ITP001 Axioms: ITP079

ITP001 Axioms: ITP079_7.ax

%------------------------------------------------------------------------------
% File     : ITP079_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : Coder.ax [Gau19]
%          : HL4079_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  275 ( 115 unt; 129 typ;   0 def)
%            Number of atoms       :  195 ( 128 equ)
%            Maximal formula atoms :    5 (   0 avg)
%            Number of connectives :   52 (   3   ~;   3   |;   9   &)
%                                         (  14 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  106 (  65   >;  41   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  125 ( 125 usr;  19 con; 0-6 aty)
%            Number of variables   :  582 ( 446   !;   2   ?; 582   :)
%                                         ( 134  !>;   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_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_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_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_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_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

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_2ECoder_2Eblist__coder_2E0,type,
    c_2ECoder_2Eblist__coder_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_2ECoder_2Eblist__coder_2E2,type,
    c_2ECoder_2Eblist__coder_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))) ) > tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_2ECoder_2Ebnum__coder_2E0,type,
    c_2ECoder_2Ebnum__coder_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))))) ).

tff(c_2ECoder_2Ebnum__coder_2E2,type,
    c_2ECoder_2Ebnum__coder_2E2: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) > tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))) ).

tff(c_2ECoder_2Ebool__coder_2E0,type,
    c_2ECoder_2Ebool__coder_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))))) ).

tff(c_2ECoder_2Ebool__coder_2E1,type,
    c_2ECoder_2Ebool__coder_2E1: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) > tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))) ).

tff(c_2ECoder_2Edecode_2E0,type,
    c_2ECoder_2Edecode_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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a))) ).

tff(c_2ECoder_2Edecode_2E2,type,
    c_2ECoder_2Edecode_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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a) ) ).

tff(c_2ECoder_2Edecode_2E3,type,
    c_2ECoder_2Edecode_2E3: 
      !>[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_2Elist_2Elist(tyop_2Emin_2Ebool) ) > A_27a ) ).

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__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__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__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__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__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__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__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__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__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_2ECoder_2Edecoder_2E0,type,
    c_2ECoder_2Edecoder_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a)) ).

tff(c_2ECoder_2Edecoder_2E1,type,
    c_2ECoder_2Edecoder_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a) ) ).

tff(c_2ECoder_2Edecoder_2E2,type,
    c_2ECoder_2Edecoder_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))) * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > A_27a ) ).

tff(c_2ECoder_2Edomain_2E0,type,
    c_2ECoder_2Edomain_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2ECoder_2Edomain_2E1,type,
    c_2ECoder_2Edomain_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2ECoder_2Edomain_2E2,type,
    c_2ECoder_2Edomain_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))) * A_27a ) > 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_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__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__bool_2E0,type,
    c_2EEncode_2Eencode__bool_2E0: tyop_2Emin_2Efun(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__num_2E0,type,
    c_2EEncode_2Eencode__num_2E0: tyop_2Emin_2Efun(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__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__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__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_2ECoder_2Eencoder_2E0,type,
    c_2ECoder_2Eencoder_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ).

tff(c_2ECoder_2Eencoder_2E1,type,
    c_2ECoder_2Eencoder_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))) > tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ) ).

tff(c_2ECoder_2Eencoder_2E2,type,
    c_2ECoder_2Eencoder_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))) * A_27a ) > 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__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__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__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__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_2ECoder_2Elist__coder_2E0,type,
    c_2ECoder_2Elist__coder_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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_2ECoder_2Elist__coder_2E1,type,
    c_2ECoder_2Elist__coder_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))) > tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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_2ECoder_2Enum__coder_2E0,type,
    c_2ECoder_2Enum__coder_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))))) ).

tff(c_2ECoder_2Enum__coder_2E1,type,
    c_2ECoder_2Enum__coder_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))) ).

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_2ECoder_2Eoption__coder_2E0,type,
    c_2ECoder_2Eoption__coder_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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_2ECoder_2Eoption__coder_2E1,type,
    c_2ECoder_2Eoption__coder_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))) > tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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_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_2ECoder_2Eprod__coder_2E0,type,
    c_2ECoder_2Eprod__coder_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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_2ECoder_2Eprod__coder_2E2,type,
    c_2ECoder_2Eprod__coder_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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)))))) * tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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_2ECoder_2Esum__coder_2E0,type,
    c_2ECoder_2Esum__coder_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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_2ECoder_2Esum__coder_2E2,type,
    c_2ECoder_2Esum__coder_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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)))))) * tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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_2ECoder_2Etree__coder_2E0,type,
    c_2ECoder_2Etree__coder_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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_2ECoder_2Etree__coder_2E1,type,
    c_2ECoder_2Etree__coder_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))) > tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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_2ECoder_2Eunit__coder_2E0,type,
    c_2ECoder_2Eunit__coder_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))))) ).

tff(c_2ECoder_2Eunit__coder_2E1,type,
    c_2ECoder_2Eunit__coder_2E1: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool) > tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))) ).

tff(c_2ECoder_2Ewf__coder_2E0,type,
    c_2ECoder_2Ewf__coder_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Ebool) ).

tff(c_2ECoder_2Ewf__coder_2E1,type,
    c_2ECoder_2Ewf__coder_2E1: 
      !>[A_27a: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))) > 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_2E0,type,
    c_2EEncode_2Ewf__pred_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Epair_2Eprod(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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28A_27c_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27c_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(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_2Epair_2E_2C_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)))),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_2Epair_2Eprod(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_2Elist_2Elist(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_2Epair_2Eprod(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_2Epair_2E_2C_2E0(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))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27d_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28A_27c_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),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_27b,tyop_2Elist_2Elist(A_27c)),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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(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_2Epair_2E_2C_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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),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_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(A_27b,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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2Epair_2E_2C_2E0(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27c,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)))),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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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_27c,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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27c,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))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Elist_2Elist(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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27d,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)))),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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_27d,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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27d,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))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Epair_2Eprod(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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(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_2Epair_2E_2C_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)))),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_2Epair_2Eprod(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_2Elist_2Elist(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_2Epair_2Eprod(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_2Epair_2E_2C_2E0(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))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Elist_2Elist_28A_27c_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Elist_2Elist_28A_27c_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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)))),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_27b),tyop_2Elist_2Elist(A_27c)),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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)))),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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_27b),tyop_2Elist_2Elist(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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Epair_2Eprod(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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(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_2Epair_2E_2C_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)))),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_2Epair_2Eprod(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_2Elist_2Elist(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_2Epair_2Eprod(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_2Epair_2E_2C_2E0(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))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Epair_2Eprod(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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Elist_2Elist(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_2Epair_2E_2C_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)))),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_2Epair_2Eprod(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_2Elist_2Elist(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_2Epair_2Eprod(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_2Epair_2E_2C_2E0(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))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28A_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28A_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Elist_2Elist(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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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)))),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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_27b),tyop_2Elist_2Elist(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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27c_2CA_27d_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27c_2CA_27d_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Elist_2Elist(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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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)))),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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_27c,A_27d),tyop_2Elist_2Elist(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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28A_27c_2CA_27d_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28A_27c_2CA_27d_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Elist_2Elist(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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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)))),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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_27c,A_27d),tyop_2Elist_2Elist(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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2EEncode_2Etree_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2EEncode_2Etree_28A_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2EEncode_2Etree_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2EEncode_2Etree_28A_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2EEncode_2Etree_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),tyop_2Elist_2Elist(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_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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)))),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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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_27b),tyop_2Elist_2Elist(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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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))))),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_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_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Emin_2E_40_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EEVERY_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EEVERY_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(A_27a),X0_2E0) ) ).

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

tff(arityeq2_2Ec_2ECoder_2Eblist__coder_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Eblist__coder_2E2(A_27a,A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Eblist__coder_2E0(A_27a,A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2ECoder_2Eblist__coder_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))] : ( c_2ECoder_2Eblist__coder_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_2ECoder_2Eblist__coder_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2ECoder_2Ebnum__coder_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ECoder_2Ebnum__coder_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Ebnum__coder_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Ebool__coder_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : ( c_2ECoder_2Ebool__coder_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Ebool__coder_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2ECoder_2Edecode_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_2ECoder_2Edecode_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),A_27a),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_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a)),c_2ECoder_2Edecode_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2ECoder_2Edecode_2E3_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)))),X2_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2ECoder_2Edecode_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a,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),A_27a),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_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a)),c_2ECoder_2Edecode_2E0(A_27a),X0_2E0),X1_2E0),X2_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(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(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__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(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__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__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(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(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(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(arityeq1_2Ec_2ECoder_2Edecoder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Edecoder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a),c_2ECoder_2Edecoder_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2ECoder_2Edecoder_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2ECoder_2Edecoder_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a),c_2ECoder_2Edecoder_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Edomain_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Edomain_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2ECoder_2Edomain_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2ECoder_2Edomain_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),X1_2E0: A_27a] : ( c_2ECoder_2Edomain_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2ECoder_2Edomain_2E0(A_27a),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(arityeq2_2Ec_2EEncode_2Eencode__blist_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c))] : ( c_2EEncode_2Eencode__blist_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),c_2EEncode_2Eencode__blist_2E0(A_27c,A_27b),X0_2E0),X1_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(arityeq1_2Ec_2EEncode_2Eencode__list_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__list_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__list_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Eencode__option_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__option_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__option_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Eencode__prod_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__prod_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EEncode_2Eencode__prod_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Eencode__sum_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__sum_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EEncode_2Eencode__sum_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Eencode__tree_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] : ( c_2EEncode_2Eencode__tree_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__tree_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Eencoder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Eencoder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2ECoder_2Eencoder_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2ECoder_2Eencoder_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),X1_2E0: A_27a] : ( c_2ECoder_2Eencoder_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2ECoder_2Eencoder_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Elift__blist_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Elift__blist_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2EEncode_2Elift__blist_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(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__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(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(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(arityeq1_2Ec_2ECoder_2Elist__coder_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Elist__coder_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Elist__coder_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Elist__coder_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))] : ( c_2ECoder_2Elist__coder_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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_2ECoder_2Elist__coder_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Enum__coder_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ECoder_2Enum__coder_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Enum__coder_2E0,X0_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),A_27a)] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),A_27a),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),A_27a),A_27a),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),A_27a),A_27a)),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Eoption__coder_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Eoption__coder_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Eoption__coder_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Eoption__coder_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))] : ( c_2ECoder_2Eoption__coder_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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_2ECoder_2Eoption__coder_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2EA_27a_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),A_27a))] : ( c_2Epair_2Epair__CASE_2E2(A_27a,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),A_27a)),A_27a,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),A_27a)),A_27a),c_2Epair_2Epair__CASE_2E0(A_27a,A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2ECoder_2Eprod__coder_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Eprod__coder_2E2(A_27a,A_27b,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Eprod__coder_2E0(A_27a,A_27b,A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2ECoder_2Eprod__coder_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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)))))),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2ECoder_2Eprod__coder_2E2(A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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_2ECoder_2Eprod__coder_2E0(A_27a,A_27b,A_27c,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2ECoder_2Esum__coder_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Esum__coder_2E2(A_27a,A_27b,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Esum__coder_2E0(A_27a,A_27b,A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2ECoder_2Esum__coder_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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)))))),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2ECoder_2Esum__coder_2E2(A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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_2ECoder_2Esum__coder_2E0(A_27a,A_27b,A_27c,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Etree__coder_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Etree__coder_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Etree__coder_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Etree__coder_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))] : ( c_2ECoder_2Etree__coder_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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_2ECoder_2Etree__coder_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Eunit__coder_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool)] : ( c_2ECoder_2Eunit__coder_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Eunit__coder_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Ewf__coder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Ewf__coder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Ebool,c_2ECoder_2Ewf__coder_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Ewf__coder_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Ewf__coder_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Ebool,c_2ECoder_2Ewf__coder_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Ewf__coder_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Ewf__coder_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Ebool,c_2ECoder_2Ewf__coder_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Ewf__coder_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Ewf__coder_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Ebool,c_2ECoder_2Ewf__coder_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Ewf__coder_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Ewf__coder_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Ebool,c_2ECoder_2Ewf__coder_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Ewf__coder_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Ewf__coder_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Ebool,c_2ECoder_2Ewf__coder_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Ewf__coder_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Ewf__coder_2E1(tyop_2Eoption_2Eoption(A_27a),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Ebool,c_2ECoder_2Ewf__coder_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Ewf__coder_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Ewf__coder_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Ebool,c_2ECoder_2Ewf__coder_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Ewf__coder_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Ewf__coder_2E1(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Ebool,c_2ECoder_2Ewf__coder_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2ECoder_2Ewf__coder_2E1_2Emono_2Etyop_2EEncode_2Etree_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2ECoder_2Ewf__coder_2E1(tyop_2EEncode_2Etree(A_27a),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),tyop_2Emin_2Ebool,c_2ECoder_2Ewf__coder_2E0(tyop_2EEncode_2Etree(A_27a)),X0_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(arityeq1_2Ec_2EEncode_2Ewf__pred_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Ewf__pred_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2EEncode_2Ewf__pred_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2EEncode_2Ewf__pred_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Ewf__pred_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2EEncode_2Ewf__pred_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).

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

tff(arityeq1_2Ec_2EEncode_2Ewf__pred_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Ewf__pred_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2EEncode_2Ewf__pred_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).

tff(arityeq2_2Ec_2EEncode_2Ewf__pred__bnum_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EEncode_2Ewf__pred__bnum_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2EEncode_2Ewf__pred__bnum_2E0,X0_2E0),X1_2E0) ) ).

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

tff(thm_2ECoder_2Edecode__def,axiom,
    ! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a)),F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),A_27a),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V5x_2E0: A_27a,V6v2_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),A_27a),F2_2E0,V5x_2E0),V6v2_2E0) = V5x_2E0 )
     => ( ! [V4v_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)),A_27a,F1_2E0,V4v_2E0) = c_2Epair_2Epair__CASE_2E2(A_27a,A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V4v_2E0,F2_2E0) )
       => ( ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0p_2E0),V3x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V3x_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)))),V2l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2ECoder_2Edecode_2E3(A_27a,V0p_2E0,V1d_2E0,V2l_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),A_27a,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),V1d_2E0,V2l_2E0),c_2Emin_2E_40_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0p_2E0)),F1_2E0) ) ) ) ) ).

tff(thm_2ECoder_2Ewf__coder__def,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),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_2ECoder_2Ewf__coder_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),V0p_2E0,c_2Epair_2E_2C_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)))),V1e_2E0,V2d_2E0))))
    <=> ( p(c_2EEncode_2Ewf__pred_2E1(A_27a,V0p_2E0))
        & p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
        & ( V2d_2E0 = c_2EDecode_2Eenc2dec_2E2(A_27a,V0p_2E0,V1e_2E0) ) ) ) ).

tff(thm_2ECoder_2Edomain__def,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),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_2ECoder_2Edomain_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),V0p_2E0,c_2Epair_2E_2C_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)))),V1e_2E0,V2d_2E0))) = V0p_2E0 ) ).

tff(thm_2ECoder_2Eencoder__def,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),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_2ECoder_2Eencoder_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),V0p_2E0,c_2Epair_2E_2C_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)))),V1e_2E0,V2d_2E0))) = V1e_2E0 ) ).

tff(thm_2ECoder_2Edecoder__def,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),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_2ECoder_2Edecoder_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),V0p_2E0,c_2Epair_2E_2C_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)))),V1e_2E0,V2d_2E0))) = c_2ECoder_2Edecode_2E2(A_27a,V0p_2E0,V2d_2E0) ) ).

tff(thm_2ECoder_2Eunit__coder__def,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool)] : ( c_2ECoder_2Eunit__coder_2E1(V0p_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),V0p_2E0,c_2Epair_2E_2C_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)))),c_2EEncode_2Eencode__unit_2E0,c_2EDecode_2Edecode__unit_2E1(V0p_2E0))) ) ).

tff(thm_2ECoder_2Ebool__coder__def,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : ( c_2ECoder_2Ebool__coder_2E1(V0p_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),V0p_2E0,c_2Epair_2E_2C_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)))),c_2EEncode_2Eencode__bool_2E0,c_2EDecode_2Edecode__bool_2E1(V0p_2E0))) ) ).

tff(thm_2ECoder_2Eprod__coder__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0p1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(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)))),V3p2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4e2_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V5d2_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_2ECoder_2Eprod__coder_2E2(A_27a,A_27b,A_27c,A_27d,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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))))),V0p1_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27c,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)))),V1e1_2E0,V2d1_2E0)),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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))))),V3p2_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27d,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)))),V4e2_2E0,V5d2_2E0))) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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_2EEncode_2Elift__prod_2E2(A_27a,A_27b,V0p1_2E0,V3p2_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),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_2EEncode_2Eencode__prod_2E2(A_27c,A_27d,V1e1_2E0,V4e2_2E0),c_2EDecode_2Edecode__prod_2E3(A_27a,A_27b,c_2EEncode_2Elift__prod_2E2(A_27a,A_27b,V0p1_2E0,V3p2_2E0),V2d1_2E0,V5d2_2E0))) ) ).

tff(thm_2ECoder_2Esum__coder__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0p1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(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)))),V3p2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4e2_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V5d2_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_2ECoder_2Esum__coder_2E2(A_27a,A_27b,A_27c,A_27d,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,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))))),V0p1_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27c,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)))),V1e1_2E0,V2d1_2E0)),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,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))))),V3p2_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27d,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)))),V4e2_2E0,V5d2_2E0))) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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_2EEncode_2Elift__sum_2E2(A_27a,A_27b,V0p1_2E0,V3p2_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),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_2EEncode_2Eencode__sum_2E2(A_27c,A_27d,V1e1_2E0,V4e2_2E0),c_2EDecode_2Edecode__sum_2E3(A_27a,A_27b,c_2EEncode_2Elift__sum_2E2(A_27a,A_27b,V0p1_2E0,V3p2_2E0),V2d1_2E0,V5d2_2E0))) ) ).

tff(thm_2ECoder_2Eoption__coder__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27b,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))))] : ( c_2ECoder_2Eoption__coder_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),V0p_2E0,c_2Epair_2E_2C_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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V1e_2E0,V2d_2E0))) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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_2EEncode_2Elift__option_2E1(A_27a,V0p_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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_2EEncode_2Eencode__option_2E1(A_27b,V1e_2E0),c_2EDecode_2Edecode__option_2E2(A_27a,c_2EEncode_2Elift__option_2E1(A_27a,V0p_2E0),V2d_2E0))) ) ).

tff(thm_2ECoder_2Elist__coder__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27b,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))))] : ( c_2ECoder_2Elist__coder_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),V0p_2E0,c_2Epair_2E_2C_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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V1e_2E0,V2d_2E0))) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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_2Elist_2EEVERY_2E1(A_27a,V0p_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),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_2EEncode_2Eencode__list_2E1(A_27b,V1e_2E0),c_2EDecode_2Edecode__list_2E2(A_27a,c_2Elist_2EEVERY_2E1(A_27a,V0p_2E0),V2d_2E0))) ) ).

tff(thm_2ECoder_2Eblist__coder__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2e_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),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))))] : ( c_2ECoder_2Eblist__coder_2E2(A_27a,A_27b,A_27c,V0m_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),V1p_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2e_2E0,V3d_2E0))) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_2EEncode_2Elift__blist_2E2(A_27a,V0m_2E0,V1p_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),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_2EEncode_2Eencode__blist_2E2(A_27c,A_27b,V0m_2E0,V2e_2E0),c_2EDecode_2Edecode__blist_2E3(A_27a,c_2EEncode_2Elift__blist_2E2(A_27a,V0m_2E0,V1p_2E0),V0m_2E0,V3d_2E0))) ) ).

tff(thm_2ECoder_2Enum__coder__def,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ECoder_2Enum__coder_2E1(V0p_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),V0p_2E0,c_2Epair_2E_2C_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)))),c_2EEncode_2Eencode__num_2E0,c_2EDecode_2Edecode__num_2E1(V0p_2E0))) ) ).

tff(thm_2ECoder_2Ebnum__coder__def,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ECoder_2Ebnum__coder_2E2(V0m_2E0,V1p_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),V1p_2E0,c_2Epair_2E_2C_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)))),c_2EEncode_2Eencode__bnum_2E1(V0m_2E0),c_2EDecode_2Edecode__bnum_2E2(V0m_2E0,V1p_2E0))) ) ).

tff(thm_2ECoder_2Etree__coder__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27b,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))))] : ( c_2ECoder_2Etree__coder_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),V0p_2E0,c_2Epair_2E_2C_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_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V1e_2E0,V2d_2E0))) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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_2EEncode_2Elift__tree_2E1(A_27a,V0p_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2EEncode_2Etree(A_27b),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_2EEncode_2Eencode__tree_2E1(A_27b,V1e_2E0),c_2EDecode_2Edecode__tree_2E2(A_27a,c_2EEncode_2Elift__tree_2E1(A_27a,V0p_2E0),V2d_2E0))) ) ).

tff(thm_2ECoder_2Edecode__encode,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_2ECoder_2Edecode_2E3(A_27a,V0p_2E0,c_2EDecode_2Eenc2dec_2E2(A_27a,V0p_2E0,V1e_2E0),app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V2x_2E0)) = V2x_2E0 ) ) ).

tff(thm_2ECoder_2Ewf__coder,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))))] :
      ( p(c_2ECoder_2Ewf__coder_2E1(A_27a,V0c_2E0))
     => ! [V1x_2E0: A_27a] :
          ( p(c_2ECoder_2Edomain_2E2(A_27a,V0c_2E0,V1x_2E0))
         => ( c_2ECoder_2Edecoder_2E2(A_27a,V0c_2E0,c_2ECoder_2Eencoder_2E2(A_27a,V0c_2E0,V1x_2E0)) = V1x_2E0 ) ) ) ).

tff(thm_2ECoder_2Ewf__coder__closed,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))))] :
      ( p(c_2ECoder_2Ewf__coder_2E1(A_27a,V0c_2E0))
     => ! [V1l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : p(c_2ECoder_2Edomain_2E2(A_27a,V0c_2E0,c_2ECoder_2Edecoder_2E2(A_27a,V0c_2E0,V1l_2E0))) ) ).

tff(thm_2ECoder_2Ewf__coder__op,axiom,
    ! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))] :
      ( ( ? [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V3x_2E0))
        & p(c_2EEncode_2Ewf__encoder_2E2(A_27a,V0p_2E0,V1e_2E0))
        & ! [V4x_2E0: A_27a] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0p_2E0,V4x_2E0))
           => ( app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1e_2E0,V4x_2E0) = app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2f_2E0,V4x_2E0) ) ) )
     => p(c_2ECoder_2Ewf__coder_2E1(A_27a,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))),V0p_2E0,c_2Epair_2E_2C_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)))),V1e_2E0,c_2EDecode_2Eenc2dec_2E2(A_27a,V0p_2E0,V2f_2E0))))) ) ).

tff(thm_2ECoder_2Ewf__coder__unit,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool)] :
      ( p(c_2EEncode_2Ewf__pred_2E1(tyop_2Eone_2Eone,V0p_2E0))
     => p(c_2ECoder_2Ewf__coder_2E1(tyop_2Eone_2Eone,c_2ECoder_2Eunit__coder_2E1(V0p_2E0))) ) ).

tff(thm_2ECoder_2Ewf__coder__bool,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
      ( p(c_2EEncode_2Ewf__pred_2E1(tyop_2Emin_2Ebool,V0p_2E0))
     => p(c_2ECoder_2Ewf__coder_2E1(tyop_2Emin_2Ebool,c_2ECoder_2Ebool__coder_2E1(V0p_2E0))) ) ).

tff(thm_2ECoder_2Ewf__coder__prod,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0c1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),V1c2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))))] :
      ( ( p(c_2ECoder_2Ewf__coder_2E1(A_27a,V0c1_2E0))
        & p(c_2ECoder_2Ewf__coder_2E1(A_27b,V1c2_2E0)) )
     => p(c_2ECoder_2Ewf__coder_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2ECoder_2Eprod__coder_2E2(A_27a,A_27b,A_27a,A_27b,V0c1_2E0,V1c2_2E0))) ) ).

tff(thm_2ECoder_2Ewf__coder__sum,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0c1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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)))))),V1c2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))))] :
      ( ( p(c_2ECoder_2Ewf__coder_2E1(A_27a,V0c1_2E0))
        & p(c_2ECoder_2Ewf__coder_2E1(A_27b,V1c2_2E0)) )
     => p(c_2ECoder_2Ewf__coder_2E1(tyop_2Esum_2Esum(A_27a,A_27b),c_2ECoder_2Esum__coder_2E2(A_27a,A_27b,A_27a,A_27b,V0c1_2E0,V1c2_2E0))) ) ).

tff(thm_2ECoder_2Ewf__coder__option,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))))] :
      ( p(c_2ECoder_2Ewf__coder_2E1(A_27a,V0c_2E0))
     => p(c_2ECoder_2Ewf__coder_2E1(tyop_2Eoption_2Eoption(A_27a),c_2ECoder_2Eoption__coder_2E1(A_27a,A_27a,V0c_2E0))) ) ).

tff(thm_2ECoder_2Ewf__coder__list,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))))] :
      ( p(c_2ECoder_2Ewf__coder_2E1(A_27a,V0c_2E0))
     => p(c_2ECoder_2Ewf__coder_2E1(tyop_2Elist_2Elist(A_27a),c_2ECoder_2Elist__coder_2E1(A_27a,A_27a,V0c_2E0))) ) ).

tff(thm_2ECoder_2Ewf__coder__blist,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1c_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))))] :
      ( p(c_2ECoder_2Ewf__coder_2E1(A_27a,V1c_2E0))
     => p(c_2ECoder_2Ewf__coder_2E1(tyop_2Elist_2Elist(A_27a),c_2ECoder_2Eblist__coder_2E2(A_27a,A_27a,tyop_2Emin_2Ebool,V0m_2E0,V1c_2E0))) ) ).

tff(thm_2ECoder_2Ewf__coder__num,axiom,
    ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2EEncode_2Ewf__pred_2E1(tyop_2Enum_2Enum,V0p_2E0))
     => p(c_2ECoder_2Ewf__coder_2E1(tyop_2Enum_2Enum,c_2ECoder_2Enum__coder_2E1(V0p_2E0))) ) ).

tff(thm_2ECoder_2Ewf__coder__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_2ECoder_2Ewf__coder_2E1(tyop_2Enum_2Enum,c_2ECoder_2Ebnum__coder_2E2(V0m_2E0,V1p_2E0))) ) ).

tff(thm_2ECoder_2Ewf__coder__tree,axiom,
    ! [A_27a: $tType,V0c_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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))))))] :
      ( p(c_2ECoder_2Ewf__coder_2E1(A_27a,V0c_2E0))
     => p(c_2ECoder_2Ewf__coder_2E1(tyop_2EEncode_2Etree(A_27a),c_2ECoder_2Etree__coder_2E1(A_27a,A_27a,V0c_2E0))) ) ).

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