27a,V1d1_2E0),c_2EDecode_2Edec2enc_2E1(A_27b,V2d2_2E0))) ) ).

tff(thm_2EDecode_2Edecode__sum__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V1d1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2d2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edecode__sum_2E3(A_27a,A_27b,V0p_2E0,V1d1_2E0,V2d2_2E0) = c_2EDecode_2Eenc2dec_2E2(tyop_2Esum_2Esum(A_27a,A_27b),V0p_2E0,c_2EEncode_2Eencode__sum_2E2(A_27a,A_27b,c_2EDecode_2Edec2enc_2E1(A_27a,V1d1_2E0),c_2EDecode_2Edec2enc_2E1(A_27b,V2d2_2E0))) ) ).

tff(thm_2EDecode_2Edecode__option__def,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edecode__option_2E2(A_27a,V0p_2E0,V1d_2E0) = c_2EDecode_2Eenc2dec_2E2(tyop_2Eoption_2Eoption(A_27a),V0p_2E0,c_2EEncode_2Eencode__option_2E1(A_27a,c_2EDecode_2Edec2enc_2E1(A_27a,V1d_2E0))) ) ).

tff(thm_2EDecode_2Edecode__list__def,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edecode__list_2E2(A_27a,V0p_2E0,V1d_2E0) = c_2EDecode_2Eenc2dec_2E2(tyop_2Elist_2Elist(A_27a),V0p_2E0,c_2EEncode_2Eencode__list_2E1(A_27a,c_2EDecode_2Edec2enc_2E1(A_27a,V1d_2E0))) ) ).

tff(thm_2EDecode_2Edecode__blist__def,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V1m_2E0: tyop_2Enum_2Enum,V2d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edecode__blist_2E3(A_27a,V0p_2E0,V1m_2E0,V2d_2E0) = c_2EDecode_2Eenc2dec_2E2(tyop_2Elist_2Elist(A_27a),V0p_2E0,c_2EEncode_2Eencode__blist_2E2(tyop_2Emin_2Ebool,A_27a,V1m_2E0,c_2EDecode_2Edec2enc_2E1(A_27a,V2d_2E0))) ) ).

tff(thm_2EDecode_2Edecode__num__def,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__num_2E1(V0p_2E0) = c_2EDecode_2Eenc2dec_2E2(tyop_2Enum_2Enum,V0p_2E0,c_2EEncode_2Eencode__num_2E0) ) ).

tff(thm_2EDecode_2Edecode__bnum__def,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__bnum_2E2(V0m_2E0,V1p_2E0) = c_2EDecode_2Eenc2dec_2E2(tyop_2Enum_2Enum,V1p_2E0,c_2EEncode_2Eencode__bnum_2E1(V0m_2E0)) ) ).

tff(thm_2EDecode_2Edec__bnum__def,axiom,
    ! [F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))] :
      ( ! [V3h_2E0: tyop_2Emin_2Ebool,V6n_2E0: tyop_2Enum_2Enum,V7t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F2_2E0,V3h_2E0),V6n_2E0),V7t_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V6n_2E0),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,V3h_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2E0_2E0)),V7t_27_2E0)) )
     => ( ! [V3h_2E0: tyop_2Emin_2Ebool,V5v_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F1_2E0,V3h_2E0),V5v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5v_2E0,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F2_2E0,V3h_2E0)) )
       => ( ! [V1m_2E0: tyop_2Enum_2Enum,V3h_2E0: tyop_2Emin_2Ebool,V4t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0,V1m_2E0),V3h_2E0),V4t_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edec__bnum_2E2(V1m_2E0,V4t_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F1_2E0,V3h_2E0)) )
         => ( ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edec__bnum_2E2(c_2Enum_2E0_2E0,V0l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Enum_2E0_2E0,V0l_2E0)) )
            & ! [V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edec__bnum_2E2(c_2Enum_2ESUC_2E1(V1m_2E0),V2l_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V2l_2E0,c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0,V1m_2E0)) ) ) ) ) ) ).

tff(thm_2EDecode_2Edecode__tree__def,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2EDecode_2Edecode__tree_2E2(A_27a,V0p_2E0,V1d_2E0) = c_2EDecode_2Eenc2dec_2E2(tyop_2EEncode_2Etree(A_27a),V0p_2E0,c_2EEncode_2Eencode__tree_2E1(A_27a,c_2EDecode_2Edec2enc_2E1(A_27a,V1d_2E0))) ) ).

tff(thm_2EDecode_2Eenc2dec__none,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)),V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
      ( ( c_2EDecode_2Eenc2dec_2E3(A_27a,V0p_2E0,V1e_2E0,V2l_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) )
    <=> ! [V3x_2E0: A_27a,V4t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V3x_2E0))
         => ( V2l_2E0 != c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V3x_2E0),V4t_2E0) ) ) ) ).

tff(thm_2EDecode_2Eenc2dec__some,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)),V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3x_2E0: A_27a,V4t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
      ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
     => ( ( c_2EDecode_2Eenc2dec_2E3(A_27a,V0p_2E0,V1e_2E0,V2l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3x_2E0,V4t_2E0)) )
      <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V3x_2E0))
          & ( V2l_2E0 = c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V3x_2E0),V4t_2E0) ) ) ) ) ).

tff(thm_2EDecode_2Eenc2dec__some__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)),V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3x_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
      ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
     => ( ( c_2EDecode_2Eenc2dec_2E3(A_27a,V0p_2E0,V1e_2E0,V2l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V3x_2E0) )
      <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,c_2Epair_2EFST_2E1(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3x_2E0)))
          & ( V2l_2E0 = c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,c_2Epair_2EFST_2E1(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3x_2E0)),c_2Epair_2ESND_2E1(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3x_2E0)) ) ) ) ) ).

tff(thm_2EDecode_2Ewf__enc2dec,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_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,c_2EDecode_2Eenc2dec_2E2(A_27a,V0p_2E0,V1e_2E0))) ) ).

tff(thm_2EDecode_2Edec2enc__some,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2x_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
      ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V1d_2E0))
     => ( ( ( c_2EDecode_2Edec2enc_2E2(A_27a,V1d_2E0,V2x_2E0) = V3l_2E0 )
          & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V2x_2E0)) )
      <=> ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V1d_2E0,V3l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2x_2E0,c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool))) ) ) ) ).

tff(thm_2EDecode_2Edecode__dec2enc,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2x_2E0: A_27a] :
      ( ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V1d_2E0))
        & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V2x_2E0)) )
     => ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V1d_2E0,c_2EDecode_2Edec2enc_2E2(A_27a,V1d_2E0,V2x_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2x_2E0,c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool))) ) ) ).

tff(thm_2EDecode_2Edecode__dec2enc__append,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2x_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
      ( ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V1d_2E0))
        & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V2x_2E0)) )
     => ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V1d_2E0,c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,c_2EDecode_2Edec2enc_2E2(A_27a,V1d_2E0,V2x_2E0),V3t_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2x_2E0,V3t_2E0)) ) ) ).

tff(thm_2EDecode_2Ewf__dec2enc,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
      ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V1d_2E0))
     => p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,c_2EDecode_2Edec2enc_2E1(A_27a,V1d_2E0))) ) ).

tff(thm_2EDecode_2Edec2enc__enc2dec,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)),V2x_2E0: A_27a] :
      ( ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
        & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V2x_2E0)) )
     => ( c_2EDecode_2Edec2enc_2E2(A_27a,c_2EDecode_2Eenc2dec_2E2(A_27a,V0p_2E0,V1e_2E0),V2x_2E0) = app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V2x_2E0) ) ) ).

tff(thm_2EDecode_2Eenc2dec__dec2enc,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
      ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V1d_2E0))
     => ( c_2EDecode_2Eenc2dec_2E2(A_27a,V0p_2E0,c_2EDecode_2Edec2enc_2E1(A_27a,V1d_2E0)) = V1d_2E0 ) ) ).

tff(thm_2EDecode_2Ewf__decode__unit,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool)] : p(c_2EDecode_2Ewf__decoder_2E2(tyop_2Eone_2Eone,V0p_2E0,c_2EDecode_2Edecode__unit_2E1(V0p_2E0))) ).

tff(thm_2EDecode_2Edec2enc__decode__unit,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Eone_2Eone] :
      ( p(app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Ebool,V0p_2E0,V1x_2E0))
     => ( c_2EDecode_2Edec2enc_2E2(tyop_2Eone_2Eone,c_2EDecode_2Edecode__unit_2E1(V0p_2E0),V1x_2E0) = c_2EEncode_2Eencode__unit_2E1(V1x_2E0) ) ) ).

tff(thm_2EDecode_2Edecode__unit,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__unit_2E2(V0p_2E0,V1l_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Ebool,V0p_2E0,c_2Eone_2Eone_2E0),c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Eone_2Eone_2E0,V1l_2E0)),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) ) ).

tff(thm_2EDecode_2Ewf__decode__bool,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : p(c_2EDecode_2Ewf__decoder_2E2(tyop_2Emin_2Ebool,V0p_2E0,c_2EDecode_2Edecode__bool_2E1(V0p_2E0))) ).

tff(thm_2EDecode_2Edec2enc__decode__bool,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Emin_2Ebool] :
      ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0p_2E0,V1x_2E0))
     => ( c_2EDecode_2Edec2enc_2E2(tyop_2Emin_2Ebool,c_2EDecode_2Edecode__bool_2E1(V0p_2E0),V1x_2E0) = c_2EEncode_2Eencode__bool_2E1(V1x_2E0) ) ) ).

tff(thm_2EDecode_2Edecode__bool,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))] :
      ( ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V2h_2E0: tyop_2Emin_2Ebool,V3t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0,V0p_2E0),V2h_2E0),V3t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0p_2E0,V2h_2E0),c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2h_2E0,V3t_2E0)),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) )
     => ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__bool_2E2(V0p_2E0,V1l_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V1l_2E0,c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0,V0p_2E0)) ) ) ).

tff(thm_2EDecode_2Ewf__decode__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),V2d1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V3d2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
      ( ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p1_2E0,V2d1_2E0))
        & p(c_2EDecode_2Ewf__decoder_2E2(A_27b,V1p2_2E0,V3d2_2E0)) )
     => p(c_2EDecode_2Ewf__decoder_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2EEncode_2Elift__prod_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0),c_2EDecode_2Edecode__prod_2E3(A_27a,A_27b,c_2EEncode_2Elift__prod_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0),V2d1_2E0,V3d2_2E0))) ) ).

tff(thm_2EDecode_2Edec2enc__decode__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),V2d1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V3d2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V4x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] :
      ( ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p1_2E0,V2d1_2E0))
        & p(c_2EDecode_2Ewf__decoder_2E2(A_27b,V1p2_2E0,V3d2_2E0))
        & p(c_2EEncode_2Elift__prod_2E3(A_27a,A_27b,V0p1_2E0,V1p2_2E0,V4x_2E0)) )
     => ( c_2EDecode_2Edec2enc_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2EDecode_2Edecode__prod_2E3(A_27a,A_27b,c_2EEncode_2Elift__prod_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0),V2d1_2E0,V3d2_2E0),V4x_2E0) = c_2EEncode_2Eencode__prod_2E3(A_27a,A_27b,c_2EDecode_2Edec2enc_2E1(A_27a,V2d1_2E0),c_2EDecode_2Edec2enc_2E1(A_27b,V3d2_2E0),V4x_2E0) ) ) ).

tff(thm_2EDecode_2Eencode__then__decode__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)),V4l_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V5t_2E0: 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_2Elift__prod_2E3(A_27a,A_27b,V0p1_2E0,V1p2_2E0,V4l_2E0)) )
     => ( c_2EDecode_2Edecode__prod_2E4(A_27a,A_27b,c_2EEncode_2Elift__prod_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0),c_2EDecode_2Eenc2dec_2E2(A_27a,V0p1_2E0,V2e1_2E0),c_2EDecode_2Eenc2dec_2E2(A_27b,V1p2_2E0,V3e2_2E0),c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,c_2EEncode_2Eencode__prod_2E3(A_27a,A_27b,V2e1_2E0,V3e2_2E0,V4l_2E0),V5t_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V4l_2E0,V5t_2E0)) ) ) ).

tff(thm_2EDecode_2Edecode__prod,axiom,
    ! [A_27a: $tType,A_27b: $tType,F3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] :
      ( ! [V6x_2E0: A_27a,V9y_2E0: A_27b,V10t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F3_2E0,V6x_2E0),V9y_2E0),V10t_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(A_27a,A_27b,V6x_2E0,V9y_2E0),V10t_27_2E0)) )
     => ( ! [V6x_2E0: A_27a,V8v_2E0: tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F2_2E0,V6x_2E0),V8v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V8v_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F3_2E0,V6x_2E0)) )
       => ( ! [V3d2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V6x_2E0: A_27a,V7t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0,V3d2_2E0),V6x_2E0),V7t_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V3d2_2E0,V7t_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F2_2E0,V6x_2E0)) )
         => ( ! [V3d2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V5v1_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F0_2E0,V3d2_2E0),V5v1_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5v1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0,V3d2_2E0)) )
           => ! [V0p2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1p1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3d2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V4d1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
                ( ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V1p1_2E0,V4d1_2E0))
                  & p(c_2EDecode_2Ewf__decoder_2E2(A_27b,V0p2_2E0,V3d2_2E0)) )
               => ( c_2EDecode_2Edecode__prod_2E4(A_27a,A_27b,c_2EEncode_2Elift__prod_2E2(A_27a,A_27b,V1p1_2E0,V0p2_2E0),V4d1_2E0,V3d2_2E0,V2l_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V4d1_2E0,V2l_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F0_2E0,V3d2_2E0)) ) ) ) ) ) ) ).

tff(thm_2EDecode_2Ewf__decode__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),V2d1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V3d2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
      ( ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p1_2E0,V2d1_2E0))
        & p(c_2EDecode_2Ewf__decoder_2E2(A_27b,V1p2_2E0,V3d2_2E0)) )
     => p(c_2EDecode_2Ewf__decoder_2E2(tyop_2Esum_2Esum(A_27a,A_27b),c_2EEncode_2Elift__sum_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0),c_2EDecode_2Edecode__sum_2E3(A_27a,A_27b,c_2EEncode_2Elift__sum_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0),V2d1_2E0,V3d2_2E0))) ) ).

tff(thm_2EDecode_2Edec2enc__decode__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),V2d1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V3d2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V4x_2E0: tyop_2Esum_2Esum(A_27a,A_27b)] :
      ( ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p1_2E0,V2d1_2E0))
        & p(c_2EDecode_2Ewf__decoder_2E2(A_27b,V1p2_2E0,V3d2_2E0))
        & p(c_2EEncode_2Elift__sum_2E3(A_27a,A_27b,V0p1_2E0,V1p2_2E0,V4x_2E0)) )
     => ( c_2EDecode_2Edec2enc_2E2(tyop_2Esum_2Esum(A_27a,A_27b),c_2EDecode_2Edecode__sum_2E3(A_27a,A_27b,c_2EEncode_2Elift__sum_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0),V2d1_2E0,V3d2_2E0),V4x_2E0) = c_2EEncode_2Eencode__sum_2E3(A_27a,A_27b,c_2EDecode_2Edec2enc_2E1(A_27a,V2d1_2E0),c_2EDecode_2Edec2enc_2E1(A_27b,V3d2_2E0),V4x_2E0) ) ) ).

tff(thm_2EDecode_2Eencode__then__decode__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)),V4l_2E0: tyop_2Esum_2Esum(A_27a,A_27b),V5t_2E0: 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_2Elift__sum_2E3(A_27a,A_27b,V0p1_2E0,V1p2_2E0,V4l_2E0)) )
     => ( c_2EDecode_2Edecode__sum_2E4(A_27a,A_27b,c_2EEncode_2Elift__sum_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0),c_2EDecode_2Eenc2dec_2E2(A_27a,V0p1_2E0,V2e1_2E0),c_2EDecode_2Eenc2dec_2E2(A_27b,V1p2_2E0,V3e2_2E0),c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,c_2EEncode_2Eencode__sum_2E3(A_27a,A_27b,V2e1_2E0,V3e2_2E0,V4l_2E0),V5t_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V4l_2E0,V5t_2E0)) ) ) ).

tff(thm_2EDecode_2Edecode__sum,axiom,
    ! [A_27a: $tType,A_27b: $tType,F4_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))))] :
      ( ! [V11x_2E0: A_27b,V12t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F4_2E0,V11x_2E0),V12t_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(A_27a,A_27b,V11x_2E0),V12t_27_2E0)) )
     => ( ! [V10v_2E0: tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F2_2E0,V10v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V10v_2E0,F4_2E0) )
       => ( ! [V8x_2E0: A_27a,V9t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F3_2E0,V8x_2E0),V9t_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(A_27a,A_27b,V8x_2E0),V9t_27_2E0)) )
         => ( ! [V7v_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F1_2E0,V7v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V7v_2E0,F3_2E0) )
           => ( ! [V4d1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V3d2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V5v1_2E0: tyop_2Emin_2Ebool,V6t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F0_2E0,V4d1_2E0),V3d2_2E0),V5v1_2E0),V6t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V5v1_2E0,c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V4d1_2E0,V6t_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F1_2E0),c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V3d2_2E0,V6t_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F2_2E0)) )
             => ! [V0p2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1p1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3d2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V4d1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
                  ( ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V1p1_2E0,V4d1_2E0))
                    & p(c_2EDecode_2Ewf__decoder_2E2(A_27b,V0p2_2E0,V3d2_2E0)) )
                 => ( c_2EDecode_2Edecode__sum_2E4(A_27a,A_27b,c_2EEncode_2Elift__sum_2E2(A_27a,A_27b,V1p1_2E0,V0p2_2E0),V4d1_2E0,V3d2_2E0,V2l_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V2l_2E0,c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F0_2E0,V4d1_2E0),V3d2_2E0)) ) ) ) ) ) ) ) ).

tff(thm_2EDecode_2Ewf__decode__option,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
      ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V1d_2E0))
     => p(c_2EDecode_2Ewf__decoder_2E2(tyop_2Eoption_2Eoption(A_27a),c_2EEncode_2Elift__option_2E1(A_27a,V0p_2E0),c_2EDecode_2Edecode__option_2E2(A_27a,c_2EEncode_2Elift__option_2E1(A_27a,V0p_2E0),V1d_2E0))) ) ).

tff(thm_2EDecode_2Edec2enc__decode__option,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2x_2E0: tyop_2Eoption_2Eoption(A_27a)] :
      ( ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V1d_2E0))
        & p(c_2EEncode_2Elift__option_2E2(A_27a,V0p_2E0,V2x_2E0)) )
     => ( c_2EDecode_2Edec2enc_2E2(tyop_2Eoption_2Eoption(A_27a),c_2EDecode_2Edecode__option_2E2(A_27a,c_2EEncode_2Elift__option_2E1(A_27a,V0p_2E0),V1d_2E0),V2x_2E0) = c_2EEncode_2Eencode__option_2E2(A_27a,c_2EDecode_2Edec2enc_2E1(A_27a,V1d_2E0),V2x_2E0) ) ) ).

tff(thm_2EDecode_2Eencode__then__decode__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)),V2l_2E0: tyop_2Eoption_2Eoption(A_27a),V3t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
      ( ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
        & p(c_2EEncode_2Elift__option_2E2(A_27a,V0p_2E0,V2l_2E0)) )
     => ( c_2EDecode_2Edecode__option_2E3(A_27a,c_2EEncode_2Elift__option_2E1(A_27a,V0p_2E0),c_2EDecode_2Eenc2dec_2E2(A_27a,V0p_2E0,V1e_2E0),c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,c_2EEncode_2Eencode__option_2E2(A_27a,V1e_2E0,V2l_2E0),V3t_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2l_2E0,V3t_2E0)) ) ) ).

tff(thm_2EDecode_2Edecode__option,axiom,
    ! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))] :
      ( ! [V6x_2E0: A_27a,V7t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F2_2E0,V6x_2E0),V7t_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Eoption_2ESOME_2E1(A_27a,V6x_2E0),V7t_27_2E0)) )
     => ( ! [V5v_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F1_2E0,V5v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5v_2E0,F2_2E0) )
       => ( ! [V2d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V3v1_2E0: tyop_2Emin_2Ebool,V4t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0,V2d_2E0),V3v1_2E0),V4t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V3v1_2E0,c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V2d_2E0,V4t_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F1_2E0),c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Eoption_2ENONE_2E0(A_27a),V4t_2E0))) )
         => ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
              ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V2d_2E0))
             => ( c_2EDecode_2Edecode__option_2E3(A_27a,c_2EEncode_2Elift__option_2E1(A_27a,V0p_2E0),V2d_2E0,V1l_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V1l_2E0,c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0,V2d_2E0)) ) ) ) ) ) ).

tff(thm_2EDecode_2Ewf__decode__list,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
      ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V1d_2E0))
     => p(c_2EDecode_2Ewf__decoder_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2EEVERY_2E1(A_27a,V0p_2E0),c_2EDecode_2Edecode__list_2E2(A_27a,c_2Elist_2EEVERY_2E1(A_27a,V0p_2E0),V1d_2E0))) ) ).

tff(thm_2EDecode_2Edec2enc__decode__list,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2x_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V1d_2E0))
        & p(c_2Elist_2EEVERY_2E2(A_27a,V0p_2E0,V2x_2E0)) )
     => ( c_2EDecode_2Edec2enc_2E2(tyop_2Elist_2Elist(A_27a),c_2EDecode_2Edecode__list_2E2(A_27a,c_2Elist_2EEVERY_2E1(A_27a,V0p_2E0),V1d_2E0),V2x_2E0) = c_2EEncode_2Eencode__list_2E2(A_27a,c_2EDecode_2Edec2enc_2E1(A_27a,V1d_2E0),V2x_2E0) ) ) ).

tff(thm_2EDecode_2Eencode__then__decode__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)),V2l_2E0: tyop_2Elist_2Elist(A_27a),V3t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
      ( ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
        & p(c_2Elist_2EEVERY_2E2(A_27a,V0p_2E0,V2l_2E0)) )
     => ( c_2EDecode_2Edecode__list_2E3(A_27a,c_2Elist_2EEVERY_2E1(A_27a,V0p_2E0),c_2EDecode_2Eenc2dec_2E2(A_27a,V0p_2E0,V1e_2E0),c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,c_2EEncode_2Eencode__list_2E2(A_27a,V1e_2E0,V2l_2E0),V3t_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2l_2E0,V3t_2E0)) ) ) ).

tff(thm_2EDecode_2Edecode__list,axiom,
    ! [A_27a: $tType,F4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))))] :
      ( ! [V6x_2E0: A_27a,V9xs_2E0: tyop_2Elist_2Elist(A_27a),V10t_27_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F4_2E0,V6x_2E0),V9xs_2E0),V10t_27_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(A_27a,V6x_2E0,V9xs_2E0),V10t_27_27_2E0)) )
     => ( ! [V6x_2E0: A_27a,V8v_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F3_2E0,V6x_2E0),V8v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V8v_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F4_2E0,V6x_2E0)) )
       => ( ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V6x_2E0: A_27a,V7t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F2_2E0,V0p_2E0),V2d_2E0),V6x_2E0),V7t_27_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edecode__list_2E3(A_27a,c_2Elist_2EEVERY_2E1(A_27a,V0p_2E0),V2d_2E0,V7t_27_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F3_2E0,V6x_2E0)) )
         => ( ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V5v1_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0,V0p_2E0),V2d_2E0),V5v1_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5v1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F2_2E0,V0p_2E0),V2d_2E0)) )
           => ( ! [V2d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3v2_2E0: tyop_2Emin_2Ebool,V4t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F0_2E0,V2d_2E0),V0p_2E0),V3v2_2E0),V4t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V3v2_2E0,c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V2d_2E0,V4t_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0,V0p_2E0),V2d_2E0)),c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ENIL_2E0(A_27a),V4t_2E0))) )
             => ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
                  ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V2d_2E0))
                 => ( c_2EDecode_2Edecode__list_2E3(A_27a,c_2Elist_2EEVERY_2E1(A_27a,V0p_2E0),V2d_2E0,V1l_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V1l_2E0,c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F0_2E0,V2d_2E0),V0p_2E0)) ) ) ) ) ) ) ) ).

tff(thm_2EDecode_2Ewf__decode__blist,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
      ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V1p_2E0,V2d_2E0))
     => p(c_2EDecode_2Ewf__decoder_2E2(tyop_2Elist_2Elist(A_27a),c_2EEncode_2Elift__blist_2E2(A_27a,V0m_2E0,V1p_2E0),c_2EDecode_2Edecode__blist_2E3(A_27a,c_2EEncode_2Elift__blist_2E2(A_27a,V0m_2E0,V1p_2E0),V0m_2E0,V2d_2E0))) ) ).

tff(thm_2EDecode_2Edec2enc__decode__blist,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V3l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V1p_2E0,V2d_2E0))
        & p(c_2EEncode_2Elift__blist_2E3(A_27a,V0m_2E0,V1p_2E0,V3l_2E0)) )
     => ( c_2EDecode_2Edec2enc_2E2(tyop_2Elist_2Elist(A_27a),c_2EDecode_2Edecode__blist_2E3(A_27a,c_2EEncode_2Elift__blist_2E2(A_27a,V0m_2E0,V1p_2E0),V0m_2E0,V2d_2E0),V3l_2E0) = c_2EEncode_2Eencode__blist_2E3(tyop_2Emin_2Ebool,A_27a,V0m_2E0,c_2EDecode_2Edec2enc_2E1(A_27a,V2d_2E0),V3l_2E0) ) ) ).

tff(thm_2EDecode_2Eencode__then__decode__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)),V3l_2E0: tyop_2Elist_2Elist(A_27a),V4t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
      ( ( p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V1p_2E0,V2e_2E0))
        & p(c_2EEncode_2Elift__blist_2E3(A_27a,V0m_2E0,V1p_2E0,V3l_2E0)) )
     => ( c_2EDecode_2Edecode__blist_2E4(A_27a,c_2EEncode_2Elift__blist_2E2(A_27a,V0m_2E0,V1p_2E0),V0m_2E0,c_2EDecode_2Eenc2dec_2E2(A_27a,V1p_2E0,V2e_2E0),c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,c_2EEncode_2Eencode__blist_2E3(tyop_2Emin_2Ebool,A_27a,V0m_2E0,V2e_2E0,V3l_2E0),V4t_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3l_2E0,V4t_2E0)) ) ) ).

tff(thm_2EDecode_2Edecode__blist,axiom,
    ! [A_27a: $tType,F4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))))] :
      ( ! [V6x_2E0: A_27a,V9xs_2E0: tyop_2Elist_2Elist(A_27a),V10t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F4_2E0,V6x_2E0),V9xs_2E0),V10t_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(A_27a,V6x_2E0,V9xs_2E0),V10t_27_2E0)) )
     => ( ! [V6x_2E0: A_27a,V8v_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F3_2E0,V6x_2E0),V8v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V8v_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F4_2E0,V6x_2E0)) )
       => ( ! [V4n_2E0: tyop_2Enum_2Enum,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V6x_2E0: A_27a,V7t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))),F2_2E0,V4n_2E0),V0p_2E0),V3d_2E0),V6x_2E0),V7t_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edecode__blist_2E4(A_27a,c_2EEncode_2Elift__blist_2E2(A_27a,V4n_2E0,V0p_2E0),V4n_2E0,V3d_2E0,V7t_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F3_2E0,V6x_2E0)) )
         => ( ! [V4n_2E0: tyop_2Enum_2Enum,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V5v1_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F1_2E0,V4n_2E0),V0p_2E0),V3d_2E0),V5v1_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5v1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))),F2_2E0,V4n_2E0),V0p_2E0),V3d_2E0)) )
           => ( ! [V3d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F0_2E0,V3d_2E0),V2l_2E0),V0p_2E0),V4n_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V3d_2E0,V2l_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F1_2E0,V4n_2E0),V0p_2E0),V3d_2E0)) )
             => ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
                  ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V3d_2E0))
                 => ( c_2EDecode_2Edecode__blist_2E4(A_27a,c_2EEncode_2Elift__blist_2E2(A_27a,V1m_2E0,V0p_2E0),V1m_2E0,V3d_2E0,V2l_2E0) = c_2Earithmetic_2Enum__CASE_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V1m_2E0,c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ENIL_2E0(A_27a),V2l_2E0)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F0_2E0,V3d_2E0),V2l_2E0),V0p_2E0)) ) ) ) ) ) ) ) ).

tff(thm_2EDecode_2Ewf__decode__num,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : p(c_2EDecode_2Ewf__decoder_2E2(tyop_2Enum_2Enum,V0p_2E0,c_2EDecode_2Edecode__num_2E1(V0p_2E0))) ).

tff(thm_2EDecode_2Edec2enc__decode__num,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Enum_2Enum] :
      ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0p_2E0,V1x_2E0))
     => ( c_2EDecode_2Edec2enc_2E2(tyop_2Enum_2Enum,c_2EDecode_2Edecode__num_2E1(V0p_2E0),V1x_2E0) = c_2EEncode_2Eencode__num_2E1(V1x_2E0) ) ) ).

tff(thm_2EDecode_2Edecode__num__total,axiom,
    ! [F5_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F4_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F3_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] :
      ( ! [V9v_2E0: tyop_2Enum_2Enum,V10t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F5_2E0,V9v_2E0),V10t_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V9v_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V10t_27_2E0)) )
     => ( ! [V8v1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F2_2E0,V8v1_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V8v1_2E0,F5_2E0) )
       => ( ! [V6v_2E0: tyop_2Enum_2Enum,V7t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F4_2E0,V6v_2E0),V7t_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V6v_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V7t_27_2E0)) )
         => ( ! [V5v1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F3_2E0,V5v1_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5v1_2E0,F4_2E0) )
           => ( ! [V3v8_2E0: tyop_2Emin_2Ebool,V4t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F1_2E0,V3v8_2E0),V4t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V3v8_2E0,c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Enum_2E0_2E0,V4t_2E0)),c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edecode__num_2E2(c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,tyop_2Enum_2Enum,c_2Ebool_2ET_2E0),V4t_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F3_2E0)) )
             => ( ! [V1v4_2E0: tyop_2Emin_2Ebool,V2t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F0_2E0,V1v4_2E0),V2t_27_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V1v4_2E0,c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V2t_27_2E0,c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F1_2E0),c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edecode__num_2E2(c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,tyop_2Enum_2Enum,c_2Ebool_2ET_2E0),V2t_27_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F2_2E0)) )
               => ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__num_2E2(c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,tyop_2Enum_2Enum,c_2Ebool_2ET_2E0),V0l_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V0l_2E0,c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F0_2E0) ) ) ) ) ) ) ) ).

tff(thm_2EDecode_2Edecode__num,axiom,
    ! [F5_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F4_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))] :
      ( ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V10v_2E0: tyop_2Enum_2Enum,V11t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F5_2E0,V0p_2E0),V10v_2E0),V11t_27_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0p_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V10v_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V10v_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V11t_27_2E0)),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) )
     => ( ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V9v1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F2_2E0,V0p_2E0),V9v1_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V9v1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F5_2E0,V0p_2E0)) )
       => ( ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V7v_2E0: tyop_2Enum_2Enum,V8t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F4_2E0,V0p_2E0),V7v_2E0),V8t_27_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0p_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V7v_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V7v_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V8t_27_2E0)),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) )
         => ( ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V6v1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F3_2E0,V0p_2E0),V6v1_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V6v1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F4_2E0,V0p_2E0)) )
           => ( ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4v8_2E0: tyop_2Emin_2Ebool,V5t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0,V0p_2E0),V4v8_2E0),V5t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V4v8_2E0,c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0p_2E0,c_2Enum_2E0_2E0),c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Enum_2E0_2E0,V5t_2E0)),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edecode__num_2E2(c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,tyop_2Enum_2Enum,c_2Ebool_2ET_2E0),V5t_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F3_2E0,V0p_2E0))) )
             => ( ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2v4_2E0: tyop_2Emin_2Ebool,V3t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0,V0p_2E0),V2v4_2E0),V3t_27_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V2v4_2E0,c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V3t_27_2E0,c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0,V0p_2E0)),c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edecode__num_2E2(c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,tyop_2Enum_2Enum,c_2Ebool_2ET_2E0),V3t_27_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F2_2E0,V0p_2E0))) )
               => ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edecode__num_2E2(V0p_2E0,V1l_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V1l_2E0,c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0,V0p_2E0)) ) ) ) ) ) ) ) ).

tff(thm_2EDecode_2Edec__bnum__def__compute,axiom,
    ! [F5_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F4_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))] :
      ( ! [V3h_2E0: tyop_2Emin_2Ebool,V6n_2E0: tyop_2Enum_2Enum,V7t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F5_2E0,V3h_2E0),V6n_2E0),V7t_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V6n_2E0),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,V3h_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2E0_2E0)),V7t_27_2E0)) )
     => ( ! [V3h_2E0: tyop_2Emin_2Ebool,V5v_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F4_2E0,V3h_2E0),V5v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5v_2E0,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F5_2E0,V3h_2E0)) )
       => ( ! [V1m_2E0: tyop_2Enum_2Enum,V3h_2E0: tyop_2Emin_2Ebool,V4t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0,V1m_2E0),V3h_2E0),V4t_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edec__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))),V4t_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F4_2E0,V3h_2E0)) )
         => ( ! [V10h_2E0: tyop_2Emin_2Ebool,V13n_2E0: tyop_2Enum_2Enum,V14t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F3_2E0,V10h_2E0),V13n_2E0),V14t_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V13n_2E0),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,V10h_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2E0_2E0)),V14t_27_2E0)) )
           => ( ! [V10h_2E0: tyop_2Emin_2Ebool,V12v_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F2_2E0,V10h_2E0),V12v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V12v_2E0,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F3_2E0,V10h_2E0)) )
             => ( ! [V8m_2E0: tyop_2Enum_2Enum,V10h_2E0: tyop_2Emin_2Ebool,V11t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0,V8m_2E0),V10h_2E0),V11t_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edec__bnum_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V8m_2E0)),V11t_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F2_2E0,V10h_2E0)) )
               => ( ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edec__bnum_2E2(c_2Enum_2E0_2E0,V0l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Enum_2E0_2E0,V0l_2E0)) )
                  & ! [V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edec__bnum_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1m_2E0)),V2l_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V2l_2E0,c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0,V1m_2E0)) )
                  & ! [V8m_2E0: tyop_2Enum_2Enum,V9l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2EDecode_2Edec__bnum_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V8m_2E0)),V9l_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V9l_2E0,c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0,V8m_2E0)) ) ) ) ) ) ) ) ) ).

tff(thm_2EDecode_2Edec__bnum__lt,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2n_2E0: tyop_2Enum_2Enum,V3t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
      ( ( c_2EDecode_2Edec__bnum_2E2(V0m_2E0,V1l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2n_2E0,V3t_2E0)) )
     => p(c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0m_2E0))) ) ).

tff(thm_2EDecode_2Edec__bnum__inj,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2n_2E0: tyop_2Enum_2Enum,V3t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
      ( ( c_2EDecode_2Edec__bnum_2E2(V0m_2E0,V1l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2n_2E0,V3t_2E0)) )
     => ( V1l_2E0 = c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,c_2EEncode_2Eencode__bnum_2E2(V0m_2E0,V2n_2E0),V3t_2E0) ) ) ).

tff(thm_2EDecode_2Ewf__decode__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_2EDecode_2Ewf__decoder_2E2(tyop_2Enum_2Enum,V1p_2E0,c_2EDecode_2Edecode__bnum_2E2(V0m_2E0,V1p_2E0))) ) ).

tff(thm_2EDecode_2Edec2enc__decode__bnum,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2EEncode_2Ewf__pred__bnum_2E2(V0m_2E0,V1p_2E0))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1p_2E0,V2x_2E0)) )
     => ( c_2EDecode_2Edec2enc_2E2(tyop_2Enum_2Enum,c_2EDecode_2Edecode__bnum_2E2(V0m_2E0,V1p_2E0),V2x_2E0) = c_2EEncode_2Eencode__bnum_2E2(V0m_2E0,V2x_2E0) ) ) ).

tff(thm_2EDecode_2Edecode__bnum,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] :
      ( ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4n_2E0: tyop_2Enum_2Enum,V5t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0,V0p_2E0),V4n_2E0),V5t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0p_2E0,V4n_2E0),c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V4n_2E0,V5t_2E0)),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))) )
     => ( ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3v_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F0_2E0,V0p_2E0),V3v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3v_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0,V0p_2E0)) )
       => ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
            ( p(c_2EEncode_2Ewf__pred__bnum_2E2(V1m_2E0,V0p_2E0))
           => ( c_2EDecode_2Edecode__bnum_2E3(V1m_2E0,V0p_2E0,V2l_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edec__bnum_2E2(V1m_2E0,V2l_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F0_2E0,V0p_2E0)) ) ) ) ) ).

tff(thm_2EDecode_2Ewf__decode__tree,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
      ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V1d_2E0))
     => p(c_2EDecode_2Ewf__decoder_2E2(tyop_2EEncode_2Etree(A_27a),c_2EEncode_2Elift__tree_2E1(A_27a,V0p_2E0),c_2EDecode_2Edecode__tree_2E2(A_27a,c_2EEncode_2Elift__tree_2E1(A_27a,V0p_2E0),V1d_2E0))) ) ).

tff(thm_2EDecode_2Edecode__tree,axiom,
    ! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))] :
      ( ! [V4a_2E0: A_27a,V7ts_2E0: tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),V8t_27_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F3_2E0,V4a_2E0),V7ts_2E0),V8t_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EEncode_2ENode_2E2(A_27a,V4a_2E0,V7ts_2E0),V8t_27_2E0)) )
     => ( ! [V4a_2E0: A_27a,V6v_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F2_2E0,V4a_2E0),V6v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V6v_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F3_2E0,V4a_2E0)) )
       => ( ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V4a_2E0: A_27a,V5t_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F1_2E0,V0p_2E0),V2d_2E0),V4a_2E0),V5t_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edecode__list_2E3(tyop_2EEncode_2Etree(A_27a),c_2Elist_2EEVERY_2E1(tyop_2EEncode_2Etree(A_27a),c_2EEncode_2Elift__tree_2E1(A_27a,V0p_2E0)),c_2EDecode_2Edecode__tree_2E2(A_27a,c_2EEncode_2Elift__tree_2E1(A_27a,V0p_2E0),V2d_2E0),V5t_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2EEncode_2Etree(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F2_2E0,V4a_2E0)) )
         => ( ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V3v1_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0,V0p_2E0),V2d_2E0),V3v1_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3v1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F1_2E0,V0p_2E0),V2d_2E0)) )
           => ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2d_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] :
                ( p(c_2EDecode_2Ewf__decoder_2E2(A_27a,V0p_2E0,V2d_2E0))
               => ( c_2EDecode_2Edecode__tree_2E3(A_27a,c_2EEncode_2Elift__tree_2E1(A_27a,V0p_2E0),V2d_2E0,V1l_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V2d_2E0,V1l_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2EEncode_2Etree(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F0_2E0,V0p_2E0),V2d_2E0)) ) ) ) ) ) ) ).

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