%------------------------------------------------------------------------------
% File     : ITP049_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    : llist.ax [Gau19]
%          : HL4049_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  643 ( 256 unt; 201 typ;   0 def)
%            Number of atoms       :  916 ( 634 equ)
%            Maximal formula atoms :   15 (   1 avg)
%            Number of connectives :  492 (  18   ~;  25   |; 158   &)
%                                         (  95 <=>; 196  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  153 (  99   >;  54   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  198 ( 198 usr;  18 con; 0-6 aty)
%            Number of variables   : 2025 (1727   !;  83   ?;2025   :)
%                                         ( 215  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: $tType > $tType ).

tff(tyop_2Ellist_2Ellist,type,
    tyop_2Ellist_2Ellist: $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_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: $tType > $tType ).

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

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

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

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

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

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

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

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

tff(c_2Epair_2E_23_23_2E0,type,
    c_2Epair_2E_23_23_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d)))) ).

tff(c_2Epair_2E_23_23_2E2,type,
    c_2Epair_2E_23_23_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27c) * tyop_2Emin_2Efun(A_27b,A_27d) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d)) ) ).

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

tff(c_2Earithmetic_2E_2B_2E1,type,
    c_2Earithmetic_2E_2B_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

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

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

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

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

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

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

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

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).

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

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

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

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

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

tff(c_2Emin_2E_3D_2E1,type,
    c_2Emin_2E_3D_2E1: 
      !>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

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

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

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

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

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

tff(c_2Ebool_2E_3F_21_2E0,type,
    c_2Ebool_2E_3F_21_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

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

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

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

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

tff(c_2Elist_2EAPPEND_2E1,type,
    c_2Elist_2EAPPEND_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ) ).

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

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

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

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

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

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

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

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

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

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

tff(c_2Elist_2ECONS_2E1,type,
    c_2Elist_2ECONS_2E1: 
      !>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ) ).

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

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

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

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

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

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

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

tff(c_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

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

tff(c_2Earithmetic_2EFUNPOW_2E0,type,
    c_2Earithmetic_2EFUNPOW_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))) ).

tff(c_2Earithmetic_2EFUNPOW_2E3,type,
    c_2Earithmetic_2EFUNPOW_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27a) * tyop_2Enum_2Enum * A_27a ) > A_27a ) ).

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

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

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

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

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

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

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

tff(c_2Eoption_2EIS__SOME_2E0,type,
    c_2Eoption_2EIS__SOME_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool) ).

tff(c_2Eoption_2EIS__SOME_2E1,type,
    c_2Eoption_2EIS__SOME_2E1: 
      !>[A_27a: $tType] : ( tyop_2Eoption_2Eoption(A_27a) > tyop_2Emin_2Ebool ) ).

tff(c_2Ecombin_2EK_2E0,type,
    c_2Ecombin_2EK_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).

tff(c_2Ellist_2ELAPPEND_2E0,type,
    c_2Ellist_2ELAPPEND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))) ).

tff(c_2Ellist_2ELAPPEND_2E2,type,
    c_2Ellist_2ELAPPEND_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Ellist_2Ellist(A_27a) * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Ellist_2Ellist(A_27a) ) ).

tff(c_2Ellist_2ELCONS_2E0,type,
    c_2Ellist_2ELCONS_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))) ).

tff(c_2Ellist_2ELCONS_2E2,type,
    c_2Ellist_2ELCONS_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Ellist_2Ellist(A_27a) ) ).

tff(c_2Ellist_2ELDROP_2E0,type,
    c_2Ellist_2ELDROP_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))) ).

tff(c_2Ellist_2ELDROP_2E1,type,
    c_2Ellist_2ELDROP_2E1: 
      !>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))) ) ).

tff(c_2Ellist_2ELDROP_2E2,type,
    c_2Ellist_2ELDROP_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)) ) ).

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

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

tff(c_2Ebool_2ELET_2E0,type,
    c_2Ebool_2ELET_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).

tff(c_2Ebool_2ELET_2E2,type,
    c_2Ebool_2ELET_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(c_2Ellist_2ELFILTER_2E0,type,
    c_2Ellist_2ELFILTER_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))) ).

tff(c_2Ellist_2ELFILTER_2E2,type,
    c_2Ellist_2ELFILTER_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Ellist_2Ellist(A_27a) ) ).

tff(c_2Ellist_2ELFINITE_2E0,type,
    c_2Ellist_2ELFINITE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool) ).

tff(c_2Ellist_2ELFINITE_2E1,type,
    c_2Ellist_2ELFINITE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ellist_2Ellist(A_27a) > tyop_2Emin_2Ebool ) ).

tff(c_2Ellist_2ELFLATTEN_2E0,type,
    c_2Ellist_2ELFLATTEN_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Ellist_2Ellist(A_27a)) ).

tff(c_2Ellist_2ELFLATTEN_2E1,type,
    c_2Ellist_2ELFLATTEN_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)) > tyop_2Ellist_2Ellist(A_27a) ) ).

tff(c_2Ellist_2ELGENLIST_2E0,type,
    c_2Ellist_2ELGENLIST_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Ellist_2Ellist(A_27a))) ).

tff(c_2Ellist_2ELGENLIST_2E2,type,
    c_2Ellist_2ELGENLIST_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) * tyop_2Eoption_2Eoption(tyop_2Enum_2Enum) ) > tyop_2Ellist_2Ellist(A_27a) ) ).

tff(c_2Ellist_2ELHD_2E0,type,
    c_2Ellist_2ELHD_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)) ).

tff(c_2Ellist_2ELHD_2E1,type,
    c_2Ellist_2ELHD_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ellist_2Ellist(A_27a) > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Ellist_2ELLENGTH_2E0,type,
    c_2Ellist_2ELLENGTH_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)) ).

tff(c_2Ellist_2ELLENGTH_2E1,type,
    c_2Ellist_2ELLENGTH_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ellist_2Ellist(A_27a) > tyop_2Eoption_2Eoption(tyop_2Enum_2Enum) ) ).

tff(c_2Ellist_2ELMAP_2E0,type,
    c_2Ellist_2ELMAP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))) ).

tff(c_2Ellist_2ELMAP_2E2,type,
    c_2Ellist_2ELMAP_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Ellist_2Ellist(A_27b) ) ).

tff(c_2Ellist_2ELNIL_2E0,type,
    c_2Ellist_2ELNIL_2E0: 
      !>[A_27a: $tType] : tyop_2Ellist_2Ellist(A_27a) ).

tff(c_2Ellist_2ELNTH_2E0,type,
    c_2Ellist_2ELNTH_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a))) ).

tff(c_2Ellist_2ELNTH_2E1,type,
    c_2Ellist_2ELNTH_2E1: 
      !>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)) ) ).

tff(c_2Ellist_2ELNTH_2E2,type,
    c_2Ellist_2ELNTH_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Ellist_2ELPREFIX_2E0,type,
    c_2Ellist_2ELPREFIX_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Ellist_2ELPREFIX_2E2,type,
    c_2Ellist_2ELPREFIX_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Ellist_2Ellist(A_27a) * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ellist_2ELREPEAT_2E0,type,
    c_2Ellist_2ELREPEAT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Ellist_2Ellist(A_27a)) ).

tff(c_2Ellist_2ELREPEAT_2E1,type,
    c_2Ellist_2ELREPEAT_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Ellist_2Ellist(A_27a) ) ).

tff(c_2Ellist_2ELTAKE_2E0,type,
    c_2Ellist_2ELTAKE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))) ).

tff(c_2Ellist_2ELTAKE_2E2,type,
    c_2Ellist_2ELTAKE_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)) ) ).

tff(c_2Ellist_2ELTL_2E0,type,
    c_2Ellist_2ELTL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))) ).

tff(c_2Ellist_2ELTL_2E1,type,
    c_2Ellist_2ELTL_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ellist_2Ellist(A_27a) > tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)) ) ).

tff(c_2Ellist_2ELTL__HD_2E0,type,
    c_2Ellist_2ELTL__HD_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))) ).

tff(c_2Ellist_2ELTL__HD_2E1,type,
    c_2Ellist_2ELTL__HD_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ellist_2Ellist(A_27a) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)) ) ).

tff(c_2Ellist_2ELUNFOLD_2E0,type,
    c_2Ellist_2ELUNFOLD_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a))) ).

tff(c_2Ellist_2ELUNFOLD_2E1,type,
    c_2Ellist_2ELUNFOLD_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))) > tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)) ) ).

tff(c_2Ellist_2ELUNFOLD_2E2,type,
    c_2Ellist_2ELUNFOLD_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))) * A_27b ) > tyop_2Ellist_2Ellist(A_27a) ) ).

tff(c_2Ellist_2ELUNZIP_2E0,type,
    c_2Ellist_2ELUNZIP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))) ).

tff(c_2Ellist_2ELUNZIP_2E1,type,
    c_2Ellist_2ELUNZIP_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)) > tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)) ) ).

tff(c_2Ellist_2ELZIP_2E0,type,
    c_2Ellist_2ELZIP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b))) ).

tff(c_2Ellist_2ELZIP_2E1,type,
    c_2Ellist_2ELZIP_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)) > tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Earithmetic_2EMOD_2E0,type,
    c_2Earithmetic_2EMOD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2EMOD_2E2,type,
    c_2Earithmetic_2EMOD_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

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

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

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

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

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

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

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

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

tff(c_2Eoption_2EOPTION__JOIN_2E0,type,
    c_2Eoption_2EOPTION__JOIN_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)) ).

tff(c_2Eoption_2EOPTION__JOIN_2E1,type,
    c_2Eoption_2EOPTION__JOIN_2E1: 
      !>[A_27a: $tType] : ( tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)) > tyop_2Eoption_2Eoption(A_27a) ) ).

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

tff(c_2Eoption_2EOPTION__MAP_2E2,type,
    c_2Eoption_2EOPTION__MAP_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Eoption_2Eoption(A_27a) ) > tyop_2Eoption_2Eoption(A_27b) ) ).

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

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

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

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

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

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

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

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

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

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

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

tff(c_2Eoption_2ETHE_2E0,type,
    c_2Eoption_2ETHE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a) ).

tff(c_2Eoption_2ETHE_2E1,type,
    c_2Eoption_2ETHE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Eoption_2Eoption(A_27a) > A_27a ) ).

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

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

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

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

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

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

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

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

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).

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

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

tff(c_2Eset__relation_2Edomain_2E0,type,
    c_2Eset__relation_2Edomain_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(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Edomain_2E1,type,
    c_2Eset__relation_2Edomain_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Ellist_2Eevery_2E0,type,
    c_2Ellist_2Eevery_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Ellist_2Eevery_2E2,type,
    c_2Ellist_2Eevery_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ellist_2Eexists_2E0,type,
    c_2Ellist_2Eexists_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Ellist_2Eexists_2E2,type,
    c_2Ellist_2Eexists_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Efinite__prefixes_2E0,type,
    c_2Eset__relation_2Efinite__prefixes_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(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Efinite__prefixes_2E2,type,
    c_2Eset__relation_2Efinite__prefixes_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ellist_2EfromList_2E0,type,
    c_2Ellist_2EfromList_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Ellist_2Ellist(A_27a)) ).

tff(c_2Ellist_2EfromList_2E1,type,
    c_2Ellist_2EfromList_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Ellist_2Ellist(A_27a) ) ).

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

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

tff(c_2Eset__relation_2Elinear__order_2E0,type,
    c_2Eset__relation_2Elinear__order_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Elinear__order_2E2,type,
    c_2Eset__relation_2Elinear__order_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ellist_2Elinear__order__to__list__f_2E0,type,
    c_2Ellist_2Elinear__order__to__list__f_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))) ).

tff(c_2Ellist_2Elinear__order__to__list__f_2E1,type,
    c_2Ellist_2Elinear__order__to__list__f_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)) ) ).

tff(c_2Ellist_2Ellength__rel_2E0,type,
    c_2Ellist_2Ellength__rel_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Ellist_2Ellength__rel_2E2,type,
    c_2Ellist_2Ellength__rel_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Ellist_2Ellist(A_27a) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ellist_2Ellist__abs_2E0,type,
    c_2Ellist_2Ellist__abs_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Ellist_2Ellist(A_27a)) ).

tff(c_2Ellist_2Ellist__abs_2E1,type,
    c_2Ellist_2Ellist__abs_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)) > tyop_2Ellist_2Ellist(A_27a) ) ).

tff(c_2Ellist_2Ellist__rep_2E0,type,
    c_2Ellist_2Ellist__rep_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))) ).

tff(c_2Ellist_2Ellist__rep_2E1,type,
    c_2Ellist_2Ellist__rep_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ellist_2Ellist(A_27a) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)) ) ).

tff(c_2Ellist_2Ellist__rep_2E2,type,
    c_2Ellist_2Ellist__rep_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Ellist_2Ellist(A_27a) * tyop_2Enum_2Enum ) > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Ellist_2Elrep__ok_2E0,type,
    c_2Ellist_2Elrep__ok_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool) ).

tff(c_2Ellist_2Elrep__ok_2E1,type,
    c_2Ellist_2Elrep__ok_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)) > tyop_2Emin_2Ebool ) ).

tff(c_2Eset__relation_2Eminimal__elements_2E0,type,
    c_2Eset__relation_2Eminimal__elements_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Eset__relation_2Eminimal__elements_2E2,type,
    c_2Eset__relation_2Eminimal__elements_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).

tff(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).

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

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

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

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

tff(c_2Eset__relation_2Erange_2E0,type,
    c_2Eset__relation_2Erange_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Eset__relation_2Erange_2E1,type,
    c_2Eset__relation_2Erange_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Eset__relation_2Errestrict_2E0,type,
    c_2Eset__relation_2Errestrict_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))) ).

tff(c_2Eset__relation_2Errestrict_2E2,type,
    c_2Eset__relation_2Errestrict_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) ).

tff(c_2Ellist_2EtoList_2E0,type,
    c_2Ellist_2EtoList_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Ellist_2EtoList_2E1,type,
    c_2Ellist_2EtoList_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ellist_2Ellist(A_27a) > tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)) ) ).

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_23_23_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : ( c_2Epair_2E_23_23_2E2(A_27b,A_27a,tyop_2Ellist_2Ellist(A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),c_2Epair_2E_23_23_2E0(A_27b,A_27a,tyop_2Ellist_2Ellist(A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2E_2B_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2E_2C_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

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

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

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

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a),X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(tyop_2Ellist_2Ellist(A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Epair_2E_2C_2E0(tyop_2Ellist_2Ellist(A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a),X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Epair_2E_2C_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),c_2Epair_2E_2C_2E0(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

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

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

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

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

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

tff(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Emin_2E_3D_2E1(tyop_2Ellist_2Ellist(A_27a),X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(tyop_2Ellist_2Ellist(A_27a)),X0_2E0) ) ).

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

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

tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Ellist_2Ellist_28A_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_21_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Emin_2E_40_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EAPPEND_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E0(A_27a),X0_2E0) ) ).

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

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

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

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

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Ellist_2Ellist(A_27a),X2_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ebool_2ECOND_2E3(tyop_2Ellist_2Ellist(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Ellist_2Ellist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Ellist_2Ellist(A_27b),X2_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ebool_2ECOND_2E3(tyop_2Ellist_2Ellist(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b))),c_2Ebool_2ECOND_2E0(tyop_2Ellist_2Ellist(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).

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

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).

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

tff(arityeq1_2Ec_2Elist_2ECONS_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Elist_2ECONS_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0) ) ).

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

tff(arityeq1_2Ec_2Elist_2ECONS_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b] : ( c_2Elist_2ECONS_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ECONS_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: A_27c] : ( c_2Elist_2ECONS_2E1(A_27c,X0_2E0) = app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E0(A_27c),X0_2E0) ) ).

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

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

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

tff(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Earithmetic_2EFUNPOW_2E3(tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Earithmetic_2EFUNPOW_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Earithmetic_2EFUNPOW_2E3(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),c_2Earithmetic_2EFUNPOW_2E0(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Earithmetic_2EFUNPOW_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Earithmetic_2EFUNPOW_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).

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

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

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0) ) ).

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

tff(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Eoption_2EIS__SOME_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))] : ( c_2Eoption_2EIS__SOME_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELAPPEND_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a),X1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELAPPEND_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELAPPEND_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELAPPEND_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27b),X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELAPPEND_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELAPPEND_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELCONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELCONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELCONS_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELCONS_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Ellist_2Ellist(A_27c)] : ( c_2Ellist_2ELCONS_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27c)),c_2Ellist_2ELCONS_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27d,axiom,
    ! [A_27d: $tType,X0_2E0: A_27d,X1_2E0: tyop_2Ellist_2Ellist(A_27d)] : ( c_2Ellist_2ELCONS_2E2(A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27d),tyop_2Ellist_2Ellist(A_27d),app_2E2(A_27d,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27d),tyop_2Ellist_2Ellist(A_27d)),c_2Ellist_2ELCONS_2E0(A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a),X1_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Ellist_2ELCONS_2E2(tyop_2Ellist_2Ellist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELCONS_2E0(tyop_2Ellist_2Ellist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27c_29,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27c),X1_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c))] : ( c_2Ellist_2ELCONS_2E2(tyop_2Ellist_2Ellist(A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),app_2E2(tyop_2Ellist_2Ellist(A_27c),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c))),c_2Ellist_2ELCONS_2E0(tyop_2Ellist_2Ellist(A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27d_29,axiom,
    ! [A_27d: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27d),X1_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d))] : ( c_2Ellist_2ELCONS_2E2(tyop_2Ellist_2Ellist(A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),app_2E2(tyop_2Ellist_2Ellist(A_27d),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d))),c_2Ellist_2ELCONS_2E0(tyop_2Ellist_2Ellist(A_27d)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ellist_2ELCONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Ellist_2ELCONS_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELDROP_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELDROP_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELDROP_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELDROP_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELDROP_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELDROP_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELDROP_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELDROP_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b))),c_2Ellist_2ELDROP_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELDROP_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ellist_2Ellist(A_27c)] : ( c_2Ellist_2ELDROP_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27c)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27c))),c_2Ellist_2ELDROP_2E0(A_27c),X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),c_2Ebool_2ELET_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2Ctyop_2Ellist_2Ellist_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2Ctyop_2Ellist_2Ellist_28A_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),X1_2E0: tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))] : ( c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),c_2Ebool_2ELET_2E0(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELFILTER_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELFILTER_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELFILTER_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELFILTER_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELFILTER_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELFILTER_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELFINITE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELFINITE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELFINITE_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELFINITE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELFLATTEN_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Ellist_2ELFLATTEN_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFLATTEN_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELFLATTEN_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c))] : ( c_2Ellist_2ELFLATTEN_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),tyop_2Ellist_2Ellist(A_27c),c_2Ellist_2ELFLATTEN_2E0(A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELFLATTEN_2E1_2Emono_2EA_27d,axiom,
    ! [A_27d: $tType,X0_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d))] : ( c_2Ellist_2ELFLATTEN_2E1(A_27d,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),tyop_2Ellist_2Ellist(A_27d),c_2Ellist_2ELFLATTEN_2E0(A_27d),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELGENLIST_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] : ( c_2Ellist_2ELGENLIST_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELGENLIST_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELGENLIST_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] : ( c_2Ellist_2ELGENLIST_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELGENLIST_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELHD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELHD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELHD_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELHD_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(A_27b),c_2Ellist_2ELHD_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELHD_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Ellist_2ELHD_2E1(tyop_2Ellist_2Ellist(A_27a),X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELHD_2E0(tyop_2Ellist_2Ellist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELLENGTH_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELLENGTH_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELLENGTH_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELLENGTH_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELMAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELMAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELMAP_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELMAP_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Ellist_2Ellist(A_27c)] : ( c_2Ellist_2ELMAP_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELMAP_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Ellist_2Ellist(A_27c)] : ( c_2Ellist_2ELMAP_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELMAP_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELNTH_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELNTH_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2ELNTH_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELNTH_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELNTH_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2ELNTH_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELNTH_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELNTH_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(A_27b)),c_2Ellist_2ELNTH_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELNTH_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ellist_2Ellist(A_27c)] : ( c_2Ellist_2ELNTH_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(A_27c),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(A_27c)),c_2Ellist_2ELNTH_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELPREFIX_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a),X1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELPREFIX_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),c_2Ellist_2ELPREFIX_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELPREFIX_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27b),X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELPREFIX_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool),c_2Ellist_2ELPREFIX_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELREPEAT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELREPEAT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELREPEAT_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTAKE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Ellist_2ELTAKE_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELTAKE_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b))),c_2Ellist_2ELTAKE_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ellist_2Ellist(A_27c)] : ( c_2Ellist_2ELTAKE_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c))),c_2Ellist_2ELTAKE_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELTL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELTL_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELTL_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELTL_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELTL_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Ellist_2ELTL_2E1(tyop_2Ellist_2Ellist(A_27a),X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELTL_2E0(tyop_2Ellist_2Ellist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELTL__HD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTL__HD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0: A_27a] : ( c_2Ellist_2ELUNFOLD_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELUNFOLD_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELUNFOLD_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Ellist_2ELUNFOLD_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELUNFOLD_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: A_27b] : ( c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELUNFOLD_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: A_27c] : ( c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELUNFOLD_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),X1_2E0: A_27c] : ( c_2Ellist_2ELUNFOLD_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27c,tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELUNFOLD_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),X1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELUNFOLD_2E2(A_27a,tyop_2Ellist_2Ellist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELUNFOLD_2E0(A_27a,tyop_2Ellist_2Ellist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELUNFOLD_2E2(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELUNFOLD_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELUNZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ellist_2ELUNZIP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELUNZIP_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))] : ( c_2Ellist_2ELZIP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELZIP_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2EMOD_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ENULL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ENULL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E0(A_27a),X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))] : ( c_2Eoption_2EOPTION__BIND_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__BIND_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))] : ( c_2Eoption_2EOPTION__BIND_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),c_2Eoption_2EOPTION__BIND_2E0(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a))] : ( c_2Eoption_2EOPTION__BIND_2E2(A_27a,tyop_2Ellist_2Ellist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__BIND_2E0(A_27a,tyop_2Ellist_2Ellist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))] : ( c_2Eoption_2EOPTION__BIND_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Eoption_2EOPTION__BIND_2E0(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))] : ( c_2Eoption_2EOPTION__BIND_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),c_2Eoption_2EOPTION__BIND_2E0(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Eoption_2EOPTION__BIND_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Eoption_2EOPTION__BIND_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a))] : ( c_2Eoption_2EOPTION__JOIN_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))] : ( c_2Eoption_2EOPTION__JOIN_2E1(tyop_2Ellist_2Ellist(A_27a),X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2EOPTION__JOIN_2E0(tyop_2Ellist_2Ellist(A_27a)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Eoption_2EOPTION__MAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Eoption_2EOPTION__MAP_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b))),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27c_29,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c))),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b))),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),A_27a),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a)),X0_2E0),X1_2E0) ) ).

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

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

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

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E0(tyop_2Ellist_2Ellist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27b),X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Eoption_2ESOME_2E0(tyop_2Ellist_2Ellist(A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27c,A_27b)] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).

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

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

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Eoption_2ETHE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),A_27a,c_2Eoption_2ETHE_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))] : ( c_2Eoption_2ETHE_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Eoption_2ETHE_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E0(tyop_2Ellist_2Ellist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Ellist_2Ellist_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)))] : ( c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ETHE_2E0(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] : ( c_2Eoption_2ETHE_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Eoption_2ETHE_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Ellist_2Ellist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Ellist_2Ellist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2Epair_2EUNCURRY_2E1(A_27b,A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epair_2EUNCURRY_2E0(A_27b,A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27c_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b)))] : ( c_2Epair_2EUNCURRY_2E1(A_27c,A_27a,tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Epair_2EUNCURRY_2E0(A_27c,A_27a,tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2Ctyop_2Ellist_2Ellist_28A_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),c_2Epair_2EUNCURRY_2E0(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),X0_2E0) ) ).

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

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

tff(arityeq1_2Ec_2Eset__relation_2Edomain_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2Eevery_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2Eevery_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),c_2Ellist_2Eevery_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2Eevery_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Ellist_2Eevery_2E2(tyop_2Ellist_2Ellist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Ebool),c_2Ellist_2Eevery_2E0(tyop_2Ellist_2Ellist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2Eexists_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2Eexists_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),c_2Ellist_2Eexists_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Efinite__prefixes_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2EfromList_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2EfromList_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E0(A_27a),X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Eset__relation_2Elinear__order_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Elinear__order_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Elinear__order_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2Elinear__order__to__list__f_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ellist_2Elinear__order__to__list__f_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Ellist_2Elinear__order__to__list__f_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2Ellength__rel_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2Ellength__rel_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ellist_2Ellength__rel_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2Ellist__abs_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] : ( c_2Ellist_2Ellist__abs_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2Ellist__abs_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2Ellist__rep_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2Ellist__rep_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2Ellist__rep_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2Ellist__rep_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2Ellist__rep_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2Ellist__rep_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2Elrep__ok_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] : ( c_2Ellist_2Elrep__ok_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2Elrep__ok_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b))] : ( c_2Ellist_2Elrep__ok_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Eminimal__elements_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Eminimal__elements_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Eminimal__elements_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E0(A_27c,A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a)] : ( c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b))),c_2Ecombin_2Eo_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b)] : ( c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a))),c_2Ecombin_2Eo_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a),A_27b),X0_2E0),X1_2E0) ) ).

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

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

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Ecombin_2Eo_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2Ecombin_2Eo_2E0(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Eoption_2Eoption__CASE_2E0(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))] : ( c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),c_2Eoption_2Eoption__CASE_2E0(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))] : ( c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),c_2Eoption_2Eoption__CASE_2E0(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eoption_2Eoption__CASE_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X2_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Ellist_2Ellist(A_27b),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),tyop_2Ellist_2Ellist(A_27b))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27b_29_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Ellist_2Ellist(A_27b),A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),tyop_2Ellist_2Ellist(A_27b)),c_2Epair_2Epair__CASE_2E0(tyop_2Ellist_2Ellist(A_27b),A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Emin_2Ebool,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Epair_2Epair__CASE_2E0(tyop_2Emin_2Ebool,A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(A_27a),A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(A_27a),A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Erange_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Errestrict_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Errestrict_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Errestrict_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2EtoList_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2EtoList_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2EtoList_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2EtoList_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Ellist_2EtoList_2E0(A_27b),X0_2E0) ) ).

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

tff(thm_2Ellist_2Elrep__ok__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V6x_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V6x_2E0))
        <=> ( V6x_2E0 = c_2Enum_2E0_2E0 ) )
     => ! [V0x_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] :
          ( p(c_2Ellist_2Elrep__ok_2E1(A_27a,V0x_2E0))
        <=> ? [V1lrep__ok_27_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)] :
              ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool,V1lrep__ok_27_2E0,V0x_2E0))
              & ! [V2a0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] :
                  ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool,V1lrep__ok_27_2E0,V2a0_2E0))
                 => ( ! [V3x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V2a0_2E0,V3x_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
                    | ? [V4h_2E0: A_27a,V5t_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] :
                        ( ! [V6x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V2a0_2E0,V6x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V6x_2E0),c_2Eoption_2ESOME_2E1(A_27a,V4h_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V5t_2E0,c_2Earithmetic_2E_2D_2E2(V6x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
                        & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool,V1lrep__ok_27_2E0,V5t_2E0)) ) ) ) ) ) ) ).

tff(thm_2Ellist_2Ellist__TY__DEF,axiom,
    ! [A_27a: $tType] :
    ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2Elrep__ok_2E0(A_27a),V0rep_2E0)) ).

tff(thm_2Ellist_2Ellist__absrep,axiom,
    ! [A_27a: $tType] :
      ( ! [V0a_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2Ellist__abs_2E1(A_27a,c_2Ellist_2Ellist__rep_2E1(A_27a,V0a_2E0)) = V0a_2E0 )
      & ! [V1r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] :
          ( p(c_2Ellist_2Elrep__ok_2E1(A_27a,V1r_2E0))
        <=> ( c_2Ellist_2Ellist__rep_2E1(A_27a,c_2Ellist_2Ellist__abs_2E1(A_27a,V1r_2E0)) = V1r_2E0 ) ) ) ).

tff(thm_2Ellist_2ELNIL,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),F0_2E0,V0n_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
     => ( c_2Ellist_2ELNIL_2E0(A_27a) = c_2Ellist_2Ellist__abs_2E1(A_27a,F0_2E0) ) ) ).

tff(thm_2Ellist_2ELCONS,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))))] :
      ( ! [V2n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V2n_2E0))
        <=> ( V2n_2E0 = c_2Enum_2E0_2E0 ) )
     => ( ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Ellist_2Ellist(A_27a),V2n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V0h_2E0),V1t_2E0),V2n_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V2n_2E0),c_2Eoption_2ESOME_2E1(A_27a,V0h_2E0),c_2Ellist_2Ellist__rep_2E2(A_27a,V1t_2E0,c_2Earithmetic_2E_2D_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
       => ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELCONS_2E2(A_27a,V0h_2E0,V1t_2E0) = c_2Ellist_2Ellist__abs_2E1(A_27a,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V0h_2E0),V1t_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELTL__HD__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))))] :
      ( ! [V0ll_2E0: tyop_2Ellist_2Ellist(A_27a),V1h_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),F0_2E0,V0ll_2E0),V1h_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),c_2Epair_2E_2C_2E2(tyop_2Ellist_2Ellist(A_27a),A_27a,c_2Ellist_2Ellist__abs_2E1(A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),tyop_2Enum_2Enum,c_2Ellist_2Ellist__rep_2E1(A_27a,V0ll_2E0),c_2Enum_2ESUC_2E0)),V1h_2E0)) )
     => ! [V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTL__HD_2E1(A_27a,V0ll_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2Ellist__rep_2E2(A_27a,V0ll_2E0,c_2Enum_2E0_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),F0_2E0,V0ll_2E0)) ) ) ).

tff(thm_2Ellist_2ELHD,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELHD_2E1(A_27a,V0ll_2E0) = c_2Ellist_2Ellist__rep_2E2(A_27a,V0ll_2E0,c_2Enum_2E0_2E0) ) ).

tff(thm_2Ellist_2ELTL,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))))] :
      ( ! [V0ll_2E0: tyop_2Ellist_2Ellist(A_27a),V2n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),F1_2E0,V0ll_2E0),V2n_2E0) = c_2Ellist_2Ellist__rep_2E2(A_27a,V0ll_2E0,c_2Earithmetic_2E_2B_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) )
     => ( ! [V0ll_2E0: tyop_2Ellist_2Ellist(A_27a),V1v_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),F0_2E0,V0ll_2E0),V1v_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2Ellist__abs_2E1(A_27a,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),F1_2E0,V0ll_2E0))) )
       => ! [V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTL_2E1(A_27a,V0ll_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELHD_2E1(A_27a,V0ll_2E0),c_2Eoption_2ENONE_2E0(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),F0_2E0,V0ll_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELNTH,axiom,
    ! [A_27a: $tType] :
      ( ! [V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELNTH_2E2(A_27a,c_2Enum_2E0_2E0,V0ll_2E0) = c_2Ellist_2ELHD_2E1(A_27a,V0ll_2E0) )
      & ! [V1n_2E0: tyop_2Enum_2Enum,V2ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELNTH_2E2(A_27a,c_2Enum_2ESUC_2E1(V1n_2E0),V2ll_2E0) = c_2Eoption_2EOPTION__JOIN_2E1(A_27a,c_2Eoption_2EOPTION__MAP_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E1(A_27a,V1n_2E0),c_2Ellist_2ELTL_2E1(A_27a,V2ll_2E0))) ) ) ).

tff(thm_2Ellist_2ELUNFOLD__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V3m_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),F1_2E0,V0f_2E0),V3m_2E0) = c_2Eoption_2EOPTION__BIND_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27b,A_27a),V3m_2E0,c_2Epair_2EUNCURRY_2E1(A_27b,A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Ecombin_2Eo_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Ecombin_2EK_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a),V0f_2E0))) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1z_2E0: A_27b,V2n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V0f_2E0),V1z_2E0),V2n_2E0) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,c_2Epair_2ESND_2E0(A_27b,A_27a),c_2Earithmetic_2EFUNPOW_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),F1_2E0,V0f_2E0),V2n_2E0,app_2E2(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V0f_2E0,V1z_2E0))) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1z_2E0: A_27b] : ( c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V0f_2E0,V1z_2E0) = c_2Ellist_2Ellist__abs_2E1(A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V0f_2E0),V1z_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELTAKE,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))))] :
      ( ! [V3hd_2E0: A_27a,V4tl_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),F1_2E0,V3hd_2E0),V4tl_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(A_27a,V3hd_2E0,V4tl_2E0)) )
     => ( ! [V1n_2E0: tyop_2Enum_2Enum,V2ll_2E0: tyop_2Ellist_2Ellist(A_27a),V3hd_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F0_2E0,V1n_2E0),V2ll_2E0),V3hd_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(A_27a,V1n_2E0,c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELTL_2E1(A_27a,V2ll_2E0))),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),F1_2E0,V3hd_2E0)) )
       => ( ! [V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTAKE_2E2(A_27a,c_2Enum_2E0_2E0,V0ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a)) )
          & ! [V1n_2E0: tyop_2Enum_2Enum,V2ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTAKE_2E2(A_27a,c_2Enum_2ESUC_2E1(V1n_2E0),V2ll_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELHD_2E1(A_27a,V2ll_2E0),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F0_2E0,V1n_2E0),V2ll_2E0)) ) ) ) ) ).

tff(thm_2Ellist_2ELMAP,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ellist_2ELMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Ellist_2ELNIL_2E0(A_27b) )
      & ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2h_2E0: A_27a,V3t_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELMAP_2E2(A_27a,A_27b,V1f_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V2h_2E0,V3t_2E0)) = c_2Ellist_2ELCONS_2E2(A_27b,app_2E2(A_27a,A_27b,V1f_2E0,V2h_2E0),c_2Ellist_2ELMAP_2E2(A_27a,A_27b,V1f_2E0,V3t_2E0)) ) ) ).

tff(thm_2Ellist_2ELAPPEND,axiom,
    ! [A_27a: $tType] :
      ( ! [V0x_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELAPPEND_2E2(A_27a,c_2Ellist_2ELNIL_2E0(A_27a),V0x_2E0) = V0x_2E0 )
      & ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Ellist_2Ellist(A_27a),V3x_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELAPPEND_2E2(A_27a,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V2t_2E0),V3x_2E0) = c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,c_2Ellist_2ELAPPEND_2E2(A_27a,V2t_2E0,V3x_2E0)) ) ) ).

tff(thm_2Ellist_2ELFINITE__def,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V0x_2E0))
    <=> ! [V1LFINITE_27_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
          ( ! [V2a0_2E0: tyop_2Ellist_2Ellist(A_27a)] :
              ( ( ( V2a0_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) )
                | ? [V3h_2E0: A_27a,V4t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
                    ( ( V2a0_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V3h_2E0,V4t_2E0) )
                    & p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1LFINITE_27_2E0,V4t_2E0)) ) )
             => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1LFINITE_27_2E0,V2a0_2E0)) )
         => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1LFINITE_27_2E0,V0x_2E0)) ) ) ).

tff(thm_2Ellist_2Ellength__rel__def,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Ellist_2Ellist(A_27a),V1x_27_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ellist_2Ellength__rel_2E2(A_27a,V0x_2E0,V1x_27_2E0))
    <=> ! [V2llength__rel_27_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
          ( ! [V3a0_2E0: tyop_2Ellist_2Ellist(A_27a),V4a1_2E0: tyop_2Enum_2Enum] :
              ( ( ( ( V3a0_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) )
                  & ( V4a1_2E0 = c_2Enum_2E0_2E0 ) )
                | ? [V5h_2E0: A_27a,V6n_2E0: tyop_2Enum_2Enum,V7t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
                    ( ( V3a0_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V5h_2E0,V7t_2E0) )
                    & ( V4a1_2E0 = c_2Enum_2ESUC_2E1(V6n_2E0) )
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2llength__rel_27_2E0,V7t_2E0),V6n_2E0)) ) )
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2llength__rel_27_2E0,V3a0_2E0),V4a1_2E0)) )
         => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2llength__rel_27_2E0,V0x_2E0),V1x_27_2E0)) ) ) ).

tff(thm_2Ellist_2ELLENGTH,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V0ll_2E0: tyop_2Ellist_2Ellist(A_27a),V1n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0ll_2E0),V1n_2E0) = c_2Ellist_2Ellength__rel_2E2(A_27a,V0ll_2E0,V1n_2E0) )
     => ! [V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELLENGTH_2E1(A_27a,V0ll_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0),c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Emin_2E_40_2E1(tyop_2Enum_2Enum,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0ll_2E0))),c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum)) ) ) ).

tff(thm_2Ellist_2EtoList,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2EtoList_2E1(A_27a,V0ll_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0),c_2Ellist_2ELTAKE_2E2(A_27a,c_2Eoption_2ETHE_2E1(tyop_2Enum_2Enum,c_2Ellist_2ELLENGTH_2E1(A_27a,V0ll_2E0)),V0ll_2E0),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a))) ) ).

tff(thm_2Ellist_2EfromList__def,axiom,
    ! [A_27a: $tType] :
      ( ( c_2Ellist_2EfromList_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ellist_2ELNIL_2E0(A_27a) )
      & ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2EfromList_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0)) = c_2Ellist_2ELCONS_2E2(A_27a,V0h_2E0,c_2Ellist_2EfromList_2E1(A_27a,V1t_2E0)) ) ) ).

tff(thm_2Ellist_2ELDROP,axiom,
    ! [A_27a: $tType] :
      ( ! [V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELDROP_2E2(A_27a,c_2Enum_2E0_2E0,V0ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) )
      & ! [V1n_2E0: tyop_2Enum_2Enum,V2ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELDROP_2E2(A_27a,c_2Enum_2ESUC_2E1(V1n_2E0),V2ll_2E0) = c_2Eoption_2EOPTION__JOIN_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2EOPTION__MAP_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E1(A_27a,V1n_2E0),c_2Ellist_2ELTL_2E1(A_27a,V2ll_2E0))) ) ) ).

tff(thm_2Ellist_2Eexists__def,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2Eexists_2E2(A_27a,V0x_2E0,V1x_27_2E0))
    <=> ! [V2exists_27_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
          ( ! [V3a0_2E0: tyop_2Ellist_2Ellist(A_27a)] :
              ( ( ? [V4h_2E0: A_27a,V5t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
                    ( ( V3a0_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V4h_2E0,V5t_2E0) )
                    & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0x_2E0,V4h_2E0)) )
                | ? [V6h_2E0: A_27a,V7t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
                    ( ( V3a0_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V6h_2E0,V7t_2E0) )
                    & p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V2exists_27_2E0,V7t_2E0)) ) )
             => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V2exists_27_2E0,V3a0_2E0)) )
         => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V2exists_27_2E0,V1x_27_2E0)) ) ) ).

tff(thm_2Ellist_2Eevery__def,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2Eevery_2E2(A_27a,V0P_2E0,V1ll_2E0))
    <=> ~ p(c_2Ellist_2Eexists_2E2(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),V1ll_2E0)) ) ).

tff(thm_2Ellist_2ELFILTER,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool))] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0P_2E0),V1ll_2E0))
        <=> ~ p(c_2Ellist_2Eexists_2E2(A_27a,V0P_2E0,V1ll_2E0)) )
     => ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELFILTER_2E2(A_27a,V0P_2E0,V1ll_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0P_2E0),V1ll_2E0),c_2Ellist_2ELNIL_2E0(A_27a),c_2Ebool_2ECOND_2E3(tyop_2Ellist_2Ellist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Eoption_2ETHE_2E1(A_27a,c_2Ellist_2ELHD_2E1(A_27a,V1ll_2E0))),c_2Ellist_2ELCONS_2E2(A_27a,c_2Eoption_2ETHE_2E1(A_27a,c_2Ellist_2ELHD_2E1(A_27a,V1ll_2E0)),c_2Ellist_2ELFILTER_2E2(A_27a,V0P_2E0,c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELTL_2E1(A_27a,V1ll_2E0)))),c_2Ellist_2ELFILTER_2E2(A_27a,V0P_2E0,c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELTL_2E1(A_27a,V1ll_2E0))))) ) ) ).

tff(thm_2Ellist_2ELFLATTEN,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Ebool)] :
      ( ! [V0ll_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Ebool,F0_2E0,V0ll_2E0))
        <=> ( c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELHD_2E1(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)) = c_2Ellist_2ELNIL_2E0(A_27a) ) )
     => ! [V0ll_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Ellist_2ELFLATTEN_2E1(A_27a,V0ll_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2Eevery_2E2(tyop_2Ellist_2Ellist(A_27a),c_2Emin_2E_3D_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0(A_27a)),V0ll_2E0),c_2Ellist_2ELNIL_2E0(A_27a),c_2Ebool_2ECOND_2E3(tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Ebool,F0_2E0,V0ll_2E0),c_2Ellist_2ELFLATTEN_2E1(A_27a,c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))),c_2Ellist_2ELCONS_2E2(A_27a,c_2Eoption_2ETHE_2E1(A_27a,c_2Ellist_2ELHD_2E1(A_27a,c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELHD_2E1(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))),c_2Ellist_2ELFLATTEN_2E1(A_27a,c_2Ellist_2ELCONS_2E2(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELTL_2E1(A_27a,c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELHD_2E1(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))),c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))))))) ) ) ).

tff(thm_2Ellist_2ELZIP__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0l1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b),V0l1_2E0,c_2Ellist_2ELNIL_2E0(A_27b))) = c_2Ellist_2ELNIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
      & ! [V1l2_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0(A_27a),V1l2_2E0)) = c_2Ellist_2ELNIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
      & ! [V2h1_2E0: A_27a,V3h2_2E0: A_27b,V4t1_2E0: tyop_2Ellist_2Ellist(A_27a),V5t2_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(A_27a,V2h1_2E0,V4t1_2E0),c_2Ellist_2ELCONS_2E2(A_27b,V3h2_2E0,V5t2_2E0))) = c_2Ellist_2ELCONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2h1_2E0,V3h2_2E0),c_2Ellist_2ELZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b),V4t1_2E0,V5t2_2E0))) ) ) ).

tff(thm_2Ellist_2ELUNZIP__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))))))] :
      ( ! [V0x_2E0: A_27a,V1y_2E0: A_27b,V3ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V4ll2_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))))),F0_2E0,V0x_2E0),V1y_2E0),V3ll1_2E0),V4ll2_2E0) = c_2Epair_2E_2C_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(A_27a,V0x_2E0,V3ll1_2E0),c_2Ellist_2ELCONS_2E2(A_27b,V1y_2E0,V4ll2_2E0)) )
     => ( ( c_2Ellist_2ELUNZIP_2E1(A_27a,A_27b,c_2Ellist_2ELNIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Epair_2E_2C_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0(A_27a),c_2Ellist_2ELNIL_2E0(A_27b)) )
        & ! [V0x_2E0: A_27a,V1y_2E0: A_27b,V2t_2E0: tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ellist_2ELUNZIP_2E1(A_27a,A_27b,c_2Ellist_2ELCONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0),V2t_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Epair_2EUNCURRY_2E1(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))))),F0_2E0,V0x_2E0),V1y_2E0)),c_2Ellist_2ELUNZIP_2E1(A_27a,A_27b,V2t_2E0)) ) ) ) ).

tff(thm_2Ellist_2Elinear__order__to__list__f__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))))] :
      ( ! [V1min_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F1_2E0,V1min_2E0))
        <=> ( V1min_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
     => ( ! [V0lo_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1min_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),F0_2E0,V0lo_2E0),V1min_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F1_2E0,V1min_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a,c_2Eset__relation_2Errestrict_2E2(A_27a,V0lo_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V0lo_2E0),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V0lo_2E0)),V1min_2E0)),c_2Epred__set_2ECHOICE_2E1(A_27a,V1min_2E0)))) )
       => ! [V0lo_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ellist_2Elinear__order__to__list__f_2E1(A_27a,V0lo_2E0) = c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),F0_2E0,V0lo_2E0),c_2Eset__relation_2Eminimal__elements_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V0lo_2E0),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V0lo_2E0)),V0lo_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELPREFIX__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F3_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] :
      ( ! [V0l1_2E0: tyop_2Ellist_2Ellist(A_27a),V1l2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0l1_2E0),V1l2_2E0))
        <=> ( V0l1_2E0 = V1l2_2E0 ) )
     => ( ! [V2xs_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F2_2E0,V2xs_2E0),V1l2_2E0))
          <=> ( c_2Ellist_2ELTAKE_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V2xs_2E0),V1l2_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V2xs_2E0) ) )
       => ( ! [V2xs_2E0: tyop_2Elist_2Elist(A_27a),V3ys_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F3_2E0,V2xs_2E0),V3ys_2E0) = c_2Elist_2EisPREFIX_2E2(A_27a,V2xs_2E0,V3ys_2E0) )
         => ( ! [V1l2_2E0: tyop_2Ellist_2Ellist(A_27a),V2xs_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F1_2E0,V1l2_2E0),V2xs_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Ellist_2EtoList_2E1(A_27a,V1l2_2E0),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F2_2E0,V2xs_2E0),V1l2_2E0),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F3_2E0,V2xs_2E0)) )
           => ! [V0l1_2E0: tyop_2Ellist_2Ellist(A_27a),V1l2_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELPREFIX_2E2(A_27a,V0l1_2E0,V1l2_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Ellist_2EtoList_2E1(A_27a,V0l1_2E0),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0l1_2E0),V1l2_2E0),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F1_2E0,V1l2_2E0)) ) ) ) ) ) ).

tff(thm_2Ellist_2ELGENLIST__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))] :
      ( ! [V3lim_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),F1_2E0,V3lim_2E0),V2f_2E0),V4n_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2E_3C_2E2(V4n_2E0,V3lim_2E0),c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,c_2Earithmetic_2E_2B_2E2(V4n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),app_2E2(tyop_2Enum_2Enum,A_27a,V2f_2E0,V4n_2E0))),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),F0_2E0,V0f_2E0),V1n_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,c_2Earithmetic_2E_2B_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),app_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,V1n_2E0))) )
       => ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Ellist_2ELGENLIST_2E2(A_27a,V0f_2E0,c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum)) = c_2Ellist_2ELUNFOLD_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),F0_2E0,V0f_2E0),c_2Enum_2E0_2E0) )
          & ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3lim_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELGENLIST_2E2(A_27a,V2f_2E0,c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,V3lim_2E0)) = c_2Ellist_2ELUNFOLD_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),F1_2E0,V3lim_2E0),V2f_2E0),c_2Enum_2E0_2E0) ) ) ) ) ).

tff(thm_2Ellist_2ELREPEAT__def,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0,V0l_2E0),V1n_2E0) = c_2Elist_2EEL_2E2(A_27a,c_2Earithmetic_2EMOD_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)),V0l_2E0) )
     => ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELREPEAT_2E1(A_27a,V0l_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Ellist_2Ellist(A_27a),c_2Elist_2ENULL_2E1(A_27a,V0l_2E0),c_2Ellist_2ELNIL_2E0(A_27a),c_2Ellist_2ELGENLIST_2E2(A_27a,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0,V0l_2E0),c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum))) ) ) ).

tff(thm_2Ellist_2Elrep__ok__rules,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))))] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),F0_2E0,V0n_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
     => ( ! [V3n_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V3n_2E0))
          <=> ( V3n_2E0 = c_2Enum_2E0_2E0 ) )
       => ( ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V3n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F1_2E0,V1h_2E0),V2t_2E0),V3n_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V3n_2E0),c_2Eoption_2ESOME_2E1(A_27a,V1h_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V2t_2E0,c_2Earithmetic_2E_2D_2E2(V3n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
         => ( p(c_2Ellist_2Elrep__ok_2E1(A_27a,F0_2E0))
            & ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] :
                ( p(c_2Ellist_2Elrep__ok_2E1(A_27a,V2t_2E0))
               => p(c_2Ellist_2Elrep__ok_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F1_2E0,V1h_2E0),V2t_2E0))) ) ) ) ) ) ).

tff(thm_2Ellist_2Elrep__ok__coind,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V5x_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V5x_2E0))
        <=> ( V5x_2E0 = c_2Enum_2E0_2E0 ) )
     => ! [V0lrep__ok_27_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)] :
          ( ! [V1a0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] :
              ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool,V0lrep__ok_27_2E0,V1a0_2E0))
             => ( ! [V2x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V1a0_2E0,V2x_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
                | ? [V3h_2E0: A_27a,V4t_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] :
                    ( ! [V5x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V1a0_2E0,V5x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V5x_2E0),c_2Eoption_2ESOME_2E1(A_27a,V3h_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V4t_2E0,c_2Earithmetic_2E_2D_2E2(V5x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
                    & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool,V0lrep__ok_27_2E0,V4t_2E0)) ) ) )
         => ! [V6a0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] :
              ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool,V0lrep__ok_27_2E0,V6a0_2E0))
             => p(c_2Ellist_2Elrep__ok_2E1(A_27a,V6a0_2E0)) ) ) ) ).

tff(thm_2Ellist_2Elrep__ok__cases,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V4x_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V4x_2E0))
        <=> ( V4x_2E0 = c_2Enum_2E0_2E0 ) )
     => ! [V0a0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] :
          ( p(c_2Ellist_2Elrep__ok_2E1(A_27a,V0a0_2E0))
        <=> ( ! [V1x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0a0_2E0,V1x_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
            | ? [V2h_2E0: A_27a,V3t_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] :
                ( ! [V4x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0a0_2E0,V4x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V4x_2E0),c_2Eoption_2ESOME_2E1(A_27a,V2h_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V3t_2E0,c_2Earithmetic_2E_2D_2E2(V4x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
                & p(c_2Ellist_2Elrep__ok_2E1(A_27a,V3t_2E0)) ) ) ) ) ).

tff(thm_2Ellist_2Elrep__ok__alt,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))] :
      ( p(c_2Ellist_2Elrep__ok_2E1(A_27a,V0f_2E0))
    <=> ! [V1n_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eoption_2EIS__SOME_2E1(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0f_2E0,c_2Enum_2ESUC_2E1(V1n_2E0))))
         => p(c_2Eoption_2EIS__SOME_2E1(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V0f_2E0,V1n_2E0))) ) ) ).

tff(thm_2Ellist_2Elrep__ok__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),V2n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V1f_2E0),V0g_2E0),V2n_2E0) = c_2Eoption_2EOPTION__MAP_2E2(A_27b,A_27a,V1f_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b),V0g_2E0,V2n_2E0)) )
     => ! [V0g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Ellist_2Elrep__ok_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V1f_2E0),V0g_2E0)) = c_2Ellist_2Elrep__ok_2E1(A_27b,V0g_2E0) ) ) ).

tff(thm_2Ellist_2Elrep__ok__FUNPOW__BIND,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))))] :
      ( ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),V3m_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),F1_2E0,V0g_2E0),V3m_2E0) = c_2Eoption_2EOPTION__BIND_2E2(A_27a,A_27a,V3m_2E0,V0g_2E0) )
     => ( ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),V1fz_2E0: tyop_2Eoption_2Eoption(A_27a),V2n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V0g_2E0),V1fz_2E0),V2n_2E0) = c_2Earithmetic_2EFUNPOW_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),F1_2E0,V0g_2E0),V2n_2E0,V1fz_2E0) )
       => ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),V1fz_2E0: tyop_2Eoption_2Eoption(A_27a)] : p(c_2Ellist_2Elrep__ok_2E1(A_27a,app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V0g_2E0),V1fz_2E0))) ) ) ).

tff(thm_2Ellist_2Ellist__rep__LCONS,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V2x_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2x_2E0))
        <=> ( V2x_2E0 = c_2Enum_2E0_2E0 ) )
     => ! [V0t_2E0: tyop_2Ellist_2Ellist(A_27a),V1h_2E0: A_27a,V2x_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2Ellist__rep_2E2(A_27a,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V0t_2E0),V2x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2x_2E0),c_2Eoption_2ESOME_2E1(A_27a,V1h_2E0),c_2Ellist_2Ellist__rep_2E2(A_27a,V0t_2E0,c_2Earithmetic_2E_2D_2E2(V2x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) ).

tff(thm_2Ellist_2Ellist__rep__LNIL,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2Ellist__rep_2E2(A_27a,c_2Ellist_2ELNIL_2E0(A_27a),V0x_2E0) = c_2Eoption_2ENONE_2E0(A_27a) ) ).

tff(thm_2Ellist_2ELTL__HD__LNIL,axiom,
    ! [A_27a: $tType] : ( c_2Ellist_2ELTL__HD_2E1(A_27a,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)) ) ).

tff(thm_2Ellist_2ELTL__HD__LCONS,axiom,
    ! [A_27a: $tType,V0t_2E0: tyop_2Ellist_2Ellist(A_27a),V1h_2E0: A_27a] : ( c_2Ellist_2ELTL__HD_2E1(A_27a,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V0t_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),c_2Epair_2E_2C_2E2(tyop_2Ellist_2Ellist(A_27a),A_27a,V0t_2E0,V1h_2E0)) ) ).

tff(thm_2Ellist_2ELTL__HD__HD,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELHD_2E1(A_27a,V0ll_2E0) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),A_27a,c_2Epair_2ESND_2E0(tyop_2Ellist_2Ellist(A_27a),A_27a),c_2Ellist_2ELTL__HD_2E1(A_27a,V0ll_2E0)) ) ).

tff(thm_2Ellist_2ELTL__HD__TL,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTL_2E1(A_27a,V0ll_2E0) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a),c_2Epair_2EFST_2E0(tyop_2Ellist_2Ellist(A_27a),A_27a),c_2Ellist_2ELTL__HD_2E1(A_27a,V0ll_2E0)) ) ).

tff(thm_2Ellist_2ELHD__LCONS,axiom,
    ! [A_27a: $tType,V0t_2E0: tyop_2Ellist_2Ellist(A_27a),V1h_2E0: A_27a] : ( c_2Ellist_2ELHD_2E1(A_27a,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V0t_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,V1h_2E0) ) ).

tff(thm_2Ellist_2ELTL__LCONS,axiom,
    ! [A_27a: $tType,V0t_2E0: tyop_2Ellist_2Ellist(A_27a),V1h_2E0: A_27a] : ( c_2Ellist_2ELTL_2E1(A_27a,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V0t_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),V0t_2E0) ) ).

tff(thm_2Ellist_2ELHDTL__CONS__THM,axiom,
    ! [A_27a: $tType,V0h_2E0: A_27a,V1t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELHD_2E1(A_27a,c_2Ellist_2ELCONS_2E2(A_27a,V0h_2E0,V1t_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,V0h_2E0) )
      & ( c_2Ellist_2ELTL_2E1(A_27a,c_2Ellist_2ELCONS_2E2(A_27a,V0h_2E0,V1t_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),V1t_2E0) ) ) ).

tff(thm_2Ellist_2Ellist__CASES,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( V0l_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) )
      | ? [V1h_2E0: A_27a,V2t_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( V0l_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V2t_2E0) ) ) ).

tff(thm_2Ellist_2ELTL__HD__11,axiom,
    ! [A_27a: $tType,V0ll2_2E0: tyop_2Ellist_2Ellist(A_27a),V1ll1_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELTL__HD_2E1(A_27a,V1ll1_2E0) = c_2Ellist_2ELTL__HD_2E1(A_27a,V0ll2_2E0) )
     => ( V1ll1_2E0 = V0ll2_2E0 ) ) ).

tff(thm_2Ellist_2ELHD__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ( c_2Ellist_2ELHD_2E1(A_27a,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(A_27a) )
      & ! [V0h_2E0: A_27b,V1t_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELHD_2E1(A_27b,c_2Ellist_2ELCONS_2E2(A_27b,V0h_2E0,V1t_2E0)) = c_2Eoption_2ESOME_2E1(A_27b,V0h_2E0) ) ) ).

tff(thm_2Ellist_2ELTL__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ( c_2Ellist_2ELTL_2E1(A_27a,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(tyop_2Ellist_2Ellist(A_27a)) )
      & ! [V0h_2E0: A_27b,V1t_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELTL_2E1(A_27b,c_2Ellist_2ELCONS_2E2(A_27b,V0h_2E0,V1t_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27b),V1t_2E0) ) ) ).

tff(thm_2Ellist_2ELCONS__NOT__NIL,axiom,
    ! [A_27a: $tType,V0h_2E0: A_27a,V1t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELCONS_2E2(A_27a,V0h_2E0,V1t_2E0) != c_2Ellist_2ELNIL_2E0(A_27a) )
      & ( c_2Ellist_2ELNIL_2E0(A_27a) != c_2Ellist_2ELCONS_2E2(A_27a,V0h_2E0,V1t_2E0) ) ) ).

tff(thm_2Ellist_2ELCONS__11,axiom,
    ! [A_27a: $tType,V0h1_2E0: A_27a,V1t1_2E0: tyop_2Ellist_2Ellist(A_27a),V2h2_2E0: A_27a,V3t2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELCONS_2E2(A_27a,V0h1_2E0,V1t1_2E0) = c_2Ellist_2ELCONS_2E2(A_27a,V2h2_2E0,V3t2_2E0) )
    <=> ( ( V0h1_2E0 = V2h2_2E0 )
        & ( V1t1_2E0 = V3t2_2E0 ) ) ) ).

tff(thm_2Ellist_2ELTL__HD__iff,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Ellist_2Ellist(A_27a),V1t_2E0: tyop_2Ellist_2Ellist(A_27a),V2h_2E0: A_27a] :
      ( ( ( c_2Ellist_2ELTL__HD_2E1(A_27a,V0x_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),c_2Epair_2E_2C_2E2(tyop_2Ellist_2Ellist(A_27a),A_27a,V1t_2E0,V2h_2E0)) )
      <=> ( V0x_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V2h_2E0,V1t_2E0) ) )
      & ( ( c_2Ellist_2ELTL__HD_2E1(A_27a,V0x_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)) )
      <=> ( V0x_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) ) ) ).

tff(thm_2Ellist_2ELHD__EQ__NONE,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( ( c_2Ellist_2ELHD_2E1(A_27a,V0ll_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
      <=> ( V0ll_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) )
      & ( ( c_2Eoption_2ENONE_2E0(A_27a) = c_2Ellist_2ELHD_2E1(A_27a,V0ll_2E0) )
      <=> ( V0ll_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) ) ) ).

tff(thm_2Ellist_2ELTL__EQ__NONE,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( ( c_2Ellist_2ELTL_2E1(A_27a,V0ll_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Ellist_2Ellist(A_27a)) )
      <=> ( V0ll_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) )
      & ( ( c_2Eoption_2ENONE_2E0(tyop_2Ellist_2Ellist(A_27a)) = c_2Ellist_2ELTL_2E1(A_27a,V0ll_2E0) )
      <=> ( V0ll_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) ) ) ).

tff(thm_2Ellist_2ELHDTL__EQ__SOME,axiom,
    ! [A_27a: $tType,V0h_2E0: A_27a,V1t_2E0: tyop_2Ellist_2Ellist(A_27a),V2ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( V2ll_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V0h_2E0,V1t_2E0) )
    <=> ( ( c_2Ellist_2ELHD_2E1(A_27a,V2ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V0h_2E0) )
        & ( c_2Ellist_2ELTL_2E1(A_27a,V2ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),V1t_2E0) ) ) ) ).

tff(thm_2Ellist_2ELNTH__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELNTH_2E2(A_27a,V0n_2E0,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(A_27a) )
      & ! [V1h_2E0: A_27b,V2t_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELNTH_2E2(A_27b,c_2Enum_2E0_2E0,c_2Ellist_2ELCONS_2E2(A_27b,V1h_2E0,V2t_2E0)) = c_2Eoption_2ESOME_2E1(A_27b,V1h_2E0) )
      & ! [V3n_2E0: tyop_2Enum_2Enum,V4h_2E0: A_27c,V5t_2E0: tyop_2Ellist_2Ellist(A_27c)] : ( c_2Ellist_2ELNTH_2E2(A_27c,c_2Enum_2ESUC_2E1(V3n_2E0),c_2Ellist_2ELCONS_2E2(A_27c,V4h_2E0,V5t_2E0)) = c_2Ellist_2ELNTH_2E2(A_27c,V3n_2E0,V5t_2E0) ) ) ).

tff(thm_2Ellist_2ELNTH__rep,axiom,
    ! [A_27a: $tType,V0i_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELNTH_2E2(A_27a,V0i_2E0,V1ll_2E0) = c_2Ellist_2Ellist__rep_2E2(A_27a,V1ll_2E0,V0i_2E0) ) ).

tff(thm_2Ellist_2ELNTH__EQ,axiom,
    ! [A_27a: $tType,V0ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( V0ll1_2E0 = V1ll2_2E0 )
    <=> ! [V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELNTH_2E2(A_27a,V2n_2E0,V0ll1_2E0) = c_2Ellist_2ELNTH_2E2(A_27a,V2n_2E0,V1ll2_2E0) ) ) ).

tff(thm_2Ellist_2ELUNFOLD,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V3v1_2E0: A_27a,V4v2_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Ellist_2Ellist(A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),F1_2E0,V0f_2E0),V3v1_2E0),V4v2_2E0) = c_2Ellist_2ELCONS_2E2(A_27b,V4v2_2E0,c_2Ellist_2ELUNFOLD_2E2(A_27b,A_27a,V0f_2E0,V3v1_2E0)) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V2v_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),F0_2E0,V0f_2E0),V2v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Ellist_2Ellist(A_27b),A_27a,A_27b,V2v_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),F1_2E0,V0f_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V1x_2E0: A_27a] : ( c_2Ellist_2ELUNFOLD_2E2(A_27b,A_27a,V0f_2E0,V1x_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V0f_2E0,V1x_2E0),c_2Ellist_2ELNIL_2E0(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),F0_2E0,V0f_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELUNFOLD__UNIQUE,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)))] :
      ( ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V4v1_2E0: A_27a,V5v2_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Ellist_2Ellist(A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),F1_2E0,V1g_2E0),V4v1_2E0),V5v2_2E0) = c_2Ellist_2ELCONS_2E2(A_27b,V5v2_2E0,app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V4v1_2E0)) )
     => ( ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V3v_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),F0_2E0,V1g_2E0),V3v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Ellist_2Ellist(A_27b),A_27a,A_27b,V3v_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),F1_2E0,V1g_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b))] :
            ( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V2x_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V0f_2E0,V2x_2E0),c_2Ellist_2ELNIL_2E0(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),F0_2E0,V1g_2E0)) )
           => ! [V6y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V6y_2E0) = c_2Ellist_2ELUNFOLD_2E2(A_27b,A_27a,V0f_2E0,V6y_2E0) ) ) ) ) ).

tff(thm_2Ellist_2ELUNFOLD__LTL__HD,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELUNFOLD_2E2(A_27a,tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELTL__HD_2E0(A_27a),V0ll_2E0) = V0ll_2E0 ) ).

tff(thm_2Ellist_2ELTL__HD__LUNFOLD,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Ellist_2ELTL__HD_2E1(A_27a,c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V1f_2E0,V0x_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),c_2Epair_2E_23_23_2E2(A_27b,A_27a,tyop_2Ellist_2Ellist(A_27a),A_27a,c_2Ellist_2ELUNFOLD_2E1(A_27a,A_27b,V1f_2E0),c_2Ecombin_2EI_2E0(A_27a)),app_2E2(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V1f_2E0,V0x_2E0)) ) ).

tff(thm_2Ellist_2ELNTH__LUNFOLD,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))))] :
      ( ! [V1n_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V4tx_2E0: A_27b,V5hx_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),F1_2E0,V1n_2E0),V2f_2E0),V4tx_2E0),V5hx_2E0) = c_2Ellist_2ELNTH_2E2(A_27a,V1n_2E0,c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V2f_2E0,V4tx_2E0)) )
     => ( ! [V1n_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V3v_2E0: tyop_2Epair_2Eprod(A_27b,A_27a)] : ( app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V1n_2E0),V2f_2E0),V3v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(A_27a),A_27b,A_27a,V3v_2E0,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),F1_2E0,V1n_2E0),V2f_2E0)) )
       => ! [V0x_2E0: A_27b,V1n_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] :
            ( ( c_2Ellist_2ELNTH_2E2(A_27a,c_2Enum_2E0_2E0,c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V2f_2E0,V0x_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,c_2Epair_2ESND_2E0(A_27b,A_27a),app_2E2(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V2f_2E0,V0x_2E0)) )
            & ( c_2Ellist_2ELNTH_2E2(A_27a,c_2Enum_2ESUC_2E1(V1n_2E0),c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V2f_2E0,V0x_2E0)) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V2f_2E0,V0x_2E0),c_2Eoption_2ENONE_2E0(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V1n_2E0),V2f_2E0)) ) ) ) ) ).

tff(thm_2Ellist_2ELNTH__LUNFOLD__compute,axiom,
    ! [A_27a: $tType,A_27b: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))))] :
      ( ! [V2n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V4tx_2E0: A_27b,V5hx_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),F3_2E0,V2n_2E0),V1f_2E0),V4tx_2E0),V5hx_2E0) = c_2Ellist_2ELNTH_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V1f_2E0,V4tx_2E0)) )
     => ( ! [V2n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V3v_2E0: tyop_2Epair_2Eprod(A_27b,A_27a)] : ( app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V2n_2E0),V1f_2E0),V3v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(A_27a),A_27b,A_27a,V3v_2E0,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),F3_2E0,V2n_2E0),V1f_2E0)) )
       => ( ! [V6n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V8tx_2E0: A_27b,V9hx_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),F2_2E0,V6n_2E0),V1f_2E0),V8tx_2E0),V9hx_2E0) = c_2Ellist_2ELNTH_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V6n_2E0)),c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V1f_2E0,V8tx_2E0)) )
         => ( ! [V6n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V7v_2E0: tyop_2Epair_2Eprod(A_27b,A_27a)] : ( app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))),F1_2E0,V6n_2E0),V1f_2E0),V7v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(A_27a),A_27b,A_27a,V7v_2E0,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),F2_2E0,V6n_2E0),V1f_2E0)) )
           => ! [V0x_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] :
                ( ( c_2Ellist_2ELNTH_2E2(A_27a,c_2Enum_2E0_2E0,c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V1f_2E0,V0x_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,c_2Epair_2ESND_2E0(A_27b,A_27a),app_2E2(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V1f_2E0,V0x_2E0)) )
                & ! [V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELNTH_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2n_2E0)),c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V1f_2E0,V0x_2E0)) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V1f_2E0,V0x_2E0),c_2Eoption_2ENONE_2E0(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V2n_2E0),V1f_2E0)) )
                & ! [V6n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELNTH_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V6n_2E0)),c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V1f_2E0,V0x_2E0)) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V1f_2E0,V0x_2E0),c_2Eoption_2ENONE_2E0(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))),F1_2E0,V6n_2E0),V1f_2E0)) ) ) ) ) ) ) ).

tff(thm_2Ellist_2ELHD__LUNFOLD,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Ellist_2ELHD_2E1(A_27a,c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V1f_2E0,V0x_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,c_2Epair_2ESND_2E0(A_27b,A_27a),app_2E2(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V1f_2E0,V0x_2E0)) ) ).

tff(thm_2Ellist_2ELTL__LUNFOLD,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Ellist_2ELTL_2E1(A_27a,c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V1f_2E0,V0x_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a),c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a),A_27b,c_2Ellist_2ELUNFOLD_2E1(A_27a,A_27b,V1f_2E0),c_2Epair_2EFST_2E0(A_27b,A_27a)),app_2E2(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V1f_2E0,V0x_2E0)) ) ).

tff(thm_2Ellist_2Ellist__Axiom__1,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)))] :
      ( ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V4a_2E0: A_27a,V5b_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Ellist_2Ellist(A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),F1_2E0,V1g_2E0),V4a_2E0),V5b_2E0) = c_2Ellist_2ELCONS_2E2(A_27b,V5b_2E0,app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V4a_2E0)) )
     => ( ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V3v_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),F0_2E0,V1g_2E0),V3v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Ellist_2Ellist(A_27b),A_27a,A_27b,V3v_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),F1_2E0,V1g_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))] :
          ? [V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b))] :
          ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V2x_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V0f_2E0,V2x_2E0),c_2Ellist_2ELNIL_2E0(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),F0_2E0,V1g_2E0)) ) ) ) ).

tff(thm_2Ellist_2Ellist__Axiom__1ue,axiom,
    ! [A_27a: $tType,A_27b: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool))] :
      ( ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V4a_2E0: A_27a,V5b_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Ellist_2Ellist(A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),F2_2E0,V1g_2E0),V4a_2E0),V5b_2E0) = c_2Ellist_2ELCONS_2E2(A_27b,V5b_2E0,app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V4a_2E0)) )
     => ( ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V3v_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),F1_2E0,V1g_2E0),V3v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Ellist_2Ellist(A_27b),A_27a,A_27b,V3v_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),F2_2E0,V1g_2E0)) )
       => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b))] :
              ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool),F0_2E0,V0f_2E0),V1g_2E0))
            <=> ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V2x_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V0f_2E0,V2x_2E0),c_2Ellist_2ELNIL_2E0(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),F1_2E0,V1g_2E0)) ) )
         => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))] : p(c_2Ebool_2E_3F_21_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool),F0_2E0,V0f_2E0))) ) ) ) ).

tff(thm_2Ellist_2Ellist__ue__Axiom,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b))] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool),F0_2E0,V0f_2E0),V1g_2E0))
        <=> ( ! [V2x_2E0: A_27a] : ( c_2Ellist_2ELHD_2E1(A_27b,app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V2x_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V0f_2E0,V2x_2E0)) )
            & ! [V3x_2E0: A_27a] : ( c_2Ellist_2ELTL_2E1(A_27b,app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V3x_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),A_27a,V1g_2E0,c_2Epair_2EFST_2E0(A_27a,A_27b)),app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V0f_2E0,V3x_2E0)) ) ) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))] : p(c_2Ebool_2E_3F_21_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool),F0_2E0,V0f_2E0))) ) ).

tff(thm_2Ellist_2Ellist__Axiom,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))] :
    ? [V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b))] :
      ( ! [V2x_2E0: A_27a] : ( c_2Ellist_2ELHD_2E1(A_27b,app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V2x_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V0f_2E0,V2x_2E0)) )
      & ! [V3x_2E0: A_27a] : ( c_2Ellist_2ELTL_2E1(A_27b,app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V3x_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),A_27a,V1g_2E0,c_2Epair_2EFST_2E0(A_27a,A_27b)),app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V0f_2E0,V3x_2E0)) ) ) ).

tff(thm_2Ellist_2ELUNFOLD__BISIMULATION,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V1f2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V2x1_2E0: A_27a,V3x2_2E0: A_27c] :
      ( ( c_2Ellist_2ELUNFOLD_2E2(A_27b,A_27a,V0f1_2E0,V2x1_2E0) = c_2Ellist_2ELUNFOLD_2E2(A_27b,A_27c,V1f2_2E0,V3x2_2E0) )
    <=> ? [V4R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))] :
          ( p(app_2E2(A_27c,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4R_2E0,V2x1_2E0),V3x2_2E0))
          & ! [V5y1_2E0: A_27a,V6y2_2E0: A_27c] :
              ( p(app_2E2(A_27c,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4R_2E0,V5y1_2E0),V6y2_2E0))
             => ( ( ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V0f1_2E0,V5y1_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
                  & ( app_2E2(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),V1f2_2E0,V6y2_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(A_27c,A_27b)) ) )
                | ? [V7h_2E0: A_27b,V8t1_2E0: A_27a,V9t2_2E0: A_27c] :
                    ( ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V0f1_2E0,V5y1_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V8t1_2E0,V7h_2E0)) )
                    & ( app_2E2(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),V1f2_2E0,V6y2_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(A_27c,A_27b,V9t2_2E0,V7h_2E0)) )
                    & p(app_2E2(A_27c,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4R_2E0,V8t1_2E0),V9t2_2E0)) ) ) ) ) ) ).

tff(thm_2Ellist_2ELLIST__BISIMULATION0,axiom,
    ! [A_27a: $tType,V0ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( V0ll1_2E0 = V1ll2_2E0 )
    <=> ? [V2R_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool))] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V2R_2E0,V0ll1_2E0),V1ll2_2E0))
          & ! [V3ll3_2E0: tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0: tyop_2Ellist_2Ellist(A_27a)] :
              ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V2R_2E0,V3ll3_2E0),V4ll4_2E0))
             => ( ( ( V3ll3_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) )
                  & ( V4ll4_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) )
                | ? [V5h_2E0: A_27a,V6t1_2E0: tyop_2Ellist_2Ellist(A_27a),V7t2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
                    ( ( V3ll3_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V5h_2E0,V6t1_2E0) )
                    & ( V4ll4_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V5h_2E0,V7t2_2E0) )
                    & p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V2R_2E0,V6t1_2E0),V7t2_2E0)) ) ) ) ) ) ).

tff(thm_2Ellist_2ELLIST__BISIMULATION,axiom,
    ! [A_27a: $tType,V0ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( V0ll1_2E0 = V1ll2_2E0 )
    <=> ? [V2R_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool))] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V2R_2E0,V0ll1_2E0),V1ll2_2E0))
          & ! [V3ll3_2E0: tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0: tyop_2Ellist_2Ellist(A_27a)] :
              ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V2R_2E0,V3ll3_2E0),V4ll4_2E0))
             => ( ( ( V3ll3_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) )
                  & ( V4ll4_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) )
                | ( ( c_2Ellist_2ELHD_2E1(A_27a,V3ll3_2E0) = c_2Ellist_2ELHD_2E1(A_27a,V4ll4_2E0) )
                  & p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V2R_2E0,c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELTL_2E1(A_27a,V3ll3_2E0))),c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELTL_2E1(A_27a,V4ll4_2E0)))) ) ) ) ) ) ).

tff(thm_2Ellist_2ELLIST__STRONG__BISIMULATION,axiom,
    ! [A_27a: $tType,V0ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( V0ll1_2E0 = V1ll2_2E0 )
    <=> ? [V2R_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool))] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V2R_2E0,V0ll1_2E0),V1ll2_2E0))
          & ! [V3ll3_2E0: tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0: tyop_2Ellist_2Ellist(A_27a)] :
              ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V2R_2E0,V3ll3_2E0),V4ll4_2E0))
             => ( ( V3ll3_2E0 = V4ll4_2E0 )
                | ? [V5h_2E0: A_27a,V6t1_2E0: tyop_2Ellist_2Ellist(A_27a),V7t2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
                    ( ( V3ll3_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V5h_2E0,V6t1_2E0) )
                    & ( V4ll4_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V5h_2E0,V7t2_2E0) )
                    & p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V2R_2E0,V6t1_2E0),V7t2_2E0)) ) ) ) ) ) ).

tff(thm_2Ellist_2ELTAKE__LUNFOLD,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))))] :
      ( ! [V1n_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V4tx_2E0: A_27b,V5hx_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),F1_2E0,V1n_2E0),V2f_2E0),V4tx_2E0),V5hx_2E0) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E1(A_27a,V5hx_2E0),c_2Ellist_2ELTAKE_2E2(A_27a,V1n_2E0,c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V2f_2E0,V4tx_2E0))) )
     => ( ! [V1n_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V3v_2E0: tyop_2Epair_2Eprod(A_27b,A_27a)] : ( app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F0_2E0,V1n_2E0),V2f_2E0),V3v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),A_27b,A_27a,V3v_2E0,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),F1_2E0,V1n_2E0),V2f_2E0)) )
       => ! [V0x_2E0: A_27b,V1n_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] :
            ( ( c_2Ellist_2ELTAKE_2E2(A_27a,c_2Enum_2E0_2E0,c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V2f_2E0,V0x_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a)) )
            & ( c_2Ellist_2ELTAKE_2E2(A_27a,c_2Enum_2ESUC_2E1(V1n_2E0),c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V2f_2E0,V0x_2E0)) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V2f_2E0,V0x_2E0),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F0_2E0,V1n_2E0),V2f_2E0)) ) ) ) ) ).

tff(thm_2Ellist_2ELTAKE__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
      ( ! [V0l_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTAKE_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a)) )
      & ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELTAKE_2E2(A_27b,c_2Enum_2ESUC_2E1(V1n_2E0),c_2Ellist_2ELNIL_2E0(A_27b)) = c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27b)) )
      & ! [V2n_2E0: tyop_2Enum_2Enum,V3h_2E0: A_27c,V4t_2E0: tyop_2Ellist_2Ellist(A_27c)] : ( c_2Ellist_2ELTAKE_2E2(A_27c,c_2Enum_2ESUC_2E1(V2n_2E0),c_2Ellist_2ELCONS_2E2(A_27c,V3h_2E0,V4t_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E1(A_27c,V3h_2E0),c_2Ellist_2ELTAKE_2E2(A_27c,V2n_2E0,V4t_2E0)) ) ) ).

tff(thm_2Ellist_2ELTAKE__SNOC__LNTH,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))))] :
      ( ! [V2l_2E0: tyop_2Elist_2Elist(A_27a),V3e_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),F1_2E0,V2l_2E0),V3e_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(A_27a,V2l_2E0,c_2Elist_2ECONS_2E2(A_27a,V3e_2E0,c_2Elist_2ENIL_2E0(A_27a)))) )
     => ( ! [V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a),V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F0_2E0,V0n_2E0),V1ll_2E0),V2l_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELNTH_2E2(A_27a,V0n_2E0,V1ll_2E0),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),F1_2E0,V2l_2E0)) )
       => ! [V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTAKE_2E2(A_27a,c_2Enum_2ESUC_2E1(V0n_2E0),V1ll_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V1ll_2E0),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F0_2E0,V0n_2E0),V1ll_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELTAKE__EQ__NONE__LNTH,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V1ll_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)) )
     => ( c_2Ellist_2ELNTH_2E2(A_27a,V0n_2E0,V1ll_2E0) = c_2Eoption_2ENONE_2E0(A_27a) ) ) ).

tff(thm_2Ellist_2ELTAKE__NIL__EQ__SOME,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1m_2E0: tyop_2Enum_2Enum] :
      ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V1m_2E0,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V0l_2E0) )
    <=> ( ( V1m_2E0 = c_2Enum_2E0_2E0 )
        & ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ) ).

tff(thm_2Ellist_2ELTAKE__NIL__EQ__NONE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum] :
      ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V0m_2E0,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)) )
    <=> p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0m_2E0)) ) ).

tff(thm_2Ellist_2ELTAKE__EQ,axiom,
    ! [A_27a: $tType,V0ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( V0ll1_2E0 = V1ll2_2E0 )
    <=> ! [V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELTAKE_2E2(A_27a,V2n_2E0,V0ll1_2E0) = c_2Ellist_2ELTAKE_2E2(A_27a,V2n_2E0,V1ll2_2E0) ) ) ).

tff(thm_2Ellist_2ELTAKE__CONS__EQ__NONE,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1h_2E0: A_27a,V2t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V0m_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V2t_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)) )
    <=> ? [V3n_2E0: tyop_2Enum_2Enum] :
          ( ( V0m_2E0 = c_2Enum_2ESUC_2E1(V3n_2E0) )
          & ( c_2Ellist_2ELTAKE_2E2(A_27a,V3n_2E0,V2t_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)) ) ) ) ).

tff(thm_2Ellist_2ELTAKE__CONS__EQ__SOME,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1h_2E0: A_27a,V2t_2E0: tyop_2Ellist_2Ellist(A_27a),V3l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V0m_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V2t_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V3l_2E0) )
    <=> ( ( ( V0m_2E0 = c_2Enum_2E0_2E0 )
          & ( V3l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
        | ? [V4n_2E0: tyop_2Enum_2Enum,V5l_27_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( ( V0m_2E0 = c_2Enum_2ESUC_2E1(V4n_2E0) )
            & ( c_2Ellist_2ELTAKE_2E2(A_27a,V4n_2E0,V2t_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V5l_27_2E0) )
            & ( V3l_2E0 = c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V5l_27_2E0) ) ) ) ) ).

tff(thm_2Ellist_2ELTAKE__EQ__SOME__CONS,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Ellist_2Ellist(A_27a),V2x_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V2x_2E0) )
     => ! [V3h_2E0: A_27a] :
        ? [V4y_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V3h_2E0,V1l_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V4y_2E0) ) ) ).

tff(thm_2Ellist_2ELMAP__APPEND,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V2ll2_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Ellist_2ELAPPEND_2E2(A_27a,V1ll1_2E0,V2ll2_2E0)) = c_2Ellist_2ELAPPEND_2E2(A_27b,c_2Ellist_2ELMAP_2E2(A_27a,A_27b,V0f_2E0,V1ll1_2E0),c_2Ellist_2ELMAP_2E2(A_27a,A_27b,V0f_2E0,V2ll2_2E0)) ) ).

tff(thm_2Ellist_2ELAPPEND__EQ__LNIL,axiom,
    ! [A_27a: $tType,V0l2_2E0: tyop_2Ellist_2Ellist(A_27a),V1l1_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELAPPEND_2E2(A_27a,V1l1_2E0,V0l2_2E0) = c_2Ellist_2ELNIL_2E0(A_27a) )
    <=> ( ( V1l1_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) )
        & ( V0l2_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) ) ) ).

tff(thm_2Ellist_2ELAPPEND__ASSOC,axiom,
    ! [A_27a: $tType,V0ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0: tyop_2Ellist_2Ellist(A_27a),V2ll3_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELAPPEND_2E2(A_27a,c_2Ellist_2ELAPPEND_2E2(A_27a,V0ll1_2E0,V1ll2_2E0),V2ll3_2E0) = c_2Ellist_2ELAPPEND_2E2(A_27a,V0ll1_2E0,c_2Ellist_2ELAPPEND_2E2(A_27a,V1ll2_2E0,V2ll3_2E0)) ) ).

tff(thm_2Ellist_2ELMAP__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V2ll_2E0: tyop_2Ellist_2Ellist(A_27c)] : ( c_2Ellist_2ELMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Ellist_2ELMAP_2E2(A_27c,A_27a,V1g_2E0,V2ll_2E0)) = c_2Ellist_2ELMAP_2E2(A_27c,A_27b,c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,V0f_2E0,V1g_2E0),V2ll_2E0) ) ).

tff(thm_2Ellist_2ELAPPEND__NIL__2ND,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELAPPEND_2E2(A_27a,V0ll_2E0,c_2Ellist_2ELNIL_2E0(A_27a)) = V0ll_2E0 ) ).

tff(thm_2Ellist_2ELHD__LAPPEND,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
      ( ! [V1l1_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1l1_2E0))
        <=> ( V1l1_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) )
     => ! [V0l2_2E0: tyop_2Ellist_2Ellist(A_27a),V1l1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELHD_2E1(A_27a,c_2Ellist_2ELAPPEND_2E2(A_27a,V1l1_2E0,V0l2_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1l1_2E0),c_2Ellist_2ELHD_2E1(A_27a,V0l2_2E0),c_2Ellist_2ELHD_2E1(A_27a,V1l1_2E0)) ) ) ).

tff(thm_2Ellist_2ELTL__LAPPEND,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
      ( ! [V1l1_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1l1_2E0))
        <=> ( V1l1_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) )
     => ! [V0l2_2E0: tyop_2Ellist_2Ellist(A_27a),V1l1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTL_2E1(A_27a,c_2Ellist_2ELAPPEND_2E2(A_27a,V1l1_2E0,V0l2_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1l1_2E0),c_2Ellist_2ELTL_2E1(A_27a,V0l2_2E0),c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(A_27a,c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELTL_2E1(A_27a,V1l1_2E0)),V0l2_2E0))) ) ) ).

tff(thm_2Ellist_2ELTAKE__LAPPEND1,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Ellist_2Ellist(A_27a),V2l2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Eoption_2EIS__SOME_2E1(tyop_2Elist_2Elist(A_27a),c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V1l1_2E0)))
     => ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,c_2Ellist_2ELAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)) = c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V1l1_2E0) ) ) ).

tff(thm_2Ellist_2ELFINITE__rules,axiom,
    ! [A_27a: $tType] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,c_2Ellist_2ELNIL_2E0(A_27a)))
      & ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V1t_2E0))
         => p(c_2Ellist_2ELFINITE_2E1(A_27a,c_2Ellist_2ELCONS_2E2(A_27a,V0h_2E0,V1t_2E0))) ) ) ).

tff(thm_2Ellist_2ELFINITE__ind,axiom,
    ! [A_27a: $tType,V0LFINITE_27_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,c_2Ellist_2ELNIL_2E0(A_27a)))
        & ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,V2t_2E0))
           => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V2t_2E0))) ) )
     => ! [V3a0_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V3a0_2E0))
         => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,V3a0_2E0)) ) ) ).

tff(thm_2Ellist_2ELFINITE__strongind,axiom,
    ! [A_27a: $tType,V0LFINITE_27_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,c_2Ellist_2ELNIL_2E0(A_27a)))
        & ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V2t_2E0))
              & p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,V2t_2E0)) )
           => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V2t_2E0))) ) )
     => ! [V3a0_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V3a0_2E0))
         => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,V3a0_2E0)) ) ) ).

tff(thm_2Ellist_2ELFINITE__cases,axiom,
    ! [A_27a: $tType,V0a0_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V0a0_2E0))
    <=> ( ( V0a0_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) )
        | ? [V1h_2E0: A_27a,V2t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( ( V0a0_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V2t_2E0) )
            & p(c_2Ellist_2ELFINITE_2E1(A_27a,V2t_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELFINITE__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ( c_2Ellist_2ELFINITE_2E1(A_27a,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
      & ! [V0h_2E0: A_27b,V1t_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELFINITE_2E1(A_27b,c_2Ellist_2ELCONS_2E2(A_27b,V0h_2E0,V1t_2E0)) = c_2Ellist_2ELFINITE_2E1(A_27b,V1t_2E0) ) ) ).

tff(thm_2Ellist_2ELFINITE,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0))
    <=> ? [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELTAKE_2E2(A_27a,V1n_2E0,V0ll_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)) ) ) ).

tff(thm_2Ellist_2Ellength__rel__rules,axiom,
    ! [A_27a: $tType] :
      ( p(c_2Ellist_2Ellength__rel_2E2(A_27a,c_2Ellist_2ELNIL_2E0(A_27a),c_2Enum_2E0_2E0))
      & ! [V0h_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum,V2t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(c_2Ellist_2Ellength__rel_2E2(A_27a,V2t_2E0,V1n_2E0))
         => p(c_2Ellist_2Ellength__rel_2E2(A_27a,c_2Ellist_2ELCONS_2E2(A_27a,V0h_2E0,V2t_2E0),c_2Enum_2ESUC_2E1(V1n_2E0))) ) ) ).

tff(thm_2Ellist_2Ellength__rel__ind,axiom,
    ! [A_27a: $tType,V0llength__rel_27_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0llength__rel_27_2E0,c_2Ellist_2ELNIL_2E0(A_27a)),c_2Enum_2E0_2E0))
        & ! [V1h_2E0: A_27a,V2n_2E0: tyop_2Enum_2Enum,V3t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0llength__rel_27_2E0,V3t_2E0),V2n_2E0))
           => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0llength__rel_27_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V3t_2E0)),c_2Enum_2ESUC_2E1(V2n_2E0))) ) )
     => ! [V4a0_2E0: tyop_2Ellist_2Ellist(A_27a),V5a1_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ellist_2Ellength__rel_2E2(A_27a,V4a0_2E0,V5a1_2E0))
         => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0llength__rel_27_2E0,V4a0_2E0),V5a1_2E0)) ) ) ).

tff(thm_2Ellist_2Ellength__rel__strongind,axiom,
    ! [A_27a: $tType,V0llength__rel_27_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0llength__rel_27_2E0,c_2Ellist_2ELNIL_2E0(A_27a)),c_2Enum_2E0_2E0))
        & ! [V1h_2E0: A_27a,V2n_2E0: tyop_2Enum_2Enum,V3t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( ( p(c_2Ellist_2Ellength__rel_2E2(A_27a,V3t_2E0,V2n_2E0))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0llength__rel_27_2E0,V3t_2E0),V2n_2E0)) )
           => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0llength__rel_27_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V3t_2E0)),c_2Enum_2ESUC_2E1(V2n_2E0))) ) )
     => ! [V4a0_2E0: tyop_2Ellist_2Ellist(A_27a),V5a1_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ellist_2Ellength__rel_2E2(A_27a,V4a0_2E0,V5a1_2E0))
         => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0llength__rel_27_2E0,V4a0_2E0),V5a1_2E0)) ) ) ).

tff(thm_2Ellist_2Ellength__rel__cases,axiom,
    ! [A_27a: $tType,V0a0_2E0: tyop_2Ellist_2Ellist(A_27a),V1a1_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ellist_2Ellength__rel_2E2(A_27a,V0a0_2E0,V1a1_2E0))
    <=> ( ( ( V0a0_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) )
          & ( V1a1_2E0 = c_2Enum_2E0_2E0 ) )
        | ? [V2h_2E0: A_27a,V3n_2E0: tyop_2Enum_2Enum,V4t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( ( V0a0_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V2h_2E0,V4t_2E0) )
            & ( V1a1_2E0 = c_2Enum_2ESUC_2E1(V3n_2E0) )
            & p(c_2Ellist_2Ellength__rel_2E2(A_27a,V4t_2E0,V3n_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELLENGTH__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ( c_2Ellist_2ELLENGTH_2E1(A_27a,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
      & ! [V0h_2E0: A_27b,V1t_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELLENGTH_2E1(A_27b,c_2Ellist_2ELCONS_2E2(A_27b,V0h_2E0,V1t_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,c_2Ellist_2ELLENGTH_2E1(A_27b,V1t_2E0)) ) ) ).

tff(thm_2Ellist_2ELLENGTH__0,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELLENGTH_2E1(A_27a,V0x_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
    <=> ( V0x_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) ) ).

tff(thm_2Ellist_2ELFINITE__HAS__LENGTH,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0))
     => ? [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELLENGTH_2E1(A_27a,V0ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,V1n_2E0) ) ) ).

tff(thm_2Ellist_2ENOT__LFINITE__NO__LENGTH,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ~ p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0))
     => ( c_2Ellist_2ELLENGTH_2E1(A_27a,V0ll_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum) ) ) ).

tff(thm_2Ellist_2ELFINITE__LLENGTH,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0))
    <=> ? [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELLENGTH_2E1(A_27a,V0ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,V1n_2E0) ) ) ).

tff(thm_2Ellist_2ELFINITE__INDUCTION,axiom,
    ! [A_27a: $tType,V0LFINITE_27_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,c_2Ellist_2ELNIL_2E0(A_27a)))
        & ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,V2t_2E0))
           => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V2t_2E0))) ) )
     => ! [V3a0_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V3a0_2E0))
         => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,V3a0_2E0)) ) ) ).

tff(thm_2Ellist_2ELFINITE__STRONG__INDUCTION,axiom,
    ! [A_27a: $tType,V0LFINITE_27_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,c_2Ellist_2ELNIL_2E0(A_27a)))
        & ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V2t_2E0))
              & p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,V2t_2E0)) )
           => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V2t_2E0))) ) )
     => ! [V3a0_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V3a0_2E0))
         => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V0LFINITE_27_2E0,V3a0_2E0)) ) ) ).

tff(thm_2Ellist_2ELFINITE__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELFINITE_2E1(A_27b,c_2Ellist_2ELMAP_2E2(A_27a,A_27b,V0f_2E0,V1ll_2E0)) = c_2Ellist_2ELFINITE_2E1(A_27a,V1ll_2E0) ) ).

tff(thm_2Ellist_2ELFINITE__APPEND,axiom,
    ! [A_27a: $tType,V0ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,c_2Ellist_2ELAPPEND_2E2(A_27a,V0ll1_2E0,V1ll2_2E0)))
    <=> ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll1_2E0))
        & p(c_2Ellist_2ELFINITE_2E1(A_27a,V1ll2_2E0)) ) ) ).

tff(thm_2Ellist_2ELTAKE__LNTH__EL,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a),V2m_2E0: tyop_2Enum_2Enum,V3l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V1ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V3l_2E0) )
        & p(c_2Eprim__rec_2E_3C_2E2(V2m_2E0,V0n_2E0)) )
     => ( c_2Ellist_2ELNTH_2E2(A_27a,V2m_2E0,V1ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,c_2Elist_2EEL_2E2(A_27a,V2m_2E0,V3l_2E0)) ) ) ).

tff(thm_2Ellist_2ENOT__LFINITE__APPEND,axiom,
    ! [A_27a: $tType,V0ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ~ p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll1_2E0))
     => ( c_2Ellist_2ELAPPEND_2E2(A_27a,V0ll1_2E0,V1ll2_2E0) = V0ll1_2E0 ) ) ).

tff(thm_2Ellist_2ELFINITE__LAPPEND__IMP__NIL,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0))
     => ! [V1l2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( ( c_2Ellist_2ELAPPEND_2E2(A_27a,V0ll_2E0,V1l2_2E0) = V0ll_2E0 )
         => ( V1l2_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) ) ) ).

tff(thm_2Ellist_2ELLENGTH__MAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ellist_2ELLENGTH_2E1(A_27b,c_2Ellist_2ELMAP_2E2(A_27a,A_27b,V1f_2E0,V0ll_2E0)) = c_2Ellist_2ELLENGTH_2E1(A_27a,V0ll_2E0) ) ).

tff(thm_2Ellist_2ELLENGTH__APPEND,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool))] :
      ( ! [V0ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0ll1_2E0),V1ll2_2E0))
        <=> ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll1_2E0))
            & p(c_2Ellist_2ELFINITE_2E1(A_27a,V1ll2_2E0)) ) )
     => ! [V0ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELLENGTH_2E1(A_27a,c_2Ellist_2ELAPPEND_2E2(A_27a,V0ll1_2E0,V1ll2_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0ll1_2E0),V1ll2_2E0),c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(c_2Eoption_2ETHE_2E1(tyop_2Enum_2Enum,c_2Ellist_2ELLENGTH_2E1(A_27a,V0ll1_2E0)),c_2Eoption_2ETHE_2E1(tyop_2Enum_2Enum,c_2Ellist_2ELLENGTH_2E1(A_27a,V1ll2_2E0)))),c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum)) ) ) ).

tff(thm_2Ellist_2EtoList__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ( c_2Ellist_2EtoList_2E1(A_27a,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a)) )
      & ! [V0h_2E0: A_27b,V1t_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2EtoList_2E1(A_27b,c_2Ellist_2ELCONS_2E2(A_27b,V0h_2E0,V1t_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E1(A_27b,V0h_2E0),c_2Ellist_2EtoList_2E1(A_27b,V1t_2E0)) ) ) ).

tff(thm_2Ellist_2EfromList__EQ__LNIL,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Ellist_2EfromList_2E1(A_27a,V0l_2E0) = c_2Ellist_2ELNIL_2E0(A_27a) )
    <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ).

tff(thm_2Ellist_2ELHD__fromList,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELHD_2E1(A_27a,c_2Ellist_2EfromList_2E1(A_27a,V0l_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2ENULL_2E1(A_27a,V0l_2E0),c_2Eoption_2ENONE_2E0(A_27a),c_2Eoption_2ESOME_2E1(A_27a,c_2Elist_2EHD_2E1(A_27a,V0l_2E0))) ) ).

tff(thm_2Ellist_2ELTL__fromList,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELTL_2E1(A_27a,c_2Ellist_2EfromList_2E1(A_27a,V0l_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Elist_2ENULL_2E1(A_27a,V0l_2E0),c_2Eoption_2ENONE_2E0(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(A_27a,c_2Elist_2ETL_2E1(A_27a,V0l_2E0)))) ) ).

tff(thm_2Ellist_2ELFINITE__fromList,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Ellist_2ELFINITE_2E1(A_27a,c_2Ellist_2EfromList_2E1(A_27a,V0l_2E0))) ).

tff(thm_2Ellist_2ELLENGTH__fromList,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELLENGTH_2E1(A_27a,c_2Ellist_2EfromList_2E1(A_27a,V0l_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)) ) ).

tff(thm_2Ellist_2ELTAKE__fromList,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELTAKE_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),c_2Ellist_2EfromList_2E1(A_27a,V0l_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) ).

tff(thm_2Ellist_2Efrom__toList,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2EtoList_2E1(A_27a,c_2Ellist_2EfromList_2E1(A_27a,V0l_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) ).

tff(thm_2Ellist_2ELFINITE__toList,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0))
     => ? [V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2EtoList_2E1(A_27a,V0ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V1l_2E0) ) ) ).

tff(thm_2Ellist_2ELFINITE__toList__SOME,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0) = c_2Eoption_2EIS__SOME_2E1(tyop_2Elist_2Elist(A_27a),c_2Ellist_2EtoList_2E1(A_27a,V0ll_2E0)) ) ).

tff(thm_2Ellist_2Eto__fromList,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0))
     => ( c_2Ellist_2EfromList_2E1(A_27a,c_2Eoption_2ETHE_2E1(tyop_2Elist_2Elist(A_27a),c_2Ellist_2EtoList_2E1(A_27a,V0ll_2E0))) = V0ll_2E0 ) ) ).

tff(thm_2Ellist_2ELTAKE__LAPPEND2,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Ellist_2Ellist(A_27a),V2l2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V1l1_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)) )
     => ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,c_2Ellist_2ELAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E1(A_27a,c_2Eoption_2ETHE_2E1(tyop_2Elist_2Elist(A_27a),c_2Ellist_2EtoList_2E1(A_27a,V1l1_2E0))),c_2Ellist_2ELTAKE_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Eoption_2ETHE_2E1(tyop_2Enum_2Enum,c_2Ellist_2ELLENGTH_2E1(A_27a,V1l1_2E0))),V2l2_2E0)) ) ) ).

tff(thm_2Ellist_2ELNTH__fromList,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELNTH_2E2(A_27a,V0n_2E0,c_2Ellist_2EfromList_2E1(A_27a,V1l_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)),c_2Eoption_2ESOME_2E1(A_27a,c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0)),c_2Eoption_2ENONE_2E0(A_27a)) ) ).

tff(thm_2Ellist_2Elnth__fromList__some,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
    <=> ( c_2Ellist_2ELNTH_2E2(A_27a,V0n_2E0,c_2Ellist_2EfromList_2E1(A_27a,V1l_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ) ).

tff(thm_2Ellist_2ELDROP__FUNPOW,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))] :
      ( ! [V2m_2E0: tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))] : ( app_2E2(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),F0_2E0,V2m_2E0) = c_2Eoption_2EOPTION__BIND_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a),V2m_2E0,c_2Ellist_2ELTL_2E0(A_27a)) )
     => ! [V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELDROP_2E2(A_27a,V0n_2E0,V1ll_2E0) = c_2Earithmetic_2EFUNPOW_2E3(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),F0_2E0,V0n_2E0,c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)) ) ) ).

tff(thm_2Ellist_2ELDROP__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
      ( ! [V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELDROP_2E2(A_27a,c_2Enum_2E0_2E0,V0ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) )
      & ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELDROP_2E2(A_27b,c_2Enum_2ESUC_2E1(V1n_2E0),c_2Ellist_2ELNIL_2E0(A_27b)) = c_2Eoption_2ENONE_2E0(tyop_2Ellist_2Ellist(A_27b)) )
      & ! [V2n_2E0: tyop_2Enum_2Enum,V3h_2E0: A_27c,V4t_2E0: tyop_2Ellist_2Ellist(A_27c)] : ( c_2Ellist_2ELDROP_2E2(A_27c,c_2Enum_2ESUC_2E1(V2n_2E0),c_2Ellist_2ELCONS_2E2(A_27c,V3h_2E0,V4t_2E0)) = c_2Ellist_2ELDROP_2E2(A_27c,V2n_2E0,V4t_2E0) ) ) ).

tff(thm_2Ellist_2ELDROP1__THM,axiom,
    ! [A_27a: $tType] : ( c_2Ellist_2ELDROP_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Ellist_2ELTL_2E0(A_27a) ) ).

tff(thm_2Ellist_2ELNTH__HD__LDROP,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELNTH_2E2(A_27a,V0n_2E0,V1ll_2E0) = c_2Eoption_2EOPTION__BIND_2E2(A_27a,tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELDROP_2E2(A_27a,V0n_2E0,V1ll_2E0),c_2Ellist_2ELHD_2E0(A_27a)) ) ).

tff(thm_2Ellist_2ENOT__LFINITE__TAKE,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ~ p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0))
     => ! [V1n_2E0: tyop_2Enum_2Enum] :
        ? [V2y_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELTAKE_2E2(A_27a,V1n_2E0,V0ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V2y_2E0) ) ) ).

tff(thm_2Ellist_2ELFINITE__TAKE,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V1ll_2E0))
        & p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Eoption_2ETHE_2E1(tyop_2Enum_2Enum,c_2Ellist_2ELLENGTH_2E1(A_27a,V1ll_2E0)))) )
     => ? [V2y_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V1ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V2y_2E0) ) ) ).

tff(thm_2Ellist_2ENOT__LFINITE__DROP,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ~ p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0))
     => ! [V1n_2E0: tyop_2Enum_2Enum] :
        ? [V2y_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELDROP_2E2(A_27a,V1n_2E0,V0ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),V2y_2E0) ) ) ).

tff(thm_2Ellist_2ELFINITE__DROP,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V1ll_2E0))
        & p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Eoption_2ETHE_2E1(tyop_2Enum_2Enum,c_2Ellist_2ELLENGTH_2E1(A_27a,V1ll_2E0)))) )
     => ? [V2y_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELDROP_2E2(A_27a,V0n_2E0,V1ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),V2y_2E0) ) ) ).

tff(thm_2Ellist_2ELTAKE__DROP,axiom,
    ! [A_27a: $tType] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( ~ p(c_2Ellist_2ELFINITE_2E1(A_27a,V1ll_2E0))
         => ( c_2Ellist_2ELAPPEND_2E2(A_27a,c_2Ellist_2EfromList_2E1(A_27a,c_2Eoption_2ETHE_2E1(tyop_2Elist_2Elist(A_27a),c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V1ll_2E0))),c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELDROP_2E2(A_27a,V0n_2E0,V1ll_2E0))) = V1ll_2E0 ) )
      & ! [V2n_2E0: tyop_2Enum_2Enum,V3ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V3ll_2E0))
            & p(c_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,c_2Eoption_2ETHE_2E1(tyop_2Enum_2Enum,c_2Ellist_2ELLENGTH_2E1(A_27a,V3ll_2E0)))) )
         => ( c_2Ellist_2ELAPPEND_2E2(A_27a,c_2Ellist_2EfromList_2E1(A_27a,c_2Eoption_2ETHE_2E1(tyop_2Elist_2Elist(A_27a),c_2Ellist_2ELTAKE_2E2(A_27a,V2n_2E0,V3ll_2E0))),c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELDROP_2E2(A_27a,V2n_2E0,V3ll_2E0))) = V3ll_2E0 ) ) ) ).

tff(thm_2Ellist_2ELDROP__ADD,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))))] :
      ( ! [V1k2_2E0: tyop_2Enum_2Enum,V3ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),F0_2E0,V1k2_2E0),V3ll_2E0) = c_2Ellist_2ELDROP_2E2(A_27a,V1k2_2E0,V3ll_2E0) )
     => ! [V0k1_2E0: tyop_2Enum_2Enum,V1k2_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELDROP_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V0k1_2E0,V1k2_2E0),V2x_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(A_27a,V0k1_2E0,V2x_2E0),c_2Eoption_2ENONE_2E0(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),F0_2E0,V1k2_2E0)) ) ) ).

tff(thm_2Ellist_2ELDROP__SOME__LLENGTH,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2ll_2E0: tyop_2Ellist_2Ellist(A_27a),V3l_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( ( c_2Ellist_2ELDROP_2E2(A_27a,V0n_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),V3l_2E0) )
        & ( c_2Ellist_2ELLENGTH_2E1(A_27a,V2ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,V1m_2E0) ) )
     => ( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,V1m_2E0))
        & ( c_2Ellist_2ELLENGTH_2E1(A_27a,V3l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(V1m_2E0,V0n_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELFINITE__LNTH__NONE,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0))
    <=> ? [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELNTH_2E2(A_27a,V1n_2E0,V0ll_2E0) = c_2Eoption_2ENONE_2E0(A_27a) ) ) ).

tff(thm_2Ellist_2Einfinite__lnth__some,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ~ p(c_2Ellist_2ELFINITE_2E1(A_27a,V0ll_2E0))
    <=> ! [V1n_2E0: tyop_2Enum_2Enum] :
        ? [V2x_2E0: A_27a] : ( c_2Ellist_2ELNTH_2E2(A_27a,V1n_2E0,V0ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V2x_2E0) ) ) ).

tff(thm_2Ellist_2ELNTH__LAPPEND,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))))] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum,V2l1_2E0: tyop_2Ellist_2Ellist(A_27a),V1l2_2E0: tyop_2Ellist_2Ellist(A_27a),V3m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0,V0n_2E0),V2l1_2E0),V1l2_2E0),V3m_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),c_2Eprim__rec_2E_3C_2E2(V0n_2E0,V3m_2E0),c_2Ellist_2ELNTH_2E2(A_27a,V0n_2E0,V2l1_2E0),c_2Ellist_2ELNTH_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V0n_2E0,V3m_2E0),V1l2_2E0)) )
     => ! [V0n_2E0: tyop_2Enum_2Enum,V1l2_2E0: tyop_2Ellist_2Ellist(A_27a),V2l1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELNTH_2E2(A_27a,V0n_2E0,c_2Ellist_2ELAPPEND_2E2(A_27a,V2l1_2E0,V1l2_2E0)) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELLENGTH_2E1(A_27a,V2l1_2E0),c_2Ellist_2ELNTH_2E2(A_27a,V0n_2E0,V2l1_2E0),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0,V0n_2E0),V2l1_2E0),V1l2_2E0)) ) ) ).

tff(thm_2Ellist_2ELNTH__ADD,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum,V2ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELNTH_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V0a_2E0,V1b_2E0),V2ll_2E0) = c_2Eoption_2EOPTION__BIND_2E2(A_27a,tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELDROP_2E2(A_27a,V0a_2E0,V2ll_2E0),c_2Ellist_2ELNTH_2E1(A_27a,V1b_2E0)) ) ).

tff(thm_2Ellist_2Elnth__some__down__closed,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a),V1x_2E0: A_27a,V2n1_2E0: tyop_2Enum_2Enum,V3n2_2E0: tyop_2Enum_2Enum] :
      ( ( ( c_2Ellist_2ELNTH_2E2(A_27a,V2n1_2E0,V0ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V1x_2E0) )
        & p(c_2Earithmetic_2E_3C_3D_2E2(V3n2_2E0,V2n1_2E0)) )
     => ? [V4y_2E0: A_27a] : ( c_2Ellist_2ELNTH_2E2(A_27a,V3n2_2E0,V0ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V4y_2E0) ) ) ).

tff(thm_2Ellist_2Eexists__rules,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1h_2E0))
         => p(c_2Ellist_2Eexists_2E2(A_27a,V0P_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V2t_2E0))) )
      & ! [V3h_2E0: A_27a,V4t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(c_2Ellist_2Eexists_2E2(A_27a,V0P_2E0,V4t_2E0))
         => p(c_2Ellist_2Eexists_2E2(A_27a,V0P_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V3h_2E0,V4t_2E0))) ) ) ).

tff(thm_2Ellist_2Eexists__ind,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1exists_27_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
      ( ( ! [V2h_2E0: A_27a,V3t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2h_2E0))
           => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1exists_27_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V2h_2E0,V3t_2E0))) )
        & ! [V4h_2E0: A_27a,V5t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1exists_27_2E0,V5t_2E0))
           => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1exists_27_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V4h_2E0,V5t_2E0))) ) )
     => ! [V6a0_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(c_2Ellist_2Eexists_2E2(A_27a,V0P_2E0,V6a0_2E0))
         => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1exists_27_2E0,V6a0_2E0)) ) ) ).

tff(thm_2Ellist_2Eexists__strongind,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1exists_27_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
      ( ( ! [V2h_2E0: A_27a,V3t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2h_2E0))
           => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1exists_27_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V2h_2E0,V3t_2E0))) )
        & ! [V4h_2E0: A_27a,V5t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( ( p(c_2Ellist_2Eexists_2E2(A_27a,V0P_2E0,V5t_2E0))
              & p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1exists_27_2E0,V5t_2E0)) )
           => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1exists_27_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V4h_2E0,V5t_2E0))) ) )
     => ! [V6a0_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(c_2Ellist_2Eexists_2E2(A_27a,V0P_2E0,V6a0_2E0))
         => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1exists_27_2E0,V6a0_2E0)) ) ) ).

tff(thm_2Ellist_2Eexists__cases,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a0_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2Eexists_2E2(A_27a,V0P_2E0,V1a0_2E0))
    <=> ( ? [V2h_2E0: A_27a,V3t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( ( V1a0_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V2h_2E0,V3t_2E0) )
            & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2h_2E0)) )
        | ? [V4h_2E0: A_27a,V5t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( ( V1a0_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V4h_2E0,V5t_2E0) )
            & p(c_2Ellist_2Eexists_2E2(A_27a,V0P_2E0,V5t_2E0)) ) ) ) ).

tff(thm_2Ellist_2Eexists__thm,axiom,
    ! [A_27a: $tType,V0t_2E0: tyop_2Ellist_2Ellist(A_27a),V1h_2E0: A_27a,V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( c_2Ellist_2Eexists_2E2(A_27a,V2P_2E0,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Ebool_2EF_2E0 )
      & ( p(c_2Ellist_2Eexists_2E2(A_27a,V2P_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V0t_2E0)))
      <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V1h_2E0))
          | p(c_2Ellist_2Eexists_2E2(A_27a,V2P_2E0,V0t_2E0)) ) ) ) ).

tff(thm_2Ellist_2Eexists__LNTH,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2Eexists_2E2(A_27a,V0P_2E0,V1l_2E0))
    <=> ? [V2n_2E0: tyop_2Enum_2Enum,V3e_2E0: A_27a] :
          ( ( c_2Eoption_2ESOME_2E1(A_27a,V3e_2E0) = c_2Ellist_2ELNTH_2E2(A_27a,V2n_2E0,V1l_2E0) )
          & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3e_2E0)) ) ) ).

tff(thm_2Ellist_2EMONO__exists,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Ellist_2Ellist(A_27a),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V3x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3x_2E0))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) )
     => ( p(c_2Ellist_2Eexists_2E2(A_27a,V2P_2E0,V0l_2E0))
       => p(c_2Ellist_2Eexists_2E2(A_27a,V1Q_2E0,V0l_2E0)) ) ) ).

tff(thm_2Ellist_2Eexists__strong__ind,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
      ( ( ! [V2h_2E0: A_27a,V3t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2h_2E0))
           => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1Q_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V2h_2E0,V3t_2E0))) )
        & ! [V4h_2E0: A_27a,V5t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1Q_2E0,V5t_2E0))
              & p(c_2Ellist_2Eexists_2E2(A_27a,V0P_2E0,V5t_2E0)) )
           => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1Q_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V4h_2E0,V5t_2E0))) ) )
     => ! [V6a0_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(c_2Ellist_2Eexists_2E2(A_27a,V0P_2E0,V6a0_2E0))
         => p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1Q_2E0,V6a0_2E0)) ) ) ).

tff(thm_2Ellist_2Eexists__LDROP,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ellist_2Eexists_2E2(A_27a,V1P_2E0,V0ll_2E0))
    <=> ? [V2n_2E0: tyop_2Enum_2Enum,V3a_2E0: A_27a,V4t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( ( c_2Ellist_2ELDROP_2E2(A_27a,V2n_2E0,V0ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(A_27a,V3a_2E0,V4t_2E0)) )
          & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3a_2E0)) ) ) ).

tff(thm_2Ellist_2Eevery__coind,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
      ( ! [V2h_2E0: A_27a,V3t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1Q_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V2h_2E0,V3t_2E0)))
         => ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2h_2E0))
            & p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1Q_2E0,V3t_2E0)) ) )
     => ! [V4ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1Q_2E0,V4ll_2E0))
         => p(c_2Ellist_2Eevery_2E2(A_27a,V0P_2E0,V4ll_2E0)) ) ) ).

tff(thm_2Ellist_2Eevery__thm,axiom,
    ! [A_27a: $tType,V0t_2E0: tyop_2Ellist_2Ellist(A_27a),V1h_2E0: A_27a,V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( c_2Ellist_2Eevery_2E2(A_27a,V2P_2E0,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
      & ( p(c_2Ellist_2Eevery_2E2(A_27a,V2P_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V0t_2E0)))
      <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V1h_2E0))
          & p(c_2Ellist_2Eevery_2E2(A_27a,V2P_2E0,V0t_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELL__ALL__THM,axiom,
    ! [A_27a: $tType,V0t_2E0: tyop_2Ellist_2Ellist(A_27a),V1h_2E0: A_27a,V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( c_2Ellist_2Eevery_2E2(A_27a,V2P_2E0,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
      & ( p(c_2Ellist_2Eevery_2E2(A_27a,V2P_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V0t_2E0)))
      <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V1h_2E0))
          & p(c_2Ellist_2Eevery_2E2(A_27a,V2P_2E0,V0t_2E0)) ) ) ) ).

tff(thm_2Ellist_2EMONO__every,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Ellist_2Ellist(A_27a),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V3x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3x_2E0))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) )
     => ( p(c_2Ellist_2Eevery_2E2(A_27a,V2P_2E0,V0l_2E0))
       => p(c_2Ellist_2Eevery_2E2(A_27a,V1Q_2E0,V0l_2E0)) ) ) ).

tff(thm_2Ellist_2Eevery__strong__coind,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)] :
      ( ( ! [V2h_2E0: A_27a,V3t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1Q_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V2h_2E0,V3t_2E0)))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2h_2E0)) )
        & ! [V4h_2E0: A_27a,V5t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
            ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1Q_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V4h_2E0,V5t_2E0)))
           => ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1Q_2E0,V5t_2E0))
              | p(c_2Ellist_2Eevery_2E2(A_27a,V0P_2E0,V5t_2E0)) ) ) )
     => ! [V6ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,V1Q_2E0,V6ll_2E0))
         => p(c_2Ellist_2Eevery_2E2(A_27a,V0P_2E0,V6ll_2E0)) ) ) ).

tff(thm_2Ellist_2ELFILTER__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ellist_2ELFILTER_2E2(A_27a,V0P_2E0,c_2Ellist_2ELNIL_2E0(A_27a)) = c_2Ellist_2ELNIL_2E0(A_27a) )
      & ! [V1P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2h_2E0: A_27b,V3t_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELFILTER_2E2(A_27b,V1P_2E0,c_2Ellist_2ELCONS_2E2(A_27b,V2h_2E0,V3t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Ellist_2Ellist(A_27b),app_2E2(A_27b,tyop_2Emin_2Ebool,V1P_2E0,V2h_2E0),c_2Ellist_2ELCONS_2E2(A_27b,V2h_2E0,c_2Ellist_2ELFILTER_2E2(A_27b,V1P_2E0,V3t_2E0)),c_2Ellist_2ELFILTER_2E2(A_27b,V1P_2E0,V3t_2E0)) ) ) ).

tff(thm_2Ellist_2ELFILTER__NIL,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2Eevery_2E2(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),V1ll_2E0))
     => ( c_2Ellist_2ELFILTER_2E2(A_27a,V0P_2E0,V1ll_2E0) = c_2Ellist_2ELNIL_2E0(A_27a) ) ) ).

tff(thm_2Ellist_2ELFILTER__EQ__NIL,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELFILTER_2E2(A_27a,V0P_2E0,V1ll_2E0) = c_2Ellist_2ELNIL_2E0(A_27a) )
    <=> p(c_2Ellist_2Eevery_2E2(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),V1ll_2E0)) ) ).

tff(thm_2Ellist_2ELFILTER__APPEND,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ll1_2E0: tyop_2Ellist_2Ellist(A_27a),V2ll2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,V1ll1_2E0))
     => ( c_2Ellist_2ELFILTER_2E2(A_27a,V0P_2E0,c_2Ellist_2ELAPPEND_2E2(A_27a,V1ll1_2E0,V2ll2_2E0)) = c_2Ellist_2ELAPPEND_2E2(A_27a,c_2Ellist_2ELFILTER_2E2(A_27a,V0P_2E0,V1ll1_2E0),c_2Ellist_2ELFILTER_2E2(A_27a,V0P_2E0,V2ll2_2E0)) ) ) ).

tff(thm_2Ellist_2ELFLATTEN__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0t_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c))] :
      ( ( c_2Ellist_2ELFLATTEN_2E1(A_27a,c_2Ellist_2ELNIL_2E0(tyop_2Ellist_2Ellist(A_27a))) = c_2Ellist_2ELNIL_2E0(A_27a) )
      & ! [V1tl_2E0: A_27b] : ( c_2Ellist_2ELFLATTEN_2E1(A_27c,c_2Ellist_2ELCONS_2E2(tyop_2Ellist_2Ellist(A_27c),c_2Ellist_2ELNIL_2E0(A_27c),V0t_2E0)) = c_2Ellist_2ELFLATTEN_2E1(A_27c,V0t_2E0) )
      & ! [V2h_2E0: A_27d,V3t_2E0: tyop_2Ellist_2Ellist(A_27d),V4tl_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d))] : ( c_2Ellist_2ELFLATTEN_2E1(A_27d,c_2Ellist_2ELCONS_2E2(tyop_2Ellist_2Ellist(A_27d),c_2Ellist_2ELCONS_2E2(A_27d,V2h_2E0,V3t_2E0),V4tl_2E0)) = c_2Ellist_2ELCONS_2E2(A_27d,V2h_2E0,c_2Ellist_2ELFLATTEN_2E1(A_27d,c_2Ellist_2ELCONS_2E2(tyop_2Ellist_2Ellist(A_27d),V3t_2E0,V4tl_2E0))) ) ) ).

tff(thm_2Ellist_2ELFLATTEN__APPEND,axiom,
    ! [A_27a: $tType,V0h_2E0: tyop_2Ellist_2Ellist(A_27a),V1t_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))] : ( c_2Ellist_2ELFLATTEN_2E1(A_27a,c_2Ellist_2ELCONS_2E2(tyop_2Ellist_2Ellist(A_27a),V0h_2E0,V1t_2E0)) = c_2Ellist_2ELAPPEND_2E2(A_27a,V0h_2E0,c_2Ellist_2ELFLATTEN_2E1(A_27a,V1t_2E0)) ) ).

tff(thm_2Ellist_2ELFLATTEN__EQ__NIL,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))] :
      ( ( c_2Ellist_2ELFLATTEN_2E1(A_27a,V0ll_2E0) = c_2Ellist_2ELNIL_2E0(A_27a) )
    <=> p(c_2Ellist_2Eevery_2E2(tyop_2Ellist_2Ellist(A_27a),c_2Emin_2E_3D_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0(A_27a)),V0ll_2E0)) ) ).

tff(thm_2Ellist_2ELFLATTEN__SINGLETON,axiom,
    ! [A_27a: $tType,V0h_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELFLATTEN_2E1(A_27a,c_2Ellist_2ELCONS_2E2(tyop_2Ellist_2Ellist(A_27a),V0h_2E0,c_2Ellist_2ELNIL_2E0(tyop_2Ellist_2Ellist(A_27a)))) = V0h_2E0 ) ).

tff(thm_2Ellist_2ELZIP__LUNZIP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ellist_2ELZIP_2E1(A_27a,A_27b,c_2Ellist_2ELUNZIP_2E1(A_27a,A_27b,V0ll_2E0)) = V0ll_2E0 ) ).

tff(thm_2Ellist_2ELUNFOLD__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V1x_2E0: A_27a,V2v1_2E0: A_27a,V3v2_2E0: A_27b] :
      ( ( ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V0f_2E0,V1x_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
       => ( c_2Ellist_2ELUNFOLD_2E2(A_27b,A_27a,V0f_2E0,V1x_2E0) = c_2Ellist_2ELNIL_2E0(A_27b) ) )
      & ( ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V0f_2E0,V1x_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2v1_2E0,V3v2_2E0)) )
       => ( c_2Ellist_2ELUNFOLD_2E2(A_27b,A_27a,V0f_2E0,V1x_2E0) = c_2Ellist_2ELCONS_2E2(A_27b,V3v2_2E0,c_2Ellist_2ELUNFOLD_2E2(A_27b,A_27a,V0f_2E0,V2v1_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELLIST__EQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b))] :
      ( ! [V2x_2E0: A_27a] :
          ( ( ( app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V0f_2E0,V2x_2E0) = c_2Ellist_2ELNIL_2E0(A_27b) )
            & ( app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V2x_2E0) = c_2Ellist_2ELNIL_2E0(A_27b) ) )
          | ? [V3h_2E0: A_27b,V4y_2E0: A_27a] :
              ( ( app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V0f_2E0,V2x_2E0) = c_2Ellist_2ELCONS_2E2(A_27b,V3h_2E0,app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V0f_2E0,V4y_2E0)) )
              & ( app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V2x_2E0) = c_2Ellist_2ELCONS_2E2(A_27b,V3h_2E0,app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V4y_2E0)) ) ) )
     => ! [V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V0f_2E0,V5x_2E0) = app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27b),V1g_2E0,V5x_2E0) ) ) ).

tff(thm_2Ellist_2ELUNFOLD__EQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V2s_2E0: A_27a,V3ll_2E0: tyop_2Ellist_2Ellist(A_27b)] :
      ( ( p(app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool),V0R_2E0,V2s_2E0),V3ll_2E0))
        & ! [V4s_2E0: A_27a,V5ll_2E0: tyop_2Ellist_2Ellist(A_27b)] :
            ( p(app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool),V0R_2E0,V4s_2E0),V5ll_2E0))
           => ( ( ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V1f_2E0,V4s_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
                & ( V5ll_2E0 = c_2Ellist_2ELNIL_2E0(A_27b) ) )
              | ? [V6s_27_2E0: A_27a,V7x_2E0: A_27b,V8ll_27_2E0: tyop_2Ellist_2Ellist(A_27b)] :
                  ( ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),V1f_2E0,V4s_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V6s_27_2E0,V7x_2E0)) )
                  & ( c_2Ellist_2ELHD_2E1(A_27b,V5ll_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V7x_2E0) )
                  & ( c_2Ellist_2ELTL_2E1(A_27b,V5ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27b),V8ll_27_2E0) )
                  & p(app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool),V0R_2E0,V6s_27_2E0),V8ll_27_2E0)) ) ) ) )
     => ( c_2Ellist_2ELUNFOLD_2E2(A_27b,A_27a,V1f_2E0,V2s_2E0) = V3ll_2E0 ) ) ).

tff(thm_2Ellist_2ELMAP__LUNFOLD,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4x_2E0: A_27c,V5y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),F1_2E0,V0f_2E0),V4x_2E0),V5y_2E0) = c_2Epair_2E_2C_2E2(A_27c,A_27b,V4x_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V5y_2E0)) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V3s_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),F0_2E0,V0f_2E0),V1g_2E0),V3s_2E0) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2EUNCURRY_2E1(A_27c,A_27a,tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),F1_2E0,V0f_2E0)),app_2E2(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),V1g_2E0,V3s_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V2s_2E0: A_27c] : ( c_2Ellist_2ELMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27c,V1g_2E0,V2s_2E0)) = c_2Ellist_2ELUNFOLD_2E2(A_27b,A_27c,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),F0_2E0,V0f_2E0),V1g_2E0),V2s_2E0) ) ) ) ).

tff(thm_2Ellist_2ELNTH__LDROP,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Ellist_2Ellist(A_27a),V2x_2E0: A_27a] :
      ( ( c_2Ellist_2ELNTH_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V2x_2E0) )
     => ( c_2Ellist_2ELHD_2E1(A_27a,c_2Eoption_2ETHE_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELDROP_2E2(A_27a,V0n_2E0,V1l_2E0))) = c_2Eoption_2ESOME_2E1(A_27a,V2x_2E0) ) ) ).

tff(thm_2Ellist_2ELAPPEND__fromList,axiom,
    ! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELAPPEND_2E2(A_27a,c_2Ellist_2EfromList_2E1(A_27a,V0l1_2E0),c_2Ellist_2EfromList_2E1(A_27a,V1l2_2E0)) = c_2Ellist_2EfromList_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) ) ).

tff(thm_2Ellist_2ELTAKE__LENGTH,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a),V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V1ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V2l_2E0) )
     => ( V0n_2E0 = c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0) ) ) ).

tff(thm_2Ellist_2ELTAKE__TAKE__LESS,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2ll_2E0: tyop_2Ellist_2Ellist(A_27a),V3l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V3l_2E0) )
        & p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V0n_2E0)) )
     => ( c_2Ellist_2ELTAKE_2E2(A_27a,V1m_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(A_27a,V1m_2E0,V3l_2E0)) ) ) ).

tff(thm_2Ellist_2ELTAKE__LLENGTH__NONE,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( ( c_2Ellist_2ELLENGTH_2E1(A_27a,V2ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,V0n_2E0) )
        & p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,V1m_2E0)) )
     => ( c_2Ellist_2ELTAKE_2E2(A_27a,V1m_2E0,V2ll_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)) ) ) ).

tff(thm_2Ellist_2ELTAKE__LLENGTH__SOME,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELLENGTH_2E1(A_27a,V1ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,V0n_2E0) )
     => ? [V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V1ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V2l_2E0) )
          & ( c_2Ellist_2EtoList_2E1(A_27a,V1ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V2l_2E0) ) ) ) ).

tff(thm_2Ellist_2EtoList__LAPPEND__APPEND,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Ellist_2Ellist(A_27a),V2l1_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2EtoList_2E1(A_27a,c_2Ellist_2ELAPPEND_2E2(A_27a,V2l1_2E0,V1l2_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V0x_2E0) )
     => ( V0x_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,c_2Eoption_2ETHE_2E1(tyop_2Elist_2Elist(A_27a),c_2Ellist_2EtoList_2E1(A_27a,V2l1_2E0)),c_2Eoption_2ETHE_2E1(tyop_2Elist_2Elist(A_27a),c_2Ellist_2EtoList_2E1(A_27a,V1l2_2E0))) ) ) ).

tff(thm_2Ellist_2ELNTH__LLENGTH__NONE,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( ( c_2Ellist_2ELLENGTH_2E1(A_27a,V2l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,V0x_2E0) )
        & p(c_2Earithmetic_2E_3C_3D_2E2(V0x_2E0,V1n_2E0)) )
     => ( c_2Ellist_2ELNTH_2E2(A_27a,V1n_2E0,V2l_2E0) = c_2Eoption_2ENONE_2E0(A_27a) ) ) ).

tff(thm_2Ellist_2ELNTH__NONE__MONO,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( ( c_2Ellist_2ELNTH_2E2(A_27a,V0m_2E0,V2l_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
        & p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0)) )
     => ( c_2Ellist_2ELNTH_2E2(A_27a,V1n_2E0,V2l_2E0) = c_2Eoption_2ENONE_2E0(A_27a) ) ) ).

tff(thm_2Ellist_2Elinear__order__to__llist__eq,axiom,
    ! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F2_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))] :
      ( ! [V2ll_2E0: tyop_2Ellist_2Ellist(A_27a),V3x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F3_2E0,V2ll_2E0),V3x_2E0))
        <=> ? [V4i_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELNTH_2E2(A_27a,V4i_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V3x_2E0) ) )
     => ( ! [V2ll_2E0: tyop_2Ellist_2Ellist(A_27a),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2ll_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F3_2E0,V2ll_2E0),V3x_2E0)) )
       => ( ! [V2ll_2E0: tyop_2Ellist_2Ellist(A_27a),V5x_2E0: A_27a,V6y_2E0: A_27a] :
              ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V2ll_2E0),V5x_2E0),V6y_2E0))
            <=> ? [V7i_2E0: tyop_2Enum_2Enum,V8j_2E0: tyop_2Enum_2Enum] :
                  ( p(c_2Earithmetic_2E_3C_3D_2E2(V7i_2E0,V8j_2E0))
                  & ( c_2Ellist_2ELNTH_2E2(A_27a,V7i_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V5x_2E0) )
                  & ( c_2Ellist_2ELNTH_2E2(A_27a,V8j_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V6y_2E0) ) ) )
         => ( ! [V2ll_2E0: tyop_2Ellist_2Ellist(A_27a),V5x_2E0: A_27a,V6y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F1_2E0,V2ll_2E0),V5x_2E0),V6y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27a,V5x_2E0,V6y_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V2ll_2E0),V5x_2E0),V6y_2E0)) )
           => ! [V0lo_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                ( ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0lo_2E0,V1X_2E0))
                  & p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,V0lo_2E0,V1X_2E0)) )
               => ? [V2ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
                    ( ( V1X_2E0 = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2ll_2E0)) )
                    & ( V0lo_2E0 = c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F1_2E0,V2ll_2E0))) )
                    & ! [V9i_2E0: tyop_2Enum_2Enum,V10j_2E0: tyop_2Enum_2Enum,V11x_2E0: A_27a] :
                        ( ( ( c_2Ellist_2ELNTH_2E2(A_27a,V9i_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V11x_2E0) )
                          & ( c_2Ellist_2ELNTH_2E2(A_27a,V10j_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V11x_2E0) ) )
                       => ( V9i_2E0 = V10j_2E0 ) ) ) ) ) ) ) ) ).

tff(thm_2Ellist_2Elinear__order__to__llist,axiom,
    ! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F2_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))] :
      ( ! [V2ll_2E0: tyop_2Ellist_2Ellist(A_27a),V3x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F3_2E0,V2ll_2E0),V3x_2E0))
        <=> ? [V4i_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELNTH_2E2(A_27a,V4i_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V3x_2E0) ) )
     => ( ! [V2ll_2E0: tyop_2Ellist_2Ellist(A_27a),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2ll_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F3_2E0,V2ll_2E0),V3x_2E0)) )
       => ( ! [V2ll_2E0: tyop_2Ellist_2Ellist(A_27a),V5x_2E0: A_27a,V6y_2E0: A_27a] :
              ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V2ll_2E0),V5x_2E0),V6y_2E0))
            <=> ? [V7i_2E0: tyop_2Enum_2Enum,V8j_2E0: tyop_2Enum_2Enum] :
                  ( p(c_2Earithmetic_2E_3C_3D_2E2(V7i_2E0,V8j_2E0))
                  & ( c_2Ellist_2ELNTH_2E2(A_27a,V7i_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V5x_2E0) )
                  & ( c_2Ellist_2ELNTH_2E2(A_27a,V8j_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V6y_2E0) ) ) )
         => ( ! [V2ll_2E0: tyop_2Ellist_2Ellist(A_27a),V5x_2E0: A_27a,V6y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F1_2E0,V2ll_2E0),V5x_2E0),V6y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27a,V5x_2E0,V6y_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V2ll_2E0),V5x_2E0),V6y_2E0)) )
           => ! [V0lo_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
                ( ( p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0lo_2E0,V1X_2E0))
                  & p(c_2Eset__relation_2Efinite__prefixes_2E2(A_27a,A_27a,V0lo_2E0,V1X_2E0)) )
               => ? [V2ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
                    ( ( V1X_2E0 = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2ll_2E0)) )
                    & p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0lo_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F1_2E0,V2ll_2E0)))))
                    & ! [V9i_2E0: tyop_2Enum_2Enum,V10j_2E0: tyop_2Enum_2Enum,V11x_2E0: A_27a] :
                        ( ( ( c_2Ellist_2ELNTH_2E2(A_27a,V9i_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V11x_2E0) )
                          & ( c_2Ellist_2ELNTH_2E2(A_27a,V10j_2E0,V2ll_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V11x_2E0) ) )
                       => ( V9i_2E0 = V10j_2E0 ) ) ) ) ) ) ) ) ).

tff(thm_2Ellist_2ELPREFIX__LNIL,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELPREFIX_2E2(A_27a,c_2Ellist_2ELNIL_2E0(A_27a),V0ll_2E0))
      & ( p(c_2Ellist_2ELPREFIX_2E2(A_27a,V0ll_2E0,c_2Ellist_2ELNIL_2E0(A_27a)))
      <=> ( V0ll_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) ) ) ).

tff(thm_2Ellist_2ELPREFIX__LCONS,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0ll_2E0: tyop_2Ellist_2Ellist(A_27a),V1h_2E0: A_27a,V2t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(c_2Ellist_2ELPREFIX_2E2(A_27a,V0ll_2E0,c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V2t_2E0)))
        <=> ( ( V0ll_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) )
            | ? [V3l_2E0: tyop_2Ellist_2Ellist(A_27a)] :
                ( ( V0ll_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V3l_2E0) )
                & p(c_2Ellist_2ELPREFIX_2E2(A_27a,V3l_2E0,V2t_2E0)) ) ) )
      & ! [V4h_2E0: A_27b,V5t_2E0: tyop_2Ellist_2Ellist(A_27b),V6ll_2E0: tyop_2Ellist_2Ellist(A_27b)] :
          ( p(c_2Ellist_2ELPREFIX_2E2(A_27b,c_2Ellist_2ELCONS_2E2(A_27b,V4h_2E0,V5t_2E0),V6ll_2E0))
        <=> ? [V7l_2E0: tyop_2Ellist_2Ellist(A_27b)] :
              ( ( V6ll_2E0 = c_2Ellist_2ELCONS_2E2(A_27b,V4h_2E0,V7l_2E0) )
              & p(c_2Ellist_2ELPREFIX_2E2(A_27b,V5t_2E0,V7l_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELPREFIX__LUNFOLD,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)))] :
      ( ! [V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1ll_2E0))
        <=> ( V1ll_2E0 = c_2Ellist_2ELNIL_2E0(A_27a) ) )
     => ( ! [V1ll_2E0: tyop_2Ellist_2Ellist(A_27a),V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V4n_2E0: A_27b,V5x_2E0: A_27a] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0,V1ll_2E0),V2f_2E0),V4n_2E0),V5x_2E0))
          <=> ! [V6h_2E0: A_27a,V7t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
                ( ( V1ll_2E0 = c_2Ellist_2ELCONS_2E2(A_27a,V6h_2E0,V7t_2E0) )
               => ( ( V6h_2E0 = V5x_2E0 )
                  & p(c_2Ellist_2ELPREFIX_2E2(A_27a,V7t_2E0,c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V2f_2E0,V4n_2E0))) ) ) )
       => ( ! [V1ll_2E0: tyop_2Ellist_2Ellist(A_27a),V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V3v_2E0: tyop_2Epair_2Eprod(A_27b,A_27a)] : ( app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)),F1_2E0,V1ll_2E0),V2f_2E0),V3v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Emin_2Ebool,A_27b,A_27a,V3v_2E0,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0,V1ll_2E0),V2f_2E0)) )
         => ! [V0n_2E0: A_27b,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a),V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Ellist_2ELPREFIX_2E2(A_27a,V1ll_2E0,c_2Ellist_2ELUNFOLD_2E2(A_27a,A_27b,V2f_2E0,V0n_2E0)) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V2f_2E0,V0n_2E0),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1ll_2E0),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)),F1_2E0,V1ll_2E0),V2f_2E0)) ) ) ) ) ).

tff(thm_2Ellist_2ELPREFIX__REFL,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : p(c_2Ellist_2ELPREFIX_2E2(A_27a,V0ll_2E0,V0ll_2E0)) ).

tff(thm_2Ellist_2ELPREFIX__ANTISYM,axiom,
    ! [A_27a: $tType,V0l2_2E0: tyop_2Ellist_2Ellist(A_27a),V1l1_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( p(c_2Ellist_2ELPREFIX_2E2(A_27a,V1l1_2E0,V0l2_2E0))
        & p(c_2Ellist_2ELPREFIX_2E2(A_27a,V0l2_2E0,V1l1_2E0)) )
     => ( V1l1_2E0 = V0l2_2E0 ) ) ).

tff(thm_2Ellist_2ELPREFIX__TRANS,axiom,
    ! [A_27a: $tType,V0l3_2E0: tyop_2Ellist_2Ellist(A_27a),V1l2_2E0: tyop_2Ellist_2Ellist(A_27a),V2l1_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( p(c_2Ellist_2ELPREFIX_2E2(A_27a,V2l1_2E0,V1l2_2E0))
        & p(c_2Ellist_2ELPREFIX_2E2(A_27a,V1l2_2E0,V0l3_2E0)) )
     => p(c_2Ellist_2ELPREFIX_2E2(A_27a,V2l1_2E0,V0l3_2E0)) ) ).

tff(thm_2Ellist_2ELPREFIX__fromList,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( p(app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0l_2E0),V1ll_2E0))
        <=> ( c_2Ellist_2ELTAKE_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),V1ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) )
     => ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V2ys_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F1_2E0,V0l_2E0),V2ys_2E0) = c_2Elist_2EisPREFIX_2E2(A_27a,V0l_2E0,V2ys_2E0) )
       => ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELPREFIX_2E2(A_27a,c_2Ellist_2EfromList_2E1(A_27a,V0l_2E0),V1ll_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Ellist_2EtoList_2E1(A_27a,V1ll_2E0),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0l_2E0),V1ll_2E0),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F1_2E0,V0l_2E0)) ) ) ) ).

tff(thm_2Ellist_2Eprefixes__lprefix__total,axiom,
    ! [A_27a: $tType,V0ll_2E0: tyop_2Ellist_2Ellist(A_27a),V1l1_2E0: tyop_2Ellist_2Ellist(A_27a),V2l2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( p(c_2Ellist_2ELPREFIX_2E2(A_27a,V1l1_2E0,V0ll_2E0))
        & p(c_2Ellist_2ELPREFIX_2E2(A_27a,V2l2_2E0,V0ll_2E0)) )
     => ( p(c_2Ellist_2ELPREFIX_2E2(A_27a,V1l1_2E0,V2l2_2E0))
        | p(c_2Ellist_2ELPREFIX_2E2(A_27a,V2l2_2E0,V1l1_2E0)) ) ) ).

tff(thm_2Ellist_2ELTAKE__IMP__LDROP,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a),V2l1_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,V1ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V2l1_2E0) )
     => ? [V3l2_2E0: tyop_2Ellist_2Ellist(A_27a)] :
          ( ( c_2Ellist_2ELDROP_2E2(A_27a,V0n_2E0,V1ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),V3l2_2E0) )
          & ( c_2Ellist_2ELAPPEND_2E2(A_27a,c_2Ellist_2EfromList_2E1(A_27a,V2l1_2E0),V3l2_2E0) = V1ll_2E0 ) ) ) ).

tff(thm_2Ellist_2ELDROP__EQ__LNIL,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ll_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELDROP_2E2(A_27a,V0n_2E0,V1ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0(A_27a)) )
    <=> ( c_2Ellist_2ELLENGTH_2E1(A_27a,V1ll_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,V0n_2E0) ) ) ).

tff(thm_2Ellist_2ELPREFIX__APPEND,axiom,
    ! [A_27a: $tType,V0l2_2E0: tyop_2Ellist_2Ellist(A_27a),V1l1_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( p(c_2Ellist_2ELPREFIX_2E2(A_27a,V1l1_2E0,V0l2_2E0))
    <=> ? [V2ll_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( V0l2_2E0 = c_2Ellist_2ELAPPEND_2E2(A_27a,V1l1_2E0,V2ll_2E0) ) ) ).

tff(thm_2Ellist_2ENOT__LFINITE__DROP__LFINITE,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Ellist_2Ellist(A_27a),V2t_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( ~ p(c_2Ellist_2ELFINITE_2E1(A_27a,V1l_2E0))
        & ( c_2Ellist_2ELDROP_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),V2t_2E0) ) )
     => ~ p(c_2Ellist_2ELFINITE_2E1(A_27a,V2t_2E0)) ) ).

tff(thm_2Ellist_2ELDROP__APPEND1,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l2_2E0: tyop_2Ellist_2Ellist(A_27a),V2l1_2E0: tyop_2Ellist_2Ellist(A_27a),V3l_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ( c_2Ellist_2ELDROP_2E2(A_27a,V0n_2E0,V2l1_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),V3l_2E0) )
     => ( c_2Ellist_2ELDROP_2E2(A_27a,V0n_2E0,c_2Ellist_2ELAPPEND_2E2(A_27a,V2l1_2E0,V1l2_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(A_27a,V3l_2E0,V1l2_2E0)) ) ) ).

tff(thm_2Ellist_2ELDROP__fromList,axiom,
    ! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELDROP_2E2(A_27a,V1n_2E0,c_2Ellist_2EfromList_2E1(A_27a,V0ls_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0ls_2E0)),c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(A_27a,c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,V0ls_2E0))),c_2Eoption_2ENONE_2E0(tyop_2Ellist_2Ellist(A_27a))) ) ).

tff(thm_2Ellist_2ELDROP__SUC,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1ls_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELDROP_2E2(A_27a,c_2Enum_2ESUC_2E1(V0n_2E0),V1ls_2E0) = c_2Eoption_2EOPTION__BIND_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELDROP_2E2(A_27a,V0n_2E0,V1ls_2E0),c_2Ellist_2ELTL_2E0(A_27a)) ) ).

tff(thm_2Ellist_2ELHD__LGENLIST,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] :
      ( ! [V0limopt_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] :
          ( p(app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,F0_2E0,V0limopt_2E0))
        <=> ( V0limopt_2E0 = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ) )
     => ! [V0limopt_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Ellist_2ELHD_2E1(A_27a,c_2Ellist_2ELGENLIST_2E2(A_27a,V1f_2E0,V0limopt_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,F0_2E0,V0limopt_2E0),c_2Eoption_2ENONE_2E0(A_27a),c_2Eoption_2ESOME_2E1(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Enum_2E0_2E0))) ) ) ).

tff(thm_2Ellist_2ELTL__LGENLIST,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)] :
      ( ! [V0limopt_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] :
          ( p(app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,F0_2E0,V0limopt_2E0))
        <=> ( V0limopt_2E0 = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ) )
     => ! [V0limopt_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Ellist_2ELTL_2E1(A_27a,c_2Ellist_2ELGENLIST_2E2(A_27a,V1f_2E0,V0limopt_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,F0_2E0,V0limopt_2E0),c_2Eoption_2ENONE_2E0(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum,V1f_2E0,c_2Enum_2ESUC_2E0),c_2Eoption_2EOPTION__MAP_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E0,V0limopt_2E0)))) ) ) ).

tff(thm_2Ellist_2Enumopt__BISIMULATION,axiom,
    ! [V0mopt_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V1nopt_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] :
      ( ( V0mopt_2E0 = V1nopt_2E0 )
    <=> ? [V2R_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool))] :
          ( p(app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V2R_2E0,V0mopt_2E0),V1nopt_2E0))
          & ! [V3m_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V4n_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] :
              ( p(app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V2R_2E0,V3m_2E0),V4n_2E0))
             => ( ( ( V3m_2E0 = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
                  & ( V4n_2E0 = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ) )
                | ( ( V3m_2E0 != c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
                  & ( V4n_2E0 != c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
                  & p(app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V2R_2E0,c_2Eoption_2EOPTION__MAP_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E0,V3m_2E0)),c_2Eoption_2EOPTION__MAP_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E0,V4n_2E0))) ) ) ) ) ) ).

tff(thm_2Ellist_2ELGENLIST__EQ__LNIL,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
      ( ( ( c_2Ellist_2ELGENLIST_2E2(A_27a,V1f_2E0,V0n_2E0) = c_2Ellist_2ELNIL_2E0(A_27a) )
      <=> ( V0n_2E0 = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ) )
      & ( ( c_2Ellist_2ELNIL_2E0(A_27a) = c_2Ellist_2ELGENLIST_2E2(A_27a,V1f_2E0,V0n_2E0) )
      <=> ( V0n_2E0 = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ) ) ) ).

tff(thm_2Ellist_2ELFINITE__LGENLIST,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
      ( p(c_2Ellist_2ELFINITE_2E1(A_27a,c_2Ellist_2ELGENLIST_2E2(A_27a,V1f_2E0,V0n_2E0)))
    <=> ( V0n_2E0 != c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum) ) ) ).

tff(thm_2Ellist_2ELTL__HD__LTL__LHD,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))))] :
      ( ! [V1h_2E0: A_27a,V2t_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),F1_2E0,V1h_2E0),V2t_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),c_2Epair_2E_2C_2E2(tyop_2Ellist_2Ellist(A_27a),A_27a,V2t_2E0,V1h_2E0)) )
     => ( ! [V0l_2E0: tyop_2Ellist_2Ellist(A_27a),V1h_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),F0_2E0,V0l_2E0),V1h_2E0) = c_2Eoption_2EOPTION__BIND_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELTL_2E1(A_27a,V0l_2E0),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),F1_2E0,V1h_2E0)) )
       => ! [V0l_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTL__HD_2E1(A_27a,V0l_2E0) = c_2Eoption_2EOPTION__BIND_2E2(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),A_27a,c_2Ellist_2ELHD_2E1(A_27a,V0l_2E0),app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),F0_2E0,V0l_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELGENLIST__SOME,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
      ( ( c_2Ellist_2ELGENLIST_2E2(A_27a,V0f_2E0,c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) = c_2Ellist_2ELNIL_2E0(A_27a) )
      & ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELGENLIST_2E2(A_27a,V0f_2E0,c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(V1n_2E0))) = c_2Ellist_2ELCONS_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,c_2Enum_2E0_2E0),c_2Ellist_2ELGENLIST_2E2(A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum,V0f_2E0,c_2Enum_2ESUC_2E0),c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,V1n_2E0))) ) ) ).

tff(thm_2Ellist_2ELGENLIST__SOME__compute,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
      ( ( c_2Ellist_2ELGENLIST_2E2(A_27a,V0f_2E0,c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) = c_2Ellist_2ELNIL_2E0(A_27a) )
      & ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELGENLIST_2E2(A_27a,V0f_2E0,c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)))) = c_2Ellist_2ELCONS_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,c_2Enum_2E0_2E0),c_2Ellist_2ELGENLIST_2E2(A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum,V0f_2E0,c_2Enum_2ESUC_2E0),c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) )
      & ! [V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ellist_2ELGENLIST_2E2(A_27a,V0f_2E0,c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V2n_2E0)))) = c_2Ellist_2ELCONS_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,c_2Enum_2E0_2E0),c_2Ellist_2ELGENLIST_2E2(A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum,V0f_2E0,c_2Enum_2ESUC_2E0),c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2n_2E0))))) ) ) ).

tff(thm_2Ellist_2ELNTH__LGENLIST,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))))] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3lim0_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V0n_2E0),V1f_2E0),V3lim0_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),c_2Eprim__rec_2E_3C_2E2(V0n_2E0,V3lim0_2E0),c_2Eoption_2ESOME_2E1(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V0n_2E0)),c_2Eoption_2ENONE_2E0(A_27a)) )
     => ! [V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2lim_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] : ( c_2Ellist_2ELNTH_2E2(A_27a,V0n_2E0,c_2Ellist_2ELGENLIST_2E2(A_27a,V1f_2E0,V2lim_2E0)) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),V2lim_2E0,c_2Eoption_2ESOME_2E1(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V0n_2E0)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V0n_2E0),V1f_2E0)) ) ) ).

tff(thm_2Ellist_2ELNTH__LMAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2l_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELNTH_2E2(A_27b,V0n_2E0,c_2Ellist_2ELMAP_2E2(A_27a,A_27b,V1f_2E0,V2l_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(A_27a,A_27b,V1f_2E0,c_2Ellist_2ELNTH_2E2(A_27a,V0n_2E0,V2l_2E0)) ) ).

tff(thm_2Ellist_2ELLENGTH__LGENLIST,axiom,
    ! [A_27a: $tType,V0limopt_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Ellist_2ELLENGTH_2E1(A_27a,c_2Ellist_2ELGENLIST_2E2(A_27a,V1f_2E0,V0limopt_2E0)) = V0limopt_2E0 ) ).

tff(thm_2Ellist_2ELMAP__LGENLIST,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0limopt_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V2f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Ellist_2ELMAP_2E2(A_27b,A_27a,V2f_2E0,c_2Ellist_2ELGENLIST_2E2(A_27b,V1g_2E0,V0limopt_2E0)) = c_2Ellist_2ELGENLIST_2E2(A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,A_27b,V2f_2E0,V1g_2E0),V0limopt_2E0) ) ).

tff(thm_2Ellist_2ELGENLIST__EQ__CONS,axiom,
    ! [A_27a: $tType,V0t_2E0: tyop_2Ellist_2Ellist(A_27a),V1h_2E0: A_27a,V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
      ( ( c_2Ellist_2ELGENLIST_2E2(A_27a,V2f_2E0,c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum)) = c_2Ellist_2ELCONS_2E2(A_27a,V1h_2E0,V0t_2E0) )
    <=> ( ( V1h_2E0 = app_2E2(tyop_2Enum_2Enum,A_27a,V2f_2E0,c_2Enum_2E0_2E0) )
        & ( V0t_2E0 = c_2Ellist_2ELGENLIST_2E2(A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum,V2f_2E0,c_2Earithmetic_2E_2B_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum)) ) ) ) ).

tff(thm_2Ellist_2ELGENLIST__CHUNK__GENLIST,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Ellist_2ELGENLIST_2E2(A_27a,V1f_2E0,c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum)) = c_2Ellist_2ELAPPEND_2E2(A_27a,c_2Ellist_2EfromList_2E1(A_27a,c_2Elist_2EGENLIST_2E2(A_27a,V1f_2E0,V0n_2E0)),c_2Ellist_2ELGENLIST_2E2(A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum,V1f_2E0,c_2Earithmetic_2E_2B_2E1(V0n_2E0)),c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum))) ) ).

tff(thm_2Ellist_2ELREPEAT__thm,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELREPEAT_2E1(A_27a,V0l_2E0) = c_2Ellist_2ELAPPEND_2E2(A_27a,c_2Ellist_2EfromList_2E1(A_27a,V0l_2E0),c_2Ellist_2ELREPEAT_2E1(A_27a,V0l_2E0)) ) ).

tff(thm_2Ellist_2ELREPEAT__NIL,axiom,
    ! [A_27a: $tType] : ( c_2Ellist_2ELREPEAT_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ellist_2ELNIL_2E0(A_27a) ) ).

tff(thm_2Ellist_2ELREPEAT__EQ__LNIL,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( ( c_2Ellist_2ELREPEAT_2E1(A_27a,V0l_2E0) = c_2Ellist_2ELNIL_2E0(A_27a) )
      <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
      & ( ( c_2Ellist_2ELNIL_2E0(A_27a) = c_2Ellist_2ELREPEAT_2E1(A_27a,V0l_2E0) )
      <=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ) ).

tff(thm_2Ellist_2ELHD__LREPEAT,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELHD_2E1(A_27a,c_2Ellist_2ELREPEAT_2E1(A_27a,V0l_2E0)) = c_2Ellist_2ELHD_2E1(A_27a,c_2Ellist_2EfromList_2E1(A_27a,V0l_2E0)) ) ).

tff(thm_2Ellist_2ELTL__LREPEAT,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)))] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1t_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),F0_2E0,V0l_2E0),V1t_2E0) = c_2Ellist_2ELAPPEND_2E2(A_27a,V1t_2E0,c_2Ellist_2ELREPEAT_2E1(A_27a,V0l_2E0)) )
     => ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELTL_2E1(A_27a,c_2Ellist_2ELREPEAT_2E1(A_27a,V0l_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),F0_2E0,V0l_2E0),c_2Ellist_2ELTL_2E1(A_27a,c_2Ellist_2EfromList_2E1(A_27a,V0l_2E0))) ) ) ).

tff(thm_2Ellist_2ELLENGTH__LREPEAT,axiom,
    ! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ellist_2ELLENGTH_2E1(A_27a,c_2Ellist_2ELREPEAT_2E1(A_27a,V0l_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elist_2ENULL_2E1(A_27a,V0l_2E0),c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum)) ) ).

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