%------------------------------------------------------------------------------
% File     : ITP030_4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : list.ax [Gau19]
%          : HL4030_4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    : 1422 ( 564 unt; 484 typ;   0 def)
%            Number of atoms       : 1789 (1215 equ)
%            Maximal formula atoms :   12 (   1 avg)
%            Number of connectives :  914 (  63   ~;  29   |; 328   &)
%                                         ( 193 <=>; 301  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Maximal term depth    :   19 (   3 avg)
%            Number of types       :   36 (  35 usr)
%            Number of type conns  :  421 ( 267   >; 154   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  448 ( 448 usr; 182 con; 0-4 aty)
%            Number of variables   : 3741 (3642   !;  99   ?;3741   :)
% SPC      : TF0_SAT_EQU_NAR

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

tff(d,type,
    d: $tType ).

tff(du,type,
    du: $tType ).

tff(mono_2Etyop_2Emin_2Ebool,type,
    mono_2Etyop_2Emin_2Ebool: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29: $tType ).

tff(mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29: $tType ).

tff(mono_2Etyop_2Enum_2Enum,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

tff(mono_2Etyop_2Eone_2Eone,type,
    mono_2Etyop_2Eone_2Eone: $tType ).

tff(mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: $tType ).

tff(tyop_2Eind__type_2Erecspace,type,
    tyop_2Eind__type_2Erecspace: d > d ).

tff(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: d > d ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( d * d ) > d ).

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

tff(tyop_2Eone_2Eone,type,
    tyop_2Eone_2Eone: d ).

tff(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: d > d ).

tff(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( d * d ) > d ).

tff(s,type,
    s: ( d * u ) > du ).

tff(app_2E2,type,
    app_2E2: ( du * du ) > u ).

tff(p,type,
    p: mono_2Etyop_2Emin_2Ebool > $o ).

tff(combin_i_2E0,type,
    combin_i_2E0: u ).

tff(combin_k_2E0,type,
    combin_k_2E0: u ).

tff(combin_s_2E0,type,
    combin_s_2E0: u ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

tff(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: du > u ).

tff(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: u ).

tff(c_2Earithmetic_2E_2B_2E1,type,
    c_2Earithmetic_2E_2B_2E1: du > u ).

tff(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: ( du * du ) > u ).

tff(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: u ).

tff(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: u ).

tff(c_2Earithmetic_2E_2D_2E2,type,
    c_2Earithmetic_2E_2D_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: u ).

tff(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: u ).

tff(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: u ).

tff(c_2Earithmetic_2E_3C_3D_2E2,type,
    c_2Earithmetic_2E_3C_3D_2E2: ( du * du ) > u ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

tff(c_2Emin_2E_3D_2E1,type,
    c_2Emin_2E_3D_2E1: du > u ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: ( du * du ) > u ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2E_3E_3D_2E0,type,
    c_2Earithmetic_2E_3E_3D_2E0: u ).

tff(c_2Earithmetic_2E_3E_3D_2E2,type,
    c_2Earithmetic_2E_3E_3D_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

tff(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: du > u ).

tff(c_2Ebool_2E_3F_21_2E0,type,
    c_2Ebool_2E_3F_21_2E0: u ).

tff(c_2Ebool_2E_3F_21_2E1,type,
    c_2Ebool_2E_3F_21_2E1: du > u ).

tff(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: u ).

tff(c_2Emin_2E_40_2E1,type,
    c_2Emin_2E_40_2E1: du > u ).

tff(c_2Elist_2EALL__DISTINCT_2E0,type,
    c_2Elist_2EALL__DISTINCT_2E0: u ).

tff(c_2Elist_2EALL__DISTINCT_2E1,type,
    c_2Elist_2EALL__DISTINCT_2E1: du > u ).

tff(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: u ).

tff(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: ( du * du ) > u ).

tff(c_2Ebool_2EARB_2E0,type,
    c_2Ebool_2EARB_2E0: u ).

tff(c_2Ecombin_2EASSOC_2E0,type,
    c_2Ecombin_2EASSOC_2E0: u ).

tff(c_2Ecombin_2EASSOC_2E1,type,
    c_2Ecombin_2EASSOC_2E1: du > u ).

tff(c_2Epred__set_2EBIGUNION_2E0,type,
    c_2Epred__set_2EBIGUNION_2E0: u ).

tff(c_2Epred__set_2EBIGUNION_2E1,type,
    c_2Epred__set_2EBIGUNION_2E1: du > u ).

tff(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: u ).

tff(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: du > u ).

tff(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: u ).

tff(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: du > u ).

tff(c_2Eind__type_2EBOTTOM_2E0,type,
    c_2Eind__type_2EBOTTOM_2E0: u ).

tff(c_2Ecombin_2EC_2E0,type,
    c_2Ecombin_2EC_2E0: u ).

tff(c_2Ecombin_2EC_2E1,type,
    c_2Ecombin_2EC_2E1: du > u ).

tff(c_2Ecombin_2EC_2E2,type,
    c_2Ecombin_2EC_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2ECARD_2E0,type,
    c_2Epred__set_2ECARD_2E0: u ).

tff(c_2Epred__set_2ECARD_2E1,type,
    c_2Epred__set_2ECARD_2E1: du > u ).

tff(c_2Epred__set_2ECHOICE_2E0,type,
    c_2Epred__set_2ECHOICE_2E0: u ).

tff(c_2Epred__set_2ECHOICE_2E1,type,
    c_2Epred__set_2ECHOICE_2E1: du > u ).

tff(c_2Ecombin_2ECOMM_2E0,type,
    c_2Ecombin_2ECOMM_2E0: u ).

tff(c_2Ecombin_2ECOMM_2E1,type,
    c_2Ecombin_2ECOMM_2E1: du > u ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: u ).

tff(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: ( du * du ) > u ).

tff(c_2Eind__type_2ECONSTR_2E0,type,
    c_2Eind__type_2ECONSTR_2E0: u ).

tff(c_2Eind__type_2ECONSTR_2E3,type,
    c_2Eind__type_2ECONSTR_2E3: ( du * du * du ) > u ).

tff(c_2Ebool_2EDATATYPE_2E0,type,
    c_2Ebool_2EDATATYPE_2E0: u ).

tff(c_2Ebool_2EDATATYPE_2E1,type,
    c_2Ebool_2EDATATYPE_2E1: du > u ).

tff(c_2Epred__set_2EDIFF_2E0,type,
    c_2Epred__set_2EDIFF_2E0: u ).

tff(c_2Epred__set_2EDIFF_2E2,type,
    c_2Epred__set_2EDIFF_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EDISJOINT_2E0,type,
    c_2Epred__set_2EDISJOINT_2E0: u ).

tff(c_2Epred__set_2EDISJOINT_2E2,type,
    c_2Epred__set_2EDISJOINT_2E2: ( du * du ) > u ).

tff(c_2Elist_2EDROP_2E0,type,
    c_2Elist_2EDROP_2E0: u ).

tff(c_2Elist_2EDROP_2E2,type,
    c_2Elist_2EDROP_2E2: ( du * du ) > u ).

tff(c_2Elist_2EEL_2E0,type,
    c_2Elist_2EEL_2E0: u ).

tff(c_2Elist_2EEL_2E1,type,
    c_2Elist_2EEL_2E1: du > u ).

tff(c_2Elist_2EEL_2E2,type,
    c_2Elist_2EEL_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: u ).

tff(c_2Elist_2EEVERY_2E0,type,
    c_2Elist_2EEVERY_2E0: u ).

tff(c_2Elist_2EEVERY_2E2,type,
    c_2Elist_2EEVERY_2E2: ( du * du ) > u ).

tff(c_2Elist_2EEVERYi_2E0,type,
    c_2Elist_2EEVERYi_2E0: u ).

tff(c_2Elist_2EEVERYi_2E2,type,
    c_2Elist_2EEVERYi_2E2: ( du * du ) > u ).

tff(c_2Elist_2EEXISTS_2E0,type,
    c_2Elist_2EEXISTS_2E0: u ).

tff(c_2Elist_2EEXISTS_2E2,type,
    c_2Elist_2EEXISTS_2E2: ( du * du ) > u ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

tff(c_2Eind__type_2EFCONS_2E0,type,
    c_2Eind__type_2EFCONS_2E0: u ).

tff(c_2Eind__type_2EFCONS_2E2,type,
    c_2Eind__type_2EFCONS_2E2: ( du * du ) > u ).

tff(c_2Elist_2EFILTER_2E0,type,
    c_2Elist_2EFILTER_2E0: u ).

tff(c_2Elist_2EFILTER_2E2,type,
    c_2Elist_2EFILTER_2E2: ( du * du ) > u ).

tff(c_2Elist_2EFIND_2E0,type,
    c_2Elist_2EFIND_2E0: u ).

tff(c_2Elist_2EFIND_2E1,type,
    c_2Elist_2EFIND_2E1: du > u ).

tff(c_2Epred__set_2EFINITE_2E0,type,
    c_2Epred__set_2EFINITE_2E0: u ).

tff(c_2Epred__set_2EFINITE_2E1,type,
    c_2Epred__set_2EFINITE_2E1: du > u ).

tff(c_2Elist_2EFLAT_2E0,type,
    c_2Elist_2EFLAT_2E0: u ).

tff(c_2Elist_2EFLAT_2E1,type,
    c_2Elist_2EFLAT_2E1: du > u ).

tff(c_2Elist_2EFOLDL_2E0,type,
    c_2Elist_2EFOLDL_2E0: u ).

tff(c_2Elist_2EFOLDL_2E3,type,
    c_2Elist_2EFOLDL_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2EFOLDL2_2E0,type,
    c_2Elist_2EFOLDL2_2E0: u ).

tff(c_2Elist_2EFOLDL2_2E4,type,
    c_2Elist_2EFOLDL2_2E4: ( du * du * du * du ) > u ).

tff(c_2Elist_2EFOLDR_2E0,type,
    c_2Elist_2EFOLDR_2E0: u ).

tff(c_2Elist_2EFOLDR_2E3,type,
    c_2Elist_2EFOLDR_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2EFRONT_2E0,type,
    c_2Elist_2EFRONT_2E0: u ).

tff(c_2Elist_2EFRONT_2E1,type,
    c_2Elist_2EFRONT_2E1: du > u ).

tff(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: u ).

tff(c_2Epair_2EFST_2E1,type,
    c_2Epair_2EFST_2E1: du > u ).

tff(c_2Elist_2EGENLIST_2E0,type,
    c_2Elist_2EGENLIST_2E0: u ).

tff(c_2Elist_2EGENLIST_2E2,type,
    c_2Elist_2EGENLIST_2E2: ( du * du ) > u ).

tff(c_2Elist_2EGENLIST__AUX_2E0,type,
    c_2Elist_2EGENLIST__AUX_2E0: u ).

tff(c_2Elist_2EGENLIST__AUX_2E3,type,
    c_2Elist_2EGENLIST__AUX_2E3: ( du * du * du ) > u ).

tff(c_2Epred__set_2EGSPEC_2E0,type,
    c_2Epred__set_2EGSPEC_2E0: u ).

tff(c_2Epred__set_2EGSPEC_2E1,type,
    c_2Epred__set_2EGSPEC_2E1: du > u ).

tff(c_2Elist_2EHD_2E0,type,
    c_2Elist_2EHD_2E0: u ).

tff(c_2Elist_2EHD_2E1,type,
    c_2Elist_2EHD_2E1: du > u ).

tff(c_2Ecombin_2EI_2E0,type,
    c_2Ecombin_2EI_2E0: u ).

tff(c_2Ecombin_2EI_2E1,type,
    c_2Ecombin_2EI_2E1: du > u ).

tff(c_2Epred__set_2EIMAGE_2E0,type,
    c_2Epred__set_2EIMAGE_2E0: u ).

tff(c_2Epred__set_2EIMAGE_2E2,type,
    c_2Epred__set_2EIMAGE_2E2: ( du * du ) > u ).

tff(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: u ).

tff(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: ( du * du ) > u ).

tff(c_2Elist_2EINDEX__FIND_2E0,type,
    c_2Elist_2EINDEX__FIND_2E0: u ).

tff(c_2Elist_2EINDEX__FIND_2E2,type,
    c_2Elist_2EINDEX__FIND_2E2: ( du * du ) > u ).

tff(c_2Elist_2EINDEX__FIND_2E3,type,
    c_2Elist_2EINDEX__FIND_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2EINDEX__OF_2E0,type,
    c_2Elist_2EINDEX__OF_2E0: u ).

tff(c_2Elist_2EINDEX__OF_2E1,type,
    c_2Elist_2EINDEX__OF_2E1: du > u ).

tff(c_2Epred__set_2EINJ_2E0,type,
    c_2Epred__set_2EINJ_2E0: u ).

tff(c_2Epred__set_2EINJ_2E3,type,
    c_2Epred__set_2EINJ_2E3: ( du * du * du ) > u ).

tff(c_2Epred__set_2EINSERT_2E0,type,
    c_2Epred__set_2EINSERT_2E0: u ).

tff(c_2Epred__set_2EINSERT_2E2,type,
    c_2Epred__set_2EINSERT_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EINTER_2E0,type,
    c_2Epred__set_2EINTER_2E0: u ).

tff(c_2Epred__set_2EINTER_2E2,type,
    c_2Epred__set_2EINTER_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EITSET_2E0,type,
    c_2Epred__set_2EITSET_2E0: u ).

tff(c_2Epred__set_2EITSET_2E3,type,
    c_2Epred__set_2EITSET_2E3: ( du * du * du ) > u ).

tff(c_2Ecombin_2EK_2E0,type,
    c_2Ecombin_2EK_2E0: u ).

tff(c_2Ecombin_2EK_2E1,type,
    c_2Ecombin_2EK_2E1: du > u ).

tff(c_2Elist_2ELAST_2E0,type,
    c_2Elist_2ELAST_2E0: u ).

tff(c_2Elist_2ELAST_2E1,type,
    c_2Elist_2ELAST_2E1: du > u ).

tff(c_2Elist_2ELEN_2E0,type,
    c_2Elist_2ELEN_2E0: u ).

tff(c_2Elist_2ELEN_2E2,type,
    c_2Elist_2ELEN_2E2: ( du * du ) > u ).

tff(c_2Elist_2ELENGTH_2E0,type,
    c_2Elist_2ELENGTH_2E0: u ).

tff(c_2Elist_2ELENGTH_2E1,type,
    c_2Elist_2ELENGTH_2E1: du > u ).

tff(c_2Ebool_2ELET_2E0,type,
    c_2Ebool_2ELET_2E0: u ).

tff(c_2Ebool_2ELET_2E2,type,
    c_2Ebool_2ELET_2E2: ( du * du ) > u ).

tff(c_2Elist_2ELIST__APPLY_2E0,type,
    c_2Elist_2ELIST__APPLY_2E0: u ).

tff(c_2Elist_2ELIST__APPLY_2E2,type,
    c_2Elist_2ELIST__APPLY_2E2: ( du * du ) > u ).

tff(c_2Elist_2ELIST__BIND_2E0,type,
    c_2Elist_2ELIST__BIND_2E0: u ).

tff(c_2Elist_2ELIST__BIND_2E2,type,
    c_2Elist_2ELIST__BIND_2E2: ( du * du ) > u ).

tff(c_2Elist_2ELIST__GUARD_2E0,type,
    c_2Elist_2ELIST__GUARD_2E0: u ).

tff(c_2Elist_2ELIST__GUARD_2E1,type,
    c_2Elist_2ELIST__GUARD_2E1: du > u ).

tff(c_2Elist_2ELIST__IGNORE__BIND_2E0,type,
    c_2Elist_2ELIST__IGNORE__BIND_2E0: u ).

tff(c_2Elist_2ELIST__IGNORE__BIND_2E2,type,
    c_2Elist_2ELIST__IGNORE__BIND_2E2: ( du * du ) > u ).

tff(c_2Elist_2ELIST__LIFT2_2E0,type,
    c_2Elist_2ELIST__LIFT2_2E0: u ).

tff(c_2Elist_2ELIST__LIFT2_2E3,type,
    c_2Elist_2ELIST__LIFT2_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2ELIST__REL_2E0,type,
    c_2Elist_2ELIST__REL_2E0: u ).

tff(c_2Elist_2ELIST__REL_2E3,type,
    c_2Elist_2ELIST__REL_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2ELIST__TO__SET_2E0,type,
    c_2Elist_2ELIST__TO__SET_2E0: u ).

tff(c_2Elist_2ELIST__TO__SET_2E1,type,
    c_2Elist_2ELIST__TO__SET_2E1: du > u ).

tff(c_2Elist_2ELIST__TO__SET_2E2,type,
    c_2Elist_2ELIST__TO__SET_2E2: ( du * du ) > u ).

tff(c_2Elist_2ELLEX_2E0,type,
    c_2Elist_2ELLEX_2E0: u ).

tff(c_2Elist_2ELLEX_2E1,type,
    c_2Elist_2ELLEX_2E1: du > u ).

tff(c_2Elist_2ELLEX_2E3,type,
    c_2Elist_2ELLEX_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2ELRC_2E0,type,
    c_2Elist_2ELRC_2E0: u ).

tff(c_2Elist_2ELRC_2E4,type,
    c_2Elist_2ELRC_2E4: ( du * du * du * du ) > u ).

tff(c_2Elist_2ELUPDATE_2E0,type,
    c_2Elist_2ELUPDATE_2E0: u ).

tff(c_2Elist_2ELUPDATE_2E3,type,
    c_2Elist_2ELUPDATE_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2EMAP_2E0,type,
    c_2Elist_2EMAP_2E0: u ).

tff(c_2Elist_2EMAP_2E1,type,
    c_2Elist_2EMAP_2E1: du > u ).

tff(c_2Elist_2EMAP_2E2,type,
    c_2Elist_2EMAP_2E2: ( du * du ) > u ).

tff(c_2Elist_2EMAP2_2E0,type,
    c_2Elist_2EMAP2_2E0: u ).

tff(c_2Elist_2EMAP2_2E3,type,
    c_2Elist_2EMAP2_2E3: ( du * du * du ) > u ).

tff(c_2Earithmetic_2EMIN_2E0,type,
    c_2Earithmetic_2EMIN_2E0: u ).

tff(c_2Earithmetic_2EMIN_2E2,type,
    c_2Earithmetic_2EMIN_2E2: ( du * du ) > u ).

tff(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: u ).

tff(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: u ).

tff(c_2Earithmetic_2ENRC_2E0,type,
    c_2Earithmetic_2ENRC_2E0: u ).

tff(c_2Earithmetic_2ENRC_2E4,type,
    c_2Earithmetic_2ENRC_2E4: ( du * du * du * du ) > u ).

tff(c_2Elist_2ENULL_2E0,type,
    c_2Elist_2ENULL_2E0: u ).

tff(c_2Elist_2ENULL_2E1,type,
    c_2Elist_2ENULL_2E1: du > u ).

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: u ).

tff(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: du > u ).

tff(c_2Ewhile_2EOLEAST_2E0,type,
    c_2Ewhile_2EOLEAST_2E0: u ).

tff(c_2Ewhile_2EOLEAST_2E1,type,
    c_2Ewhile_2EOLEAST_2E1: du > u ).

tff(c_2Eoption_2EOPTION__BIND_2E0,type,
    c_2Eoption_2EOPTION__BIND_2E0: u ).

tff(c_2Eoption_2EOPTION__BIND_2E2,type,
    c_2Eoption_2EOPTION__BIND_2E2: ( du * du ) > u ).

tff(c_2Eoption_2EOPTION__MAP_2E0,type,
    c_2Eoption_2EOPTION__MAP_2E0: u ).

tff(c_2Eoption_2EOPTION__MAP_2E1,type,
    c_2Eoption_2EOPTION__MAP_2E1: du > u ).

tff(c_2Elist_2EOPT__MMAP_2E0,type,
    c_2Elist_2EOPT__MMAP_2E0: u ).

tff(c_2Elist_2EOPT__MMAP_2E2,type,
    c_2Elist_2EOPT__MMAP_2E2: ( du * du ) > u ).

tff(c_2Elist_2EPAD__LEFT_2E0,type,
    c_2Elist_2EPAD__LEFT_2E0: u ).

tff(c_2Elist_2EPAD__LEFT_2E3,type,
    c_2Elist_2EPAD__LEFT_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2EPAD__RIGHT_2E0,type,
    c_2Elist_2EPAD__RIGHT_2E0: u ).

tff(c_2Elist_2EPAD__RIGHT_2E3,type,
    c_2Elist_2EPAD__RIGHT_2E3: ( du * du * du ) > u ).

tff(c_2Eprim__rec_2EPRE_2E0,type,
    c_2Eprim__rec_2EPRE_2E0: u ).

tff(c_2Eprim__rec_2EPRE_2E1,type,
    c_2Eprim__rec_2EPRE_2E1: du > u ).

tff(c_2Erelation_2ERC_2E0,type,
    c_2Erelation_2ERC_2E0: u ).

tff(c_2Erelation_2ERC_2E1,type,
    c_2Erelation_2ERC_2E1: du > u ).

tff(c_2Epred__set_2EREST_2E0,type,
    c_2Epred__set_2EREST_2E0: u ).

tff(c_2Epred__set_2EREST_2E1,type,
    c_2Epred__set_2EREST_2E1: du > u ).

tff(c_2Elist_2EREV_2E0,type,
    c_2Elist_2EREV_2E0: u ).

tff(c_2Elist_2EREV_2E2,type,
    c_2Elist_2EREV_2E2: ( du * du ) > u ).

tff(c_2Elist_2EREVERSE_2E0,type,
    c_2Elist_2EREVERSE_2E0: u ).

tff(c_2Elist_2EREVERSE_2E1,type,
    c_2Elist_2EREVERSE_2E1: du > u ).

tff(c_2Elist_2ESET__TO__LIST_2E0,type,
    c_2Elist_2ESET__TO__LIST_2E0: u ).

tff(c_2Elist_2ESET__TO__LIST_2E1,type,
    c_2Elist_2ESET__TO__LIST_2E1: du > u ).

tff(c_2Elist_2ESHORTLEX_2E0,type,
    c_2Elist_2ESHORTLEX_2E0: u ).

tff(c_2Elist_2ESHORTLEX_2E1,type,
    c_2Elist_2ESHORTLEX_2E1: du > u ).

tff(c_2Elist_2ESHORTLEX_2E3,type,
    c_2Elist_2ESHORTLEX_2E3: ( du * du * du ) > u ).

tff(c_2Epair_2ESND_2E0,type,
    c_2Epair_2ESND_2E0: u ).

tff(c_2Epair_2ESND_2E1,type,
    c_2Epair_2ESND_2E1: du > u ).

tff(c_2Elist_2ESNOC_2E0,type,
    c_2Elist_2ESNOC_2E0: u ).

tff(c_2Elist_2ESNOC_2E2,type,
    c_2Elist_2ESNOC_2E2: ( du * du ) > u ).

tff(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: u ).

tff(c_2Eoption_2ESOME_2E1,type,
    c_2Eoption_2ESOME_2E1: du > u ).

tff(c_2Epred__set_2ESUBSET_2E0,type,
    c_2Epred__set_2ESUBSET_2E0: u ).

tff(c_2Epred__set_2ESUBSET_2E2,type,
    c_2Epred__set_2ESUBSET_2E2: ( du * du ) > u ).

tff(c_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: u ).

tff(c_2Enum_2ESUC_2E1,type,
    c_2Enum_2ESUC_2E1: du > u ).

tff(c_2Elist_2ESUM_2E0,type,
    c_2Elist_2ESUM_2E0: u ).

tff(c_2Elist_2ESUM_2E1,type,
    c_2Elist_2ESUM_2E1: du > u ).

tff(c_2Elist_2ESUM__ACC_2E0,type,
    c_2Elist_2ESUM__ACC_2E0: u ).

tff(c_2Elist_2ESUM__ACC_2E2,type,
    c_2Elist_2ESUM__ACC_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2ESUM__IMAGE_2E0,type,
    c_2Epred__set_2ESUM__IMAGE_2E0: u ).

tff(c_2Epred__set_2ESUM__IMAGE_2E2,type,
    c_2Epred__set_2ESUM__IMAGE_2E2: ( du * du ) > u ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

tff(c_2Elist_2ETAKE_2E0,type,
    c_2Elist_2ETAKE_2E0: u ).

tff(c_2Elist_2ETAKE_2E2,type,
    c_2Elist_2ETAKE_2E2: ( du * du ) > u ).

tff(c_2Elist_2ETL_2E0,type,
    c_2Elist_2ETL_2E0: u ).

tff(c_2Elist_2ETL_2E1,type,
    c_2Elist_2ETL_2E1: du > u ).

tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
    c_2Ebool_2ETYPE__DEFINITION_2E0: u ).

tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
    c_2Ebool_2ETYPE__DEFINITION_2E2: ( du * du ) > u ).

tff(c_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_2E0: u ).

tff(c_2Epair_2EUNCURRY_2E1,type,
    c_2Epair_2EUNCURRY_2E1: du > u ).

tff(c_2Epair_2EUNCURRY_2E2,type,
    c_2Epair_2EUNCURRY_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EUNION_2E0,type,
    c_2Epred__set_2EUNION_2E0: u ).

tff(c_2Epred__set_2EUNION_2E2,type,
    c_2Epred__set_2EUNION_2E2: ( du * du ) > u ).

tff(c_2Elist_2EUNIQUE_2E0,type,
    c_2Elist_2EUNIQUE_2E0: u ).

tff(c_2Elist_2EUNIQUE_2E2,type,
    c_2Elist_2EUNIQUE_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EUNIV_2E0,type,
    c_2Epred__set_2EUNIV_2E0: u ).

tff(c_2Elist_2EUNZIP_2E0,type,
    c_2Elist_2EUNZIP_2E0: u ).

tff(c_2Elist_2EUNZIP_2E1,type,
    c_2Elist_2EUNZIP_2E1: du > u ).

tff(c_2Erelation_2EWF_2E0,type,
    c_2Erelation_2EWF_2E0: u ).

tff(c_2Erelation_2EWF_2E1,type,
    c_2Erelation_2EWF_2E1: du > u ).

tff(c_2Erelation_2EWFREC_2E0,type,
    c_2Erelation_2EWFREC_2E0: u ).

tff(c_2Erelation_2EWFREC_2E2,type,
    c_2Erelation_2EWFREC_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: u ).

tff(c_2Elist_2EZIP_2E0,type,
    c_2Elist_2EZIP_2E0: u ).

tff(c_2Elist_2EZIP_2E1,type,
    c_2Elist_2EZIP_2E1: du > u ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2Ecount_2E0,type,
    c_2Epred__set_2Ecount_2E0: u ).

tff(c_2Epred__set_2Ecount_2E1,type,
    c_2Epred__set_2Ecount_2E1: du > u ).

tff(c_2Elist_2EdropWhile_2E0,type,
    c_2Elist_2EdropWhile_2E0: u ).

tff(c_2Elist_2EdropWhile_2E1,type,
    c_2Elist_2EdropWhile_2E1: du > u ).

tff(c_2Elist_2EdropWhile_2E2,type,
    c_2Elist_2EdropWhile_2E2: ( du * du ) > u ).

tff(c_2Elist_2EisPREFIX_2E0,type,
    c_2Elist_2EisPREFIX_2E0: u ).

tff(c_2Elist_2EisPREFIX_2E2,type,
    c_2Elist_2EisPREFIX_2E2: ( du * du ) > u ).

tff(c_2Elist_2Elist__CASE_2E0,type,
    c_2Elist_2Elist__CASE_2E0: u ).

tff(c_2Elist_2Elist__CASE_2E3,type,
    c_2Elist_2Elist__CASE_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2Elist__size_2E0,type,
    c_2Elist_2Elist__size_2E0: u ).

tff(c_2Elist_2Elist__size_2E2,type,
    c_2Elist_2Elist__size_2E2: ( du * du ) > u ).

tff(c_2Elist_2Enub_2E0,type,
    c_2Elist_2Enub_2E0: u ).

tff(c_2Elist_2Enub_2E1,type,
    c_2Elist_2Enub_2E1: du > u ).

tff(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: u ).

tff(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: ( du * du ) > u ).

tff(c_2Elist_2EoEL_2E0,type,
    c_2Elist_2EoEL_2E0: u ).

tff(c_2Elist_2EoEL_2E2,type,
    c_2Elist_2EoEL_2E2: ( du * du ) > u ).

tff(c_2Elist_2EoHD_2E0,type,
    c_2Elist_2EoHD_2E0: u ).

tff(c_2Elist_2EoHD_2E1,type,
    c_2Elist_2EoHD_2E1: du > u ).

tff(c_2Eone_2Eone_2E0,type,
    c_2Eone_2Eone_2E0: u ).

tff(c_2Eoption_2Eoption__CASE_2E0,type,
    c_2Eoption_2Eoption__CASE_2E0: u ).

tff(c_2Eoption_2Eoption__CASE_2E3,type,
    c_2Eoption_2Eoption__CASE_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2EsplitAtPki_2E0,type,
    c_2Elist_2EsplitAtPki_2E0: u ).

tff(c_2Elist_2EsplitAtPki_2E2,type,
    c_2Elist_2EsplitAtPki_2E2: ( du * du ) > u ).

tff(c_2Elist_2EsplitAtPki_2E3,type,
    c_2Elist_2EsplitAtPki_2E3: ( du * du * du ) > u ).

tff(c_2Erelation_2Etotal_2E0,type,
    c_2Erelation_2Etotal_2E0: u ).

tff(c_2Erelation_2Etotal_2E1,type,
    c_2Erelation_2Etotal_2E1: du > u ).

tff(c_2Erelation_2Etransitive_2E0,type,
    c_2Erelation_2Etransitive_2E0: u ).

tff(c_2Erelation_2Etransitive_2E1,type,
    c_2Erelation_2Etransitive_2E1: du > u ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

tff(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: du > u ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29 * mono_2Etyop_2Eone_2Eone ) > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_2B_2E0,type,
    mono_2Ec_2Earithmetic_2E_2B_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_2B_2E1,type,
    mono_2Ec_2Earithmetic_2E_2B_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2E_2B_2E2,type,
    mono_2Ec_2Earithmetic_2E_2B_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2E_2D_2E0,type,
    mono_2Ec_2Earithmetic_2E_2D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_2D_2E2,type,
    mono_2Ec_2Earithmetic_2E_2D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2E_2F_5C_2E0,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2E_2F_5C_2E2,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Enum_2E0_2E0,type,
    mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Eprim__rec_2E_3C_2E0,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Eprim__rec_2E_3C_2E2,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2E_3C_3D_2E0,type,
    mono_2Ec_2Earithmetic_2E_3C_3D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_3C_3D_2E2,type,
    mono_2Ec_2Earithmetic_2E_3C_3D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E2,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2E_3E_3D_2E0,type,
    mono_2Ec_2Earithmetic_2E_3E_3D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_3E_3D_2E2,type,
    mono_2Ec_2Earithmetic_2E_3E_3D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Elist_2EAPPEND_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2EAPPEND_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2EBIT1_2E0,type,
    mono_2Ec_2Earithmetic_2EBIT1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2EBIT1_2E1,type,
    mono_2Ec_2Earithmetic_2EBIT1_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2EBIT2_2E0,type,
    mono_2Ec_2Earithmetic_2EBIT2_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2EBIT2_2E1,type,
    mono_2Ec_2Earithmetic_2EBIT2_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,type,
    mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29 ).

tff(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,type,
    mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29 ).

tff(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eone_2Eone: ( mono_2Etyop_2Eone_2Eone * mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Epred__set_2EDISJOINT_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EDISJOINT_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2EF_2E0,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Elist_2EGENLIST_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2EGENLIST_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ecombin_2EK_2E0_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ecombin_2EK_2E0_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Elist_2ELIST__GUARD_2E0,type,
    mono_2Ec_2Elist_2ELIST__GUARD_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Ec_2Elist_2ELIST__GUARD_2E1,type,
    mono_2Ec_2Elist_2ELIST__GUARD_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Elist_2ELIST__TO__SET_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ELIST__TO__SET_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Earithmetic_2EMIN_2E0,type,
    mono_2Ec_2Earithmetic_2EMIN_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2EMIN_2E2,type,
    mono_2Ec_2Earithmetic_2EMIN_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Earithmetic_2ENUMERAL_2E0,type,
    mono_2Ec_2Earithmetic_2ENUMERAL_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2ENUMERAL_2E1,type,
    mono_2Ec_2Earithmetic_2ENUMERAL_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ewhile_2EOLEAST_2E0,type,
    mono_2Ec_2Ewhile_2EOLEAST_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Ewhile_2EOLEAST_2E1,type,
    mono_2Ec_2Ewhile_2EOLEAST_2E1: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Eprim__rec_2EPRE_2E0,type,
    mono_2Ec_2Eprim__rec_2EPRE_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Eprim__rec_2EPRE_2E1,type,
    mono_2Ec_2Eprim__rec_2EPRE_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Elist_2ESNOC_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ESNOC_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Enum_2ESUC_2E0,type,
    mono_2Ec_2Enum_2ESUC_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Enum_2ESUC_2E1,type,
    mono_2Ec_2Enum_2ESUC_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Elist_2ESUM_2E0,type,
    mono_2Ec_2Elist_2ESUM_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Elist_2ESUM_2E1,type,
    mono_2Ec_2Elist_2ESUM_2E1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Elist_2ESUM__ACC_2E0,type,
    mono_2Ec_2Elist_2ESUM__ACC_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Elist_2ESUM__ACC_2E2,type,
    mono_2Ec_2Elist_2ESUM__ACC_2E2: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2ET_2E0,type,
    mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2EZERO_2E0,type,
    mono_2Ec_2Earithmetic_2EZERO_2E0: mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E0,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E2,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Epred__set_2Ecount_2E0,type,
    mono_2Ec_2Epred__set_2Ecount_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Epred__set_2Ecount_2E1,type,
    mono_2Ec_2Epred__set_2Ecount_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Eone_2Eone_2E0,type,
    mono_2Ec_2Eone_2Eone_2E0: mono_2Etyop_2Eone_2Eone ).

tff(mono_2Ec_2Ebool_2E_7E_2E0,type,
    mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2E_7E_2E1,type,
    mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

tff(i_mono_2Etyop_2Emin_2Ebool,type,
    i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29 > u ).

tff(i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > u ).

tff(i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,type,
    i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29: mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 > u ).

tff(i_mono_2Etyop_2Enum_2Enum,type,
    i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).

tff(i_mono_2Etyop_2Eone_2Eone,type,
    i_mono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eone_2Eone > u ).

tff(i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > u ).

tff(j_mono_2Etyop_2Emin_2Ebool,type,
    j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29 ).

tff(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(j_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,type,
    j_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29 ).

tff(j_mono_2Etyop_2Enum_2Enum,type,
    j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).

tff(j_mono_2Etyop_2Eone_2Eone,type,
    j_mono_2Etyop_2Eone_2Eone: du > mono_2Etyop_2Eone_2Eone ).

tff(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ! [V2x_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) )
     => ( s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ) ).

tff(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V0_2E0)
      <=> p(V1_2E0) )
     => ( V0_2E0 = V1_2E0 ) ) ).

tff(reserved_2Eho_2Etruth,axiom,
    p(mono_2Ec_2Ebool_2ET_2E0) ).

tff(reserved_2Eho_2Enotfalse,axiom,
    ~ p(mono_2Ec_2Ebool_2EF_2E0) ).

tff(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( V0t_2E0 = mono_2Ec_2Ebool_2ET_2E0 )
      | ( V0t_2E0 = mono_2Ec_2Ebool_2EF_2E0 ) ) ).

tff(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a: d,V0x_2E0: u] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ) ).

tff(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ) ).

tff(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] : ( s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(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))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ) ).

tff(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        & p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        | p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_7E_2E1(V0_2E0))
    <=> ~ p(V0_2E0) ) ).

tff(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
       => p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))
    <=> ( s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ) ).

tff(reserved_2Equant_2E_21,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))
    <=> ! [V1x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) ) ).

tff(reserved_2Equant_2E_3F,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))
    <=> ? [V1x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,V0_2E0)))) = s(tyop_2Emin_2Ebool,V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Eone_2Eone)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Eone_2Eone)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(j_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),V0_2E0)))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,V0_2E0)))) = s(tyop_2Enum_2Enum,V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(j_mono_2Etyop_2Eone_2Eone(s(tyop_2Eone_2Eone,V0_2E0)))) = s(tyop_2Eone_2Eone,V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V0_2E0) ) ).

tff(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29] : ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Eone_2Eone] : ( j_mono_2Etyop_2Eone_2Eone(s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Earithmetic_2E_2B_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2B_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2B_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).

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

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

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

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))) ) ).

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

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

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

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

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

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

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

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(A_27a,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0) )
    <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))))) ) ).

tff(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3E_3D_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Earithmetic_2E_3E_3D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0)))) ) ).

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

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

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

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

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,X1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(mono_2Ec_2Elist_2EAPPEND_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EASSOC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT1_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT2_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EC_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))) ) ).

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

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

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

tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epred__set_2ECHOICE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2ECOMM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0)))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool,X2_2E0: mono_2Etyop_2Emin_2Ebool] : ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(X0_2E0,X1_2E0,X2_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,X2_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(X0_2E0,X1_2E0,X2_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0,X2_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(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),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),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: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(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(s(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)))),app_2E2(s(tyop_2Emin_2Efun(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),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0))) ) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: mono_2Etyop_2Eone_2Eone,X1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eone_2Eone(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Eone_2Eone,X0_2E0),X1_2E0) ) ).

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

tff(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0))) ) ).

tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool] : ( mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EDISJOINT_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EDROP_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EDROP_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EDROP_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2EDROP_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EEL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(A_27c,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27c)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERYi_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEVERYi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEXISTS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Elist_2EEXISTS_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) ) ).

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

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

tff(arityeq1_2Ec_2Elist_2EFIND_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2EFIND_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2EFIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EFLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EFLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EFLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),X0_2E0))) ) ).

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

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

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

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

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

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

tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) ) ).

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

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

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

tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ) ).

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

tff(arityeq1_2Ec_2Elist_2EFRONT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EFRONT_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27a)),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(mono_2Ec_2Elist_2EGENLIST_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq3_2Ec_2Elist_2EGENLIST__AUX_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EGENLIST__AUX_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(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),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EHD_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

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

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ) ).

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

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(X1_2E0)))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(X1_2E0)))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EINDEX__FIND_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Elist_2EINDEX__FIND_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),c_2Elist_2EINDEX__FIND_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Elist_2EINDEX__FIND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),c_2Elist_2EINDEX__FIND_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ) ).

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

tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ) ).

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

tff(arityeq3_2Ec_2Epred__set_2EITSET_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Epred__set_2EITSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0))) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Ecombin_2EK_2E0),s(A_27a,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0))) ) ).

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

tff(arityeq1_2Ec_2Elist_2ELAST_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2ELAST_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2ELAST_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(A_27b,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),c_2Elist_2ELAST_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2ELEN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0))))) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elist_2ELEN_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27c),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0)))) ) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(arityeq1_2Ec_2Elist_2ELIST__GUARD_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool] : ( mono_2Ec_2Elist_2ELIST__GUARD_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(mono_2Ec_2Elist_2ELIST__GUARD_2E0,X0_2E0) ) ).

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

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

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27c),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27c),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0),s(tyop_2Elist_2Elist(A_27d),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))),s(tyop_2Elist_2Elist(A_27d),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27e_20mono_2EA_27f,axiom,
    ! [A_27e: d,A_27f: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27e),X1_2E0),s(tyop_2Elist_2Elist(A_27f),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27e),X1_2E0))),s(tyop_2Elist_2Elist(A_27f),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27g_20mono_2EA_27h,axiom,
    ! [A_27g: d,A_27h: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27g),X1_2E0),s(tyop_2Elist_2Elist(A_27h),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27g),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27g),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27g),X1_2E0))),s(tyop_2Elist_2Elist(A_27h),X2_2E0)))) ) ).

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

tff(arityeq2_2Ec_2Elist_2ELIST__TO__SET_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__TO__SET_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(A_27a,X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(A_27a,X1_2E0)))) ) ).

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

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

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

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Elist_2ELIST__TO__SET_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

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

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

tff(arityeq3_2Ec_2Elist_2ELLEX_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ELLEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) ) ).

tff(arityeq4_2Ec_2Elist_2ELRC_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Elist_2ELRC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0)))) ) ).

tff(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2ELUPDATE_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELUPDATE_2E3(s(A_27b,X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),c_2Elist_2ELUPDATE_2E0),s(A_27b,X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2ELUPDATE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a))))),c_2Elist_2ELUPDATE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2ELUPDATE_2E3(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b))))),c_2Elist_2ELUPDATE_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),X2_2E0))) ) ).

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

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

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

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

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

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

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

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ) ).

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

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

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

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

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

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) = j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) ) ).

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

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

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

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

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

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

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

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

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

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

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) = j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) ) ).

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

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

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

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

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

tff(arityeq2_2Ec_2Earithmetic_2EMIN_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EMIN_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2EMIN_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq4_2Ec_2Earithmetic_2ENRC_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Earithmetic_2ENRC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0)))) ) ).

tff(arityeq1_2Ec_2Elist_2ENULL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2ENULL_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Ewhile_2EOLEAST_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Ewhile_2EOLEAST_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Ewhile_2EOLEAST_2E0,X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(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(s(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__BIND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(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),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) ) ).

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

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

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

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

tff(arityeq3_2Ec_2Elist_2EPAD__LEFT_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EPAD__LEFT_2E3(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EPAD__LEFT_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Elist_2EPAD__RIGHT_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EPAD__RIGHT_2E3(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EPAD__RIGHT_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ) ).

tff(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2EPRE_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2EPRE_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2ERC_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ) ).

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

tff(arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ) ).

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

tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),c_2Elist_2EREVERSE_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))) ) ).

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

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

tff(arityeq3_2Ec_2Elist_2ESHORTLEX_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ESHORTLEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) ) ).

tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b)),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0))) ) ).

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

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

tff(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(mono_2Ec_2Elist_2ESNOC_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(A_27b,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Enum_2ESUC_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ESUM_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2ESUM_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Elist_2ESUM_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ESUM__ACC_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Elist_2ESUM__ACC_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Elist_2ESUM__ACC_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ETAKE_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ETAKE_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2ETAKE_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ETL_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ETL_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) ) ).

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

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

tff(arityeq2_2Ec_2Epair_2EUNCURRY_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) ) ).

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

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

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

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

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

tff(arityeq2_2Ec_2Elist_2EUNIQUE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EUNIQUE_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EUNIQUE_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Elist_2EUNZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EUNZIP_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) ) ).

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

tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27d,axiom,
    ! [A_27a: d,A_27d: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        | p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Epred__set_2Ecount_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Epred__set_2Ecount_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2Ecount_2E0,X0_2E0) ) ).

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

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

tff(arityeq2_2Ec_2Elist_2EisPREFIX_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EisPREFIX_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

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

tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Ebool,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X2_2E0)))) ) ).

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

tff(arityeq2_2Ec_2Elist_2Elist__size_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),c_2Elist_2Elist__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Elist_2Enub_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2Enub_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

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

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

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) ) ).

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

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

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

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(X0_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(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),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(X0_2E0)))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(X1_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(X0_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(X0_2E0)))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ) ).

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

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

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

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

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

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

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(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),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) ) ).

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

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

tff(arityeq2_2Ec_2Elist_2EoEL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2EoEL_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EoHD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2EoHD_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EoHD_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EoHD_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,X1_2E0: u,X2_2E0: u] : ( s(A_27a,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(X0_2E0)),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(X0_2E0)))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0))) ) ).

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

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

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

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

tff(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ p(X0_2E0)
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,X0_2E0)) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29] : ( s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29,V1_2E0: mono_2Etyop_2Eone_2Eone] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(V0_2E0)),s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0) ).

tff(monoeq_2Emono_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Elist_2EAPPEND_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(mono_2Ec_2Elist_2EAPPEND_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EAPPEND_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool,V2_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0,V2_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V2_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)))),c_2Ebool_2ECOND_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29,V2_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29] : ( s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0,V2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(V1_2E0)),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(V2_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Enum_2Enum,V2_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0,V2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2ECONS_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_29_29(mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),c_2Elist_2ECONS_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Eone_2Eone,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29] : ( s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eone_2Eone(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ECONS_2E2(s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool(V0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EDISJOINT_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Epred__set_2EDISJOINT_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Elist_2EGENLIST_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(mono_2Ec_2Elist_2EGENLIST_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EGENLIST_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ecombin_2EK_2E0_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Ecombin_2EK_2E0_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2ELIST__TO__SET_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Elist_2ELIST__TO__SET_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ENIL_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),i_mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ENIL_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2ESNOC_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(mono_2Ec_2Elist_2ESNOC_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2ESNOC_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ESNOC_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(thm_2Elist_2ESUM__ACC__DEF,axiom,
    ( ! [V0acc_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Elist_2ESUM__ACC_2E2(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum,V0acc_2E0) = V0acc_2E0 )
    & ! [V1h_2E0: mono_2Etyop_2Enum_2Enum,V2t_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V3acc_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Elist_2ESUM__ACC_2E2(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum(V1h_2E0,V2t_2E0),V3acc_2E0) = mono_2Ec_2Elist_2ESUM__ACC_2E2(V2t_2E0,mono_2Ec_2Earithmetic_2E_2B_2E2(V1h_2E0,V3acc_2E0)) ) ) ).

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

tff(thm_2Elist_2ELEN__DEF,axiom,
    ! [A_27a: d] :
      ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0))))) = V0n_2E0 )
      & ! [V1h_2E0: u,V2t_2E0: u,V3n_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),V2t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V3n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)))))))) ) ) ).

tff(thm_2Elist_2EPAD__RIGHT,axiom,
    ! [A_27a: d,V0c_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2s_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EPAD__RIGHT_2E3(s(A_27a,V0c_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2s_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2s_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V0c_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2s_2E0))))))))))) ) ).

tff(thm_2Elist_2EPAD__LEFT,axiom,
    ! [A_27a: d,V0c_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2s_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EPAD__LEFT_2E3(s(A_27a,V0c_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2s_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V0c_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2s_2E0))))))))),s(tyop_2Elist_2Elist(A_27a),V2s_2E0))) ) ).

tff(thm_2Elist_2EGENLIST__AUX,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u,V1l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) )
      & ! [V2f_2E0: u,V3n_2E0: mono_2Etyop_2Enum_2Enum,V4l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V3n_2E0))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))))) ) ) ).

tff(thm_2Elist_2EGENLIST,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V1f_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V2n_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))))) ) ) ).

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

tff(thm_2Elist_2EisPREFIX,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1h_2E0: u,V2t_2E0: u,V4h_27_2E0: u,V5t_27_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),F0_2E0),s(A_27a,V1h_2E0))),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(A_27a,V4h_27_2E0))),s(tyop_2Elist_2Elist(A_27a),V5t_27_2E0)))))
        <=> ( ( s(A_27a,V1h_2E0) = s(A_27a,V4h_27_2E0) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V2t_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_27_2E0))))) ) )
     => ( ! [V0l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
        & ! [V1h_2E0: u,V2t_2E0: u,V3l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V3l_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),F0_2E0),s(A_27a,V1h_2E0))),s(tyop_2Elist_2Elist(A_27a),V2t_2E0)))))) ) ) ) ).

tff(thm_2Elist_2ESET__TO__LIST__primitive__def,axiom,
    ! [A_27a: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V3a_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0)))))
        <=> ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) ) )
     => ( ! [V2SET__TO__LIST_2E0: u,V3a_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),V2SET__TO__LIST_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))),s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),V2SET__TO__LIST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))))))))),s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2EARB_2E0))))) )
       => ( ! [V0R_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(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)),V0R_2E0)))))
            <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(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)),V0R_2E0)))))
                & ! [V1s_2E0: u] :
                    ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))
                      & ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) ) )
                   => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(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)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) ) ) )
         => ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ESET__TO__LIST_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),F1_2E0))) ) ) ) ) ).

tff(thm_2Elist_2ELRC__def,axiom,
    ! [A_27a: d] :
      ( ! [V0R_2E0: u,V1x_2E0: u,V2y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))
        <=> ( s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) ) )
      & ! [V3R_2E0: u,V4h_2E0: u,V5t_2E0: u,V6x_2E0: u,V7y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0))),s(A_27a,V6x_2E0),s(A_27a,V7y_2E0)))))
        <=> ( ( s(A_27a,V6x_2E0) = s(A_27a,V4h_2E0) )
            & ? [V8z_2E0: u] :
                ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V6x_2E0))),s(A_27a,V8z_2E0)))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0),s(A_27a,V8z_2E0),s(A_27a,V7y_2E0))))) ) ) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT,axiom,
    ! [A_27a: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ! [V0h_2E0: u,V1t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))))
        <=> ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) ) ) ) ).

tff(thm_2Elist_2EDROP__def,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1n_2E0))
        <=> ( V1n_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
        & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2x_2E0: u,V3xs_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V1n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))) ) ) ) ).

tff(thm_2Elist_2ETAKE__def,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1n_2E0))
        <=> ( V1n_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
        & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2x_2E0: u,V3xs_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V1n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))))) ) ) ) ).

tff(thm_2Elist_2EFRONT__DEF,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))
        <=> ( s(tyop_2Elist_2Elist(A_27a),V1t_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
     => ! [V0h_2E0: u,V1t_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))))) ) ) ).

tff(thm_2Elist_2ELAST__DEF,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))
        <=> ( s(tyop_2Elist_2Elist(A_27a),V1t_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
     => ! [V0h_2E0: u,V1t_2E0: u] : ( s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(A_27a,V0h_2E0),s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) ) ) ).

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

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

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

tff(thm_2Elist_2Elist__size__def,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) = mono_2Ec_2Enum_2E0_2E0 )
      & ! [V1f_2E0: u,V2a0_2E0: u,V3a1_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a0_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_2E0)))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V2a0_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_2E0)))))) ) ) ).

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

tff(thm_2Elist_2Elist__TY__DEF,axiom,
    ! [A_27a: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V7n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V7n_2E0)))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) )
     => ( ! [V4n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4n_2E0)))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) )
       => ( ! [V1a0_27_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V1a0_27_2E0)))))
            <=> ! [V2_27list_27_2E0: u] :
                  ( ! [V3a0_27_2E0: u] :
                      ( ( ( s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(A_27a,c_2Ebool_2EARB_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0))) )
                        | ? [V5a0_2E0: u,V6a1_2E0: u] :
                            ( ( s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))),s(A_27a,V5a0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(A_27a),V6a1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F2_2E0))))) )
                            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27list_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V6a1_2E0))))) ) )
                     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27list_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0))))) )
                 => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27list_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V1a0_27_2E0))))) ) )
         => ? [V0rep_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),V0rep_2E0))))) ) ) ) ).

tff(thm_2Elist_2ENULL__DEF,axiom,
    ! [A_27a: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ! [V0h_2E0: u,V1t_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) = mono_2Ec_2Ebool_2EF_2E0 ) ) ).

tff(thm_2Elist_2EHD,axiom,
    ! [A_27a: d,V0h_2E0: u,V1t_2E0: u] : ( s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(A_27a,V0h_2E0) ) ).

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

tff(thm_2Elist_2ESUM,axiom,
    ( ( mono_2Ec_2Elist_2ESUM_2E1(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum) = mono_2Ec_2Enum_2E0_2E0 )
    & ! [V0h_2E0: mono_2Etyop_2Enum_2Enum,V1t_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2ESUM_2E1(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum(V0h_2E0,V1t_2E0)) = mono_2Ec_2Earithmetic_2E_2B_2E2(V0h_2E0,mono_2Ec_2Elist_2ESUM_2E1(V1t_2E0)) ) ) ).

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

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

tff(thm_2Elist_2ELENGTH,axiom,
    ! [A_27a: d] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) = mono_2Ec_2Enum_2E0_2E0 )
      & ! [V0h_2E0: u,V1t_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) = mono_2Ec_2Enum_2ESUC_2E1(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) ) ) ).

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

tff(thm_2Elist_2ELIST__TO__SET__DEF,axiom,
    ! [A_27a: d] :
      ( ! [V0x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__TO__SET_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(A_27a,V0x_2E0)))) = mono_2Ec_2Ebool_2EF_2E0 )
      & ! [V1h_2E0: u,V2t_2E0: u,V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__TO__SET_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(A_27a,V3x_2E0)))))
        <=> ( ( s(A_27a,V3x_2E0) = s(A_27a,V1h_2E0) )
            | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__TO__SET_2E2(s(tyop_2Elist_2Elist(A_27a),V2t_2E0),s(A_27a,V3x_2E0))))) ) ) ) ).

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

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

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

tff(thm_2Elist_2EEVERY__DEF,axiom,
    ! [A_27a: d] :
      ( ! [V0P_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ! [V1P_2E0: u,V2h_2E0: u,V3t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))
        <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))) ) ) ) ).

tff(thm_2Elist_2EEXISTS__DEF,axiom,
    ! [A_27a: d] :
      ( ! [V0P_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) = mono_2Ec_2Ebool_2EF_2E0 )
      & ! [V1P_2E0: u,V2h_2E0: u,V3t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))
        <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0)))))
            | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))) ) ) ) ).

tff(thm_2Elist_2EEL,axiom,
    ! [A_27a: d] :
      ( ! [V0l_2E0: u] : ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) )
      & ! [V1l_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V2n_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ) ).

tff(thm_2Elist_2EINDEX__FIND__def,axiom,
    ! [A_27a: d] :
      ( ! [V0i_2E0: mono_2Etyop_2Enum_2Enum,V1P_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0i_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ENONE_2E0) )
      & ! [V2i_2E0: mono_2Etyop_2Enum_2Enum,V3P_2E0: u,V4h_2E0: u,V5t_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V4h_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)),s(A_27a,V4h_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V2i_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0))))) ) ) ).

tff(thm_2Elist_2EFIND__def,axiom,
    ! [A_27a: d,V0P_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2EFIND_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a),c_2Epair_2ESND_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Elist_2EINDEX__FIND_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) ) ).

tff(thm_2Elist_2EINDEX__OF__def,axiom,
    ! [A_27a: d,V0x_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Elist_2EINDEX__OF_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Elist_2EINDEX__FIND_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V0x_2E0))))))) ) ).

tff(thm_2Elist_2ELUPDATE__def,axiom,
    ! [A_27a: d] :
      ( ! [V0e_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0e_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V2e_2E0: u,V3x_2E0: u,V4l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2e_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3x_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))) )
      & ! [V5e_2E0: u,V6n_2E0: mono_2Etyop_2Enum_2Enum,V7x_2E0: u,V8l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V5e_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V6n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),V8l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V5e_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6n_2E0)),s(tyop_2Elist_2Elist(A_27a),V8l_2E0))))) ) ) ).

tff(thm_2Elist_2EEVERYi__def,axiom,
    ! [A_27a: d] :
      ( ! [V0P_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ! [V1P_2E0: u,V2h_2E0: u,V3t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))
        <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),s(A_27a,V2h_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Enum_2ESUC_2E0)))),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))) ) ) ) ).

tff(thm_2Elist_2EsplitAtPki__def,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V3k_2E0: u,V4h_2E0: u,V6p_2E0: u,V7s_2E0: u] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0))),s(A_27b,V4h_2E0))),s(tyop_2Elist_2Elist(A_27b),V6p_2E0))),s(tyop_2Elist_2Elist(A_27b),V7s_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_2E0),s(tyop_2Elist_2Elist(A_27b),V6p_2E0))))),s(tyop_2Elist_2Elist(A_27b),V7s_2E0))) )
     => ( ! [V0P_2E0: u,V1k_2E0: u] : ( s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) )
        & ! [V2P_2E0: u,V3k_2E0: u,V4h_2E0: u,V5t_2E0: u] : ( s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_2E0))))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),s(A_27b,V4h_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_2E0))))),s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Enum_2ESUC_2E0)))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0))),s(A_27b,V4h_2E0))),s(tyop_2Elist_2Elist(A_27b),V5t_2E0))))) ) ) ) ).

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

tff(thm_2Elist_2ELIST__IGNORE__BIND__def,axiom,
    ! [A_27a: d,A_27b: d,V0m1_2E0: u,V1m2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__IGNORE__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0m1_2E0),s(tyop_2Elist_2Elist(A_27a),V1m2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0m1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Elist_2Elist(A_27a),V1m2_2E0))))) ) ).

tff(thm_2Elist_2ELIST__GUARD__def,axiom,
    ! [V0b_2E0: mono_2Etyop_2Emin_2Ebool] : ( mono_2Ec_2Elist_2ELIST__GUARD_2E1(V0b_2E0) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29(V0b_2E0,mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Eone_2Eone_2E0,mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Eone_2Eone),mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Eone_2Eone) ) ).

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

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

tff(thm_2Elist_2ESHORTLEX__def,axiom,
    ! [A_27a: d,F1_2E0: u,F2_2E0: u,F0_2E0: u] :
      ( ! [V4t1_2E0: u,V7t2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0)))))
        <=> ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4t1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V7t2_2E0)))) ) )
     => ( ! [V3h1_2E0: u,V6h2_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0)))))
          <=> ( s(A_27a,V3h1_2E0) = s(A_27a,V6h2_2E0) ) )
       => ( ! [V4t1_2E0: u,V2R_2E0: u,V3h1_2E0: u,V6h2_2E0: u,V7t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0))),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0)))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(mono_2Ec_2Eprim__rec_2E_3C_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4t1_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))))),mono_2Ec_2Ebool_2ET_2E0,mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0)))),mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0)))),mono_2Ec_2Ebool_2ET_2E0,mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0)))),j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0)))),mono_2Ec_2Ebool_2EF_2E0)),mono_2Ec_2Ebool_2EF_2E0)) )
         => ( ! [V0R_2E0: u,V1l2_2E0: u] :
                ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))
              <=> ( s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
            & ! [V2R_2E0: u,V3h1_2E0: u,V4t1_2E0: u,V5l2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V5l2_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3h1_2E0)))))) ) ) ) ) ) ).

tff(thm_2Elist_2ELLEX__def,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V3h1_2E0: u,V6h2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0)))))
        <=> ( s(A_27a,V3h1_2E0) = s(A_27a,V6h2_2E0) ) )
     => ( ! [V2R_2E0: u,V3h1_2E0: u,V4t1_2E0: u,V6h2_2E0: u,V7t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3h1_2E0))),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(A_27a,V6h2_2E0))),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0)))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0)))),mono_2Ec_2Ebool_2ET_2E0,mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0)))),j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0)))),mono_2Ec_2Ebool_2EF_2E0)) )
       => ( ! [V0R_2E0: u,V1l2_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))
            <=> ( s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
          & ! [V2R_2E0: u,V3h1_2E0: u,V4t1_2E0: u,V5l2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V5l2_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3h1_2E0))),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0)))))) ) ) ) ) ).

tff(thm_2Elist_2Enub__def,axiom,
    ! [A_27a: d] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V0x_2E0: u,V1l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))) ) ) ).

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

tff(thm_2Elist_2EUNIQUE__DEF,axiom,
    ! [A_27a: d,V0e_2E0: u,V1L_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EUNIQUE_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))))
    <=> ? [V2L1_2E0: u,V3L2_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2L1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3L2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1L_2E0) )
          & ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2L1_2E0)))))))
          & ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3L2_2E0))))))) ) ) ).

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

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

tff(thm_2Elist_2EoEL__def,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1n_2E0))
        <=> ( V1n_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
        & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2x_2E0: u,V3xs_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1n_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V1n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))) ) ) ) ).

tff(thm_2Elist_2EEXISTS__LIST,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ? [V1l_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
    <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
        | ? [V2h_2E0: u,V3t_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))))) ) ) ).

tff(thm_2Elist_2ESUM__SUM__ACC,axiom,
    ! [V0L_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2ESUM_2E1(V0L_2E0) = mono_2Ec_2Elist_2ESUM__ACC_2E2(V0L_2E0,mono_2Ec_2Enum_2E0_2E0) ) ).

tff(thm_2Elist_2ESUM__ACC__SUM__LEM,axiom,
    ! [V0L_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Elist_2ESUM__ACC_2E2(V0L_2E0,V1n_2E0) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Elist_2ESUM_2E1(V0L_2E0),V1n_2E0) ) ).

tff(thm_2Elist_2EREVERSE__REV,axiom,
    ! [A_27a: d,V0L_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0L_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),V0L_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) ) ).

tff(thm_2Elist_2ELENGTH__LEN,axiom,
    ! [A_27a: d,V0L_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0L_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),V0L_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0))))) ) ).

tff(thm_2Elist_2EREV__REVERSE__LEM,axiom,
    ! [A_27a: d,V0L1_2E0: u,V1L2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),V0L1_2E0),s(tyop_2Elist_2Elist(A_27a),V1L2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0L1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1L2_2E0))) ) ).

tff(thm_2Elist_2ELEN__LENGTH__LEM,axiom,
    ! [A_27a: d,V0L_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),V0L_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0L_2E0)))),V1n_2E0) ) ).

tff(thm_2Elist_2EINFINITE__LIST__UNIV,axiom,
    ! [A_27a: d] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) ).

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

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

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

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

tff(thm_2Elist_2EREVERSE__GENLIST,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1f_2E0: u,V0n_2E0: mono_2Etyop_2Enum_2Enum,V2m_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2m_2E0)))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(mono_2Ec_2Eprim__rec_2EPRE_2E1(V0n_2E0),V2m_2E0))))) )
     => ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))) ) ) ).

tff(thm_2Elist_2EEL__REVERSE,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))
     => ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2EPRE_2E1(mono_2Ec_2Earithmetic_2E_2D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))),V0n_2E0)))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) ) ) ).

tff(thm_2Elist_2ESUM__IMAGE__eq__SUM__MAP__SET__TO__LIST,axiom,
    ! [A_27a: d,V0s_2E0: u,V1f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) = mono_2Ec_2Elist_2ESUM_2E1(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) ) ) ).

tff(thm_2Elist_2ESUM__MAP__FOLDL,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V2a_2E0: mono_2Etyop_2Enum_2Enum,V3e_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2a_2E0)))),s(A_27a,V3e_2E0)))) = mono_2Ec_2Earithmetic_2E_2B_2E2(V2a_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V3e_2E0))))) )
     => ! [V0f_2E0: u,V1ls_2E0: u] : ( mono_2Ec_2Elist_2ESUM_2E1(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))) ) ) ).

tff(thm_2Elist_2ESUM__APPEND,axiom,
    ! [V0l1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1l2_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2ESUM_2E1(mono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum(V0l1_2E0,V1l2_2E0)) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Elist_2ESUM_2E1(V0l1_2E0),mono_2Ec_2Elist_2ESUM_2E1(V1l2_2E0)) ) ).

tff(thm_2Elist_2ESUM__SNOC,axiom,
    ! [V0x_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2ESUM_2E1(mono_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Enum_2Enum(V0x_2E0,V1l_2E0)) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Elist_2ESUM_2E1(V1l_2E0),V0x_2E0) ) ).

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

tff(thm_2Elist_2EALL__DISTINCT__GENLIST,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0))))))))
    <=> ! [V2m1_2E0: mono_2Etyop_2Enum_2Enum,V3m2_2E0: mono_2Etyop_2Enum_2Enum] :
          ( ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2m1_2E0,V0n_2E0))
            & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3m2_2E0,V0n_2E0))
            & ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2m1_2E0)))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3m2_2E0)))) ) )
         => ( V2m1_2E0 = V3m2_2E0 ) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT__SNOC,axiom,
    ! [A_27a: d,V0x_2E0: u,V1l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))
    <=> ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ) ).

tff(thm_2Elist_2EMEM__GENLIST,axiom,
    ! [A_27a: d,V0x_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0))))))))))
    <=> ? [V3m_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3m_2E0,V1n_2E0))
          & ( s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3m_2E0)))) ) ) ) ).

tff(thm_2Elist_2EGENLIST__NUMERALS,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(V0n_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(V0n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) ) ) ).

tff(thm_2Elist_2EGENLIST__GENLIST__AUX,axiom,
    ! [A_27a: d,V0f_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) ) ).

tff(thm_2Elist_2ENULL__GENLIST,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0))))))))
    <=> ( V0n_2E0 = mono_2Ec_2Enum_2E0_2E0 ) ) ).

tff(thm_2Elist_2EGENLIST__CONS,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V0n_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Enum_2ESUC_2E0)))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))))) ) ).

tff(thm_2Elist_2EZIP__GENLIST,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0l_2E0: u,V1f_2E0: u,V3x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)))),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3x_2E0)))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3x_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3x_2E0)))))) )
     => ! [V0l_2E0: u,V1f_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) = V2n_2E0 )
         => ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)))),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))) ) ) ) ).

tff(thm_2Elist_2ETL__GENLIST,axiom,
    ! [A_27a: d,V0f_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Enum_2ESUC_2E0)))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))) ) ).

tff(thm_2Elist_2EEXISTS__GENLIST,axiom,
    ! [A_27a: d,V0f_2E0: u,V1P_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0))))))))
    <=> ? [V3i_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3i_2E0,V2n_2E0))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)))))))) ) ) ).

tff(thm_2Elist_2EEVERY__GENLIST,axiom,
    ! [A_27a: d,V0f_2E0: u,V1P_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0))))))))
    <=> ! [V3i_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3i_2E0,V2n_2E0))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)))))))) ) ) ).

tff(thm_2Elist_2EGENLIST__APPEND,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V2b_2E0: mono_2Etyop_2Enum_2Enum,V3t_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2b_2E0)))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3t_2E0)))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V3t_2E0,V2b_2E0))))) )
     => ! [V0f_2E0: u,V1a_2E0: mono_2Etyop_2Enum_2Enum,V2b_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V1a_2E0,V2b_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2b_2E0)))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2b_2E0)))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)))))) ) ) ).

tff(thm_2Elist_2EGENLIST__FUN__EQ,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V2g_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))) )
    <=> ! [V3x_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3x_2E0,V0n_2E0))
         => ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3x_2E0)))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3x_2E0)))) ) ) ) ).

tff(thm_2Elist_2EHD__GENLIST__COR,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,V0n_2E0))
     => ( s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) ) ) ).

tff(thm_2Elist_2EHD__GENLIST,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u] : ( s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V0n_2E0))))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) ) ).

tff(thm_2Elist_2EEL__GENLIST,axiom,
    ! [A_27a: d,V0f_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2x_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2x_2E0,V1n_2E0))
     => ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)))) ) ) ).

tff(thm_2Elist_2EMAP__GENLIST,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))) ) ).

tff(thm_2Elist_2EGENLIST__AUX__compute,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u,V1l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) )
      & ! [V2f_2E0: u,V3n_2E0: mono_2Etyop_2Enum_2Enum,V4l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0)))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0)),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0)),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))))) )
      & ! [V5f_2E0: u,V6n_2E0: mono_2Etyop_2Enum_2Enum,V7l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V6n_2E0)))),s(tyop_2Elist_2Elist(A_27a),V7l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V6n_2E0)))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V6n_2E0)))))),s(tyop_2Elist_2Elist(A_27a),V7l_2E0))))) ) ) ).

tff(thm_2Elist_2ELENGTH__GENLIST,axiom,
    ! [A_27a: d,V0f_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0))))))) = V1n_2E0 ) ).

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

tff(thm_2Elist_2ESNOC__INDUCT,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
        & ! [V1l_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
           => ! [V2x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))) ) )
     => ! [V3l_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))) ) ).

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

tff(thm_2Elist_2EREVERSE__SNOC,axiom,
    ! [A_27a: d,V0x_2E0: u,V1l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ).

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

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

tff(thm_2Elist_2EMEM__SNOC,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))))
    <=> ( ( s(A_27a,V0y_2E0) = s(A_27a,V1x_2E0) )
        | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))))) ) ) ).

tff(thm_2Elist_2EEXISTS__SNOC,axiom,
    ! [A_27a: d,V0P_2E0: u,V1x_2E0: u,V2l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))
    <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))))
        | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) ) ) ).

tff(thm_2Elist_2EEVERY__SNOC,axiom,
    ! [A_27a: d,V0P_2E0: u,V1x_2E0: u,V2l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))
    <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))))) ) ) ).

tff(thm_2Elist_2EAPPEND__SNOC,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1x_2E0: u,V2l2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) ) ).

tff(thm_2Elist_2EEL__LENGTH__SNOC,axiom,
    ! [A_27a: d,V0l_2E0: u,V1x_2E0: u] : ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(A_27a,V1x_2E0) ) ).

tff(thm_2Elist_2EEL__SNOC,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))
     => ! [V2x_2E0: u] : ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) ) ) ).

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

tff(thm_2Elist_2ELIST__TO__SET__SNOC,axiom,
    ! [A_27a: d,V0x_2E0: u,V1ls_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) ) ).

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

tff(thm_2Elist_2EFRONT__SNOC,axiom,
    ! [A_27a: d,V0x_2E0: u,V1l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) ) ).

tff(thm_2Elist_2ELAST__SNOC,axiom,
    ! [A_27a: d,V0x_2E0: u,V1l_2E0: u] : ( s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27a,V0x_2E0) ) ).

tff(thm_2Elist_2ELENGTH__SNOC,axiom,
    ! [A_27a: d,V0x_2E0: u,V1l_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) = mono_2Ec_2Enum_2ESUC_2E1(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ).

tff(thm_2Elist_2EisPREFIX__CONSR,axiom,
    ! [A_27a: d,V0ys_2E0: u,V1y_2E0: u,V2x_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V2x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1y_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))))
    <=> ( ( s(tyop_2Elist_2Elist(A_27a),V2x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
        | ? [V3xs_2E0: u] :
            ( ( s(tyop_2Elist_2Elist(A_27a),V2x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1y_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V3xs_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))))) ) ) ) ).

tff(thm_2Elist_2EisPREFIX__NILR,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
    <=> ( s(tyop_2Elist_2Elist(A_27a),V0x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ).

tff(thm_2Elist_2EisPREFIX__THM,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2t_2E0: u,V3l_2E0: u,V4h2_2E0: u,V5h1_2E0: u,V6h_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) = mono_2Ec_2Ebool_2EF_2E0 )
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))))))
      <=> ( ( s(A_27a,V5h1_2E0) = s(A_27a,V4h2_2E0) )
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V1t1_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0))))) ) ) ) ).

tff(thm_2Elist_2EITSET__eq__FOLDL__SET__TO__LIST,axiom,
    ! [A_27a: d,A_27b: d,V0s_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))
     => ! [V1f_2E0: u,V2a_2E0: u] : ( s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27b,V2a_2E0))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0))),s(A_27b,V2a_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT__SET__TO__LIST,axiom,
    ! [A_27a: d,V0s_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) ) ).

tff(thm_2Elist_2ESET__TO__LIST__SING,axiom,
    ! [A_27a: d,V0x_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) ) ).

tff(thm_2Elist_2EMEM__SET__TO__LIST,axiom,
    ! [A_27a: d,V0s_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))
     => ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) ) ) ).

tff(thm_2Elist_2ESET__TO__LIST__IN__MEM,axiom,
    ! [A_27a: d,V0s_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))
     => ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) ) ) ).

tff(thm_2Elist_2ESET__TO__LIST__CARD,axiom,
    ! [A_27a: d,V0s_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) ) ) ).

tff(thm_2Elist_2ESET__TO__LIST__INV,axiom,
    ! [A_27a: d,V0s_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))
     => ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) ) ) ).

tff(thm_2Elist_2ESET__TO__LIST__EMPTY,axiom,
    ! [A_27a: d] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ).

tff(thm_2Elist_2ESET__TO__LIST__IND,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ! [V1s_2E0: u] :
          ( ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))
              & ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) ) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) )
     => ! [V2v_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2v_2E0))))) ) ).

tff(thm_2Elist_2ESET__TO__LIST__THM,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0s_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))
        <=> ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) ) )
     => ! [V0s_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))
         => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))))) ) ) ) ).

tff(thm_2Elist_2ELIST__TO__SET__FILTER,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1P_2E0: u,V2x_2E0: u] : ( s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0))))) )
     => ! [V0l_2E0: u,V1P_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) ) ) ).

tff(thm_2Elist_2ELIST__TO__SET__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1l_2E0: u] : ( s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ).

tff(thm_2Elist_2ELIST__TO__SET__THM,axiom,
    ! [A_27a: d,A_27b: d,V0t_2E0: u,V1h_2E0: u] :
      ( ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) )
      & ( s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V1h_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) ) ) ).

tff(thm_2Elist_2ELIST__TO__SET__REVERSE,axiom,
    ! [A_27a: d,V0ls_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) ) ).

tff(thm_2Elist_2ECARD__LIST__TO__SET__ALL__DISTINCT,axiom,
    ! [A_27a: d,V0ls_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) ) ).

tff(thm_2Elist_2EALL__DISTINCT__CARD__LIST__TO__SET,axiom,
    ! [A_27a: d,V0ls_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) ) ) ).

tff(thm_2Elist_2ECARD__LIST__TO__SET,axiom,
    ! [A_27a: d,V0ls_2E0: u] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) ).

tff(thm_2Elist_2EINJ__MAP__EQ__IFF,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))
     => ( ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) )
      <=> ( s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) ) ) ) ).

tff(thm_2Elist_2EINJ__MAP__EQ,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))
        & ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) ) )
     => ( s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) ) ) ).

tff(thm_2Elist_2ESUM__MAP__MEM__bound,axiom,
    ! [A_27a: d,V0f_2E0: u,V1x_2E0: u,V2ls_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2ls_2E0)))))))
     => p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1x_2E0)))),mono_2Ec_2Elist_2ESUM_2E1(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0))))))) ) ).

tff(thm_2Elist_2ESUM__IMAGE__LIST__TO__SET__upper__bound,axiom,
    ! [A_27a: d,V0f_2E0: u,V1ls_2E0: u] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))),mono_2Ec_2Elist_2ESUM_2E1(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))) ).

tff(thm_2Elist_2EFINITE__LIST__TO__SET,axiom,
    ! [A_27a: d,V0l_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) ).

tff(thm_2Elist_2ELIST__TO__SET__EQ__EMPTY,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ( ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) )
      <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
      & ( ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) )
      <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ) ).

tff(thm_2Elist_2EUNION__APPEND,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) ) ).

tff(thm_2Elist_2ELIST__TO__SET__APPEND,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) ) ).

tff(thm_2Elist_2ELRC__MEM__right,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2t_2E0: u,V3h_2E0: u,V4e_2E0: u,V5R_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2t_2E0))))))) )
     => ? [V6z_2E0: u,V7p_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R_2E0),s(A_27a,V6z_2E0))),s(A_27a,V4e_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R_2E0),s(tyop_2Elist_2Elist(A_27a),V7p_2E0),s(A_27a,V1x_2E0),s(A_27a,V6z_2E0))))) ) ) ).

tff(thm_2Elist_2ELRC__MEM,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2ls_2E0: u,V3e_2E0: u,V4R_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2ls_2E0))))))) )
     => ? [V5z_2E0: u,V6t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(A_27a,V3e_2E0))),s(A_27a,V5z_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V6t_2E0),s(A_27a,V5z_2E0),s(A_27a,V0y_2E0))))) ) ) ).

tff(thm_2Elist_2ENRC__LRC,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum,V3R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))))
    <=> ? [V4ls_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V4ls_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))))
          & ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4ls_2E0)))) = V2n_2E0 ) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT__FLAT__REVERSE,axiom,
    ! [A_27a: d,V0xs_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0xs_2E0)))))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0xs_2E0)))))) ) ).

tff(thm_2Elist_2EALL__DISTINCT__REVERSE,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) ) ).

tff(thm_2Elist_2EALL__DISTINCT__ZIP__SWAP,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))))
        & ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) ) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))))))) ) ).

tff(thm_2Elist_2EALL__DISTINCT__ZIP,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))
        & ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) ) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))))) ) ).

tff(thm_2Elist_2EALL__DISTINCT__SING,axiom,
    ! [A_27a: d,V0x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))))) ).

tff(thm_2Elist_2EALL__DISTINCT__APPEND,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))
    <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))
        & ! [V2e_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))))
           => ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))))) ) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT__EL__IMP,axiom,
    ! [A_27a: d,V0l_2E0: u,V1n1_2E0: mono_2Etyop_2Enum_2Enum,V2n2_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
        & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V1n1_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))
        & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2n2_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) )
     => ( ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n1_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n2_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) )
      <=> ( V1n1_2E0 = V2n2_2E0 ) ) ) ).

tff(thm_2Elist_2EEL__ALL__DISTINCT__EL__EQ,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
    <=> ! [V1n1_2E0: mono_2Etyop_2Enum_2Enum,V2n2_2E0: mono_2Etyop_2Enum_2Enum] :
          ( ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V1n1_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))
            & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2n2_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) )
         => ( ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n1_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n2_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) )
          <=> ( V1n1_2E0 = V2n2_2E0 ) ) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1ls_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) ) ).

tff(thm_2Elist_2EFILTER__ALL__DISTINCT,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))) ) ).

tff(thm_2Elist_2EALL__DISTINCT__FILTER,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
    <=> ! [V1x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))
         => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V1x_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) ) ) ) ).

tff(thm_2Elist_2EEVERY2__mono,axiom,
    ! [A_27a: d,A_27b: d,V0l2_2E0: u,V1l1_2E0: u,V2R2_2E0: u,V3R1_2E0: u] :
      ( ! [V4x_2E0: u,V5y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))) ) ) ).

tff(thm_2Elist_2EEVERY2__LENGTH,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) ) ) ).

tff(thm_2Elist_2EEVERY2__EVERY,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u,V2f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))
    <=> ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) )
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))))) ) ) ).

tff(thm_2Elist_2EMAP__EQ__EVERY2,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V0f1_2E0: u,V1f2_2E0: u,V4x_2E0: u,V5y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),V1f2_2E0))),s(A_27a,V4x_2E0))),s(A_27c,V5y_2E0)))))
        <=> ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f2_2E0),s(A_27c,V5y_2E0))) ) )
     => ! [V0f1_2E0: u,V1f2_2E0: u,V2l1_2E0: u,V3l2_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f2_2E0),s(tyop_2Elist_2Elist(A_27c),V3l2_2E0))) )
        <=> ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27c),V3l2_2E0)))) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),V1f2_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27c),V3l2_2E0))))) ) ) ) ).

tff(thm_2Elist_2EEVERY2__cong,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l1_27_2E0: u,V2l2_2E0: u,V3l2_27_2E0: u,V4P_2E0: u,V5P_27_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0) )
        & ( s(tyop_2Elist_2Elist(A_27b),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0) )
        & ! [V6x_2E0: u,V7y_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0)))))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V7y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0))))))) )
           => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4P_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_27_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0)))) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0)))) ) ) ).

tff(thm_2Elist_2EFOLDL2__FOLDL,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V2f_2E0: u,V4a_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0))),s(A_27c,V4a_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0),s(A_27c,V4a_2E0))))) )
     => ! [V0l1_2E0: u,V1l2_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) )
         => ! [V2f_2E0: u,V3a_2E0: u] : ( s(A_27c,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0),s(A_27c,V3a_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(A_27c,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0))),s(A_27c,V3a_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) ) ) ) ).

tff(thm_2Elist_2EFOLDL2__cong,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0l1_2E0: u,V1l1_27_2E0: u,V2l2_2E0: u,V3l2_27_2E0: u,V4a_2E0: u,V5a_27_2E0: u,V6f_2E0: u,V7f_27_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0) )
        & ( s(tyop_2Elist_2Elist(A_27b),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0) )
        & ( s(A_27c,V4a_2E0) = s(A_27c,V5a_27_2E0) )
        & ! [V8z_2E0: u,V9b_2E0: u,V10c_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V9b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0)))))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V10c_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0))))))) )
           => ( s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V6f_2E0),s(A_27c,V8z_2E0))),s(A_27a,V9b_2E0))),s(A_27b,V10c_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V7f_27_2E0),s(A_27c,V8z_2E0))),s(A_27a,V9b_2E0))),s(A_27b,V10c_2E0))) ) ) )
     => ( s(A_27c,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V6f_2E0),s(A_27c,V4a_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) = s(A_27c,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V7f_27_2E0),s(A_27c,V5a_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0))) ) ) ).

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

tff(thm_2Elist_2EFOLDL2__ind,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0P_2E0: u] :
      ( ( ! [V1f_2E0: u,V2a_2E0: u,V3b_2E0: u,V4bs_2E0: u,V5c_2E0: u,V6cs_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1f_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1f_2E0),s(A_27a,V2a_2E0))),s(A_27b,V3b_2E0))),s(A_27c,V5c_2E0))))),s(tyop_2Elist_2Elist(A_27b),V4bs_2E0))),s(tyop_2Elist_2Elist(A_27c),V6cs_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1f_2E0))),s(A_27a,V2a_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3b_2E0),s(tyop_2Elist_2Elist(A_27b),V4bs_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V5c_2E0),s(tyop_2Elist_2Elist(A_27c),V6cs_2E0))))))) )
        & ! [V7f_2E0: u,V8a_2E0: u,V9cs_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V7f_2E0))),s(A_27a,V8a_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27c),V9cs_2E0)))))
        & ! [V10f_2E0: u,V11a_2E0: u,V12v6_2E0: u,V13v7_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V10f_2E0))),s(A_27a,V11a_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V12v6_2E0),s(tyop_2Elist_2Elist(A_27b),V13v7_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))))) )
     => ! [V14v_2E0: u,V15v1_2E0: u,V16v2_2E0: u,V17v3_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V14v_2E0))),s(A_27a,V15v1_2E0))),s(tyop_2Elist_2Elist(A_27b),V16v2_2E0))),s(tyop_2Elist_2Elist(A_27c),V17v3_2E0))))) ) ).

tff(thm_2Elist_2EDROP__NIL,axiom,
    ! [A_27a: d,V0ls_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
    <=> p(mono_2Ec_2Earithmetic_2E_3E_3D_2E2(V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) ) ).

tff(thm_2Elist_2EMEM__DROP,axiom,
    ! [A_27a: d,V0x_2E0: u,V1ls_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))))
    <=> ( ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))
          & ( s(A_27a,V0x_2E0) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) ) )
        | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V2n_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))))) ) ) ).

tff(thm_2Elist_2ELENGTH__DROP,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) = mono_2Ec_2Earithmetic_2E_2D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))),V0n_2E0) ) ).

tff(thm_2Elist_2ETAKE__DROP,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) ) ).

tff(thm_2Elist_2EDROP__0,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) ).

tff(thm_2Elist_2ETAKE__APPEND2,axiom,
    ! [A_27a: d,V0l2_2E0: u,V1l1_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))),V2n_2E0))
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V2n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))) ) ) ).

tff(thm_2Elist_2ETAKE__APPEND1,axiom,
    ! [A_27a: d,V0l2_2E0: u,V1l1_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))))
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) ) ) ).

tff(thm_2Elist_2EMAP__TAKE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) ) ).

tff(thm_2Elist_2ELENGTH__TAKE,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] :
      ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) = V0n_2E0 ) ) ).

tff(thm_2Elist_2ETAKE__LENGTH__ID,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) ).

tff(thm_2Elist_2ETAKE__0,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ).

tff(thm_2Elist_2EDROP__cons,axiom,
    ! [A_27a: d,V0xs_2E0: u,V1x_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,V2n_2E0))
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V2n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) ) ) ).

tff(thm_2Elist_2EDROP__nil,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ).

tff(thm_2Elist_2ETAKE__cons,axiom,
    ! [A_27a: d,V0xs_2E0: u,V1x_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,V2n_2E0))
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V2n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) ) ) ).

tff(thm_2Elist_2ETAKE__nil,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ).

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

tff(thm_2Elist_2ELAST__CONS__cond,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0)))))
        <=> ( s(tyop_2Elist_2Elist(A_27a),V0t_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
     => ! [V0t_2E0: u,V1h_2E0: u] : ( s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0))))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0))),s(A_27a,V1h_2E0),s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0t_2E0))))) ) ) ).

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

tff(thm_2Elist_2EFRONT__CONS__EQ__NIL,axiom,
    ! [A_27a: d] :
      ( ! [V0x_2E0: u,V1xs_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
        <=> ( s(tyop_2Elist_2Elist(A_27a),V1xs_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
      & ! [V2x_2E0: u,V3xs_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))) )
        <=> ( s(tyop_2Elist_2Elist(A_27a),V3xs_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
      & ! [V4x_2E0: u,V5xs_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V5xs_2E0)))))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V5xs_2E0)))) ) ) ).

tff(thm_2Elist_2ELENGTH__FRONT__CONS,axiom,
    ! [A_27a: d,V0x_2E0: u,V1xs_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0)))))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1xs_2E0)))) ) ).

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

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

tff(thm_2Elist_2ELAST__EL,axiom,
    ! [A_27a: d,V0ls_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V0ls_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
     => ( s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2EPRE_2E1(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) ) ) ).

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

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

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

tff(thm_2Elist_2EREVERSE__EQ__NIL,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
    <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ).

tff(thm_2Elist_2ELENGTH__REVERSE,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) ) ).

tff(thm_2Elist_2EMEM__REVERSE,axiom,
    ! [A_27a: d,V0l_2E0: u,V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) ) ).

tff(thm_2Elist_2EREVERSE__11,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) )
    <=> ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) ) ) ).

tff(thm_2Elist_2EREVERSE__REVERSE,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) ).

tff(thm_2Elist_2EREVERSE__APPEND,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) ) ).

tff(thm_2Elist_2ELIST__REL__EVERY__ZIP,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))
    <=> ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) )
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))))))))) ) ) ).

tff(thm_2Elist_2ESUM__MAP__PLUS__ZIP,axiom,
    ! [A_27a: d,A_27b: d,V0h_2E0: u,V1g_2E0: u,V2f_2E0: u,V3ls1_2E0: u,V4ls2_2E0: u] :
      ( ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3ls1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V4ls2_2E0)))) )
        & ! [V5x_2E0: u,V6y_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27b,V6y_2E0)))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(A_27a,V5x_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V0h_2E0),s(A_27b,V6y_2E0))))) ) )
     => ( mono_2Ec_2Elist_2ESUM_2E1(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V3ls1_2E0),s(tyop_2Elist_2Elist(A_27b),V4ls2_2E0))))))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Elist_2ESUM_2E1(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(tyop_2Elist_2Elist(A_27a),V3ls1_2E0))))),mono_2Ec_2Elist_2ESUM_2E1(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Elist_2Elist(A_27b),V4ls2_2E0)))))) ) ) ).

tff(thm_2Elist_2EMEM__EL,axiom,
    ! [A_27a: d,V0l_2E0: u,V1x_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))
    <=> ? [V2n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))
          & ( s(A_27a,V1x_2E0) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) ) ) ) ).

tff(thm_2Elist_2EMAP__ZIP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0l2_2E0: u,V1l1_2E0: u,V2g_2E0: u,V3f_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) )
     => ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) )
        & ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) = s(tyop_2Elist_2Elist(A_27b),V0l2_2E0) )
        & ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) )
        & ( s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) = s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) ) ) ) ).

tff(thm_2Elist_2EMAP2__MAP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) )
     => ! [V2f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) ) ) ).

tff(thm_2Elist_2EMAP2__ZIP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) )
     => ! [V2f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) ) ) ).

tff(thm_2Elist_2EEL__ZIP,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) )
        & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) )
     => ( s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))) ) ) ).

tff(thm_2Elist_2EMEM__ZIP,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u,V2p_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))))))
      <=> ? [V3n_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))))
            & ( s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))) ) ) ) ) ).

tff(thm_2Elist_2EZIP__MAP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V3f2_2E0: u,V5p_2E0: u] : ( s(tyop_2Epair_2Eprod(A_27a,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V3f2_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V5p_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27d),c_2Epair_2E_2C_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V5p_2E0))),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V3f2_2E0),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V5p_2E0))))))) )
     => ( ! [V2f1_2E0: u,V4p_2E0: u] : ( s(tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V2f1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V4p_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f1_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V4p_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V4p_2E0))))) )
       => ! [V0l1_2E0: u,V1l2_2E0: u,V2f1_2E0: u,V3f2_2E0: u] :
            ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) )
           => ( ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V2f1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) )
              & ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V3f2_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V3f2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) ) ) ) ) ) ).

tff(thm_2Elist_2EUNZIP__ZIP,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) )
     => ( s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) ) ) ).

tff(thm_2Elist_2EZIP__UNZIP,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0) ) ).

tff(thm_2Elist_2ELENGTH__UNZIP,axiom,
    ! [A_27a: d,A_27b: d,V0pl_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0pl_2E0)))))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0pl_2E0)))) )
      & ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0pl_2E0)))))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0pl_2E0)))) ) ) ).

tff(thm_2Elist_2ELENGTH__ZIP,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) )
     => ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) )
        & ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) ) ) ) ).

tff(thm_2Elist_2EUNZIP__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0L_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0L_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0L_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0L_2E0))))) ) ).

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

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

tff(thm_2Elist_2EEVERY__MONOTONIC,axiom,
    ! [A_27a: d,V0P_2E0: u,V1Q_2E0: u] :
      ( ! [V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0))))) )
     => ! [V3l_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))) ) ) ).

tff(thm_2Elist_2EEVERY__CONG,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u,V2P_2E0: u,V3P_27_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) )
        & ! [V4x_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))
           => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V4x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V4x_2E0)))) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))) ) ) ).

tff(thm_2Elist_2EEXISTS__CONG,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u,V2P_2E0: u,V3P_27_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) )
        & ! [V4x_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))
           => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V4x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V4x_2E0)))) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))) ) ) ).

tff(thm_2Elist_2EMAP2__CONG,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0l1_2E0: u,V1l1_27_2E0: u,V2l2_2E0: u,V3l2_27_2E0: u,V4f_2E0: u,V5f_27_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0) )
        & ( s(tyop_2Elist_2Elist(A_27b),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0) )
        & ! [V6x_2E0: u,V7y_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0)))))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V7y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0))))))) )
           => ( s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V4f_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V5f_27_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))) ) ) )
     => ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V4f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V5f_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0))) ) ) ).

tff(thm_2Elist_2EMAP__CONG,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u,V2f_2E0: u,V3f_27_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) )
        & ! [V4x_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_27_2E0),s(A_27a,V4x_2E0))) ) ) )
     => ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) ) ) ).

tff(thm_2Elist_2EFOLDL__CONG,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u,V1l_27_2E0: u,V2b_2E0: u,V3b_27_2E0: u,V4f_2E0: u,V5f_27_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0) )
        & ( s(A_27b,V2b_2E0) = s(A_27b,V3b_27_2E0) )
        & ! [V6x_2E0: u,V7a_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0)))))))
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V4f_2E0),s(A_27b,V7a_2E0))),s(A_27a,V6x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V5f_27_2E0),s(A_27b,V7a_2E0))),s(A_27a,V6x_2E0))) ) ) )
     => ( s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V4f_2E0),s(A_27b,V2b_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V5f_27_2E0),s(A_27b,V3b_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0))) ) ) ).

tff(thm_2Elist_2EFOLDR__CONG,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u,V1l_27_2E0: u,V2b_2E0: u,V3b_27_2E0: u,V4f_2E0: u,V5f_27_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0) )
        & ( s(A_27b,V2b_2E0) = s(A_27b,V3b_27_2E0) )
        & ! [V6x_2E0: u,V7a_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0)))))))
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V4f_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V5f_27_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7a_2E0))) ) ) )
     => ( s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V4f_2E0),s(A_27b,V2b_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V5f_27_2E0),s(A_27b,V3b_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0))) ) ) ).

tff(thm_2Elist_2Elist__size__cong,axiom,
    ! [A_27a: d,V0M_2E0: u,V1N_2E0: u,V2f_2E0: u,V3f_27_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V0M_2E0) = s(tyop_2Elist_2Elist(A_27a),V1N_2E0) )
        & ! [V4x_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1N_2E0)))))))
           => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(A_27a,V4x_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f_27_2E0),s(A_27a,V4x_2E0)))) ) ) )
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0M_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1N_2E0)))) ) ) ).

tff(thm_2Elist_2ELIST__REL__SPLIT2,axiom,
    ! [A_27a: d,A_27b: d,V0xs2_2E0: u,V1P_2E0: u,V2xs1_2E0: u,V3zs_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27b),V3zs_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2xs1_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs2_2E0)))))))
    <=> ? [V4ys1_2E0: u,V5ys2_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27b),V3zs_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V4ys1_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys2_2E0))) )
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27b),V4ys1_2E0),s(tyop_2Elist_2Elist(A_27a),V2xs1_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys2_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs2_2E0))))) ) ) ).

tff(thm_2Elist_2ELIST__REL__SPLIT1,axiom,
    ! [A_27a: d,A_27b: d,V0xs2_2E0: u,V1P_2E0: u,V2xs1_2E0: u,V3zs_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2xs1_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs2_2E0))),s(tyop_2Elist_2Elist(A_27b),V3zs_2E0)))))
    <=> ? [V4ys1_2E0: u,V5ys2_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27b),V3zs_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V4ys1_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys2_2E0))) )
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V2xs1_2E0),s(tyop_2Elist_2Elist(A_27b),V4ys1_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs2_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys2_2E0))))) ) ) ).

tff(thm_2Elist_2ELIST__REL__LENGTH,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) ) ) ).

tff(thm_2Elist_2ELIST__REL__MAP2,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V3R_2E0: u,V2f_2E0: u,V6a_2E0: u,V7b_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0))),s(A_27a,V6a_2E0))),s(A_27c,V7b_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V6a_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(A_27c,V7b_2E0)))))) )
     => ( ! [V3R_2E0: u,V4a_2E0: u,V5b_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0))),s(A_27a,V4a_2E0))),s(A_27b,V5b_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V4a_2E0))),s(A_27b,V5b_2E0)))) )
       => ! [V0l2_2E0: u,V1l1_2E0: u,V2f_2E0: u,V3R_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V0l2_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27c),V0l2_2E0)))) ) ) ) ).

tff(thm_2Elist_2ELIST__REL__MAP1,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0l2_2E0: u,V1l1_2E0: u,V2f_2E0: u,V3R_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_2E0))),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) ) ).

tff(thm_2Elist_2ELIST__REL__CONJ,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u,F2_2E0: u,F1_2E0: u] :
      ( ! [V3P_2E0: u,V2Q_2E0: u,V4a_2E0: u,V5b_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0))),s(A_27a,V4a_2E0))),s(A_27b,V5b_2E0)))))
        <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V4a_2E0))),s(A_27b,V5b_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27a,V4a_2E0))),s(A_27b,V5b_2E0))))) ) )
     => ( ! [V2Q_2E0: u,V8a_2E0: u,V9b_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0))),s(A_27a,V8a_2E0))),s(A_27b,V9b_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27a,V8a_2E0))),s(A_27b,V9b_2E0)))) )
       => ( ! [V3P_2E0: u,V6a_2E0: u,V7b_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0))),s(A_27a,V6a_2E0))),s(A_27b,V7b_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V6a_2E0))),s(A_27b,V7b_2E0)))) )
         => ! [V0l2_2E0: u,V1l1_2E0: u,V2Q_2E0: u,V3P_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))))
            <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))) ) ) ) ) ) ).

tff(thm_2Elist_2ELIST__REL__CONS2,axiom,
    ! [A_27a: d,A_27b: d,V0xs_2E0: u,V1t_2E0: u,V2h_2E0: u,V3R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h_2E0),s(tyop_2Elist_2Elist(A_27b),V1t_2E0)))))))
    <=> ? [V4h_27_2E0: u,V5t_27_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),V0xs_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_27_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_27_2E0))) )
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V4h_27_2E0))),s(A_27b,V2h_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_27_2E0),s(tyop_2Elist_2Elist(A_27b),V1t_2E0))))) ) ) ).

tff(thm_2Elist_2ELIST__REL__CONS1,axiom,
    ! [A_27a: d,A_27b: d,V0xs_2E0: u,V1t_2E0: u,V2h_2E0: u,V3R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Elist_2Elist(A_27b),V0xs_2E0)))))
    <=> ? [V4h_27_2E0: u,V5t_27_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27b),V0xs_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_27_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_27_2E0))) )
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V2h_2E0))),s(A_27b,V4h_27_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_27_2E0))))) ) ) ).

tff(thm_2Elist_2ELIST__REL__NIL,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_2E0: u,V2R_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),V0y_2E0)))))
      <=> ( s(tyop_2Elist_2Elist(A_27b),V0y_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) ) )
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))
      <=> ( s(tyop_2Elist_2Elist(A_27a),V1x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ) ).

tff(thm_2Elist_2ELIST__REL__mono,axiom,
    ! [A_27a: d,A_27b: d,V0l2_2E0: u,V1l1_2E0: u,V2R2_2E0: u,V3R1_2E0: u] :
      ( ! [V4x_2E0: u,V5y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))) ) ) ).

tff(thm_2Elist_2ELIST__REL__def,axiom,
    ! [A_27a: d,A_27b: d,V0bs_2E0: u,V1b_2E0: u,V2as_2E0: u,V3a_2E0: u,V4R_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3a_2E0),s(tyop_2Elist_2Elist(A_27a),V2as_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) = mono_2Ec_2Ebool_2EF_2E0 )
      & ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1b_2E0),s(tyop_2Elist_2Elist(A_27b),V0bs_2E0)))))) = mono_2Ec_2Ebool_2EF_2E0 )
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3a_2E0),s(tyop_2Elist_2Elist(A_27a),V2as_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1b_2E0),s(tyop_2Elist_2Elist(A_27b),V0bs_2E0)))))))
      <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(A_27a,V3a_2E0))),s(A_27b,V1b_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V2as_2E0),s(tyop_2Elist_2Elist(A_27b),V0bs_2E0))))) ) ) ) ).

tff(thm_2Elist_2EWF__LIST__PRED,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0L1_2E0: u,V1L2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0L1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1L2_2E0)))))
        <=> ? [V2h_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),V1L2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V0L1_2E0))) ) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0))))) ) ).

tff(thm_2Elist_2ENULL__FILTER,axiom,
    ! [A_27a: d,V0P_2E0: u,V1ls_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))
    <=> ! [V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))
         => ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) ) ) ).

tff(thm_2Elist_2ESUM__eq__0,axiom,
    ! [V0ls_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( mono_2Ec_2Elist_2ESUM_2E1(V0ls_2E0) = mono_2Ec_2Enum_2E0_2E0 )
    <=> ! [V1x_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V1x_2E0,mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(V0ls_2E0)))
         => ( V1x_2E0 = mono_2Ec_2Enum_2E0_2E0 ) ) ) ).

tff(thm_2Elist_2EEL__simp__restricted,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ls_2E0: u,V2l_2E0: u] :
      ( ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V0n_2E0)))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2l_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2EPRE_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) )
      & ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V0n_2E0)))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2l_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V0n_2E0)))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) ) ) ).

tff(thm_2Elist_2EEL__restricted,axiom,
    ! [A_27a: d,A_27b: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ls_2E0: u,V2l_2E0: u] :
      ( ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EHD_2E0) )
      & ( s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V0n_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2l_2E0),s(tyop_2Elist_2Elist(A_27b),V1ls_2E0))))) = s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27b),V1ls_2E0))) ) ) ).

tff(thm_2Elist_2EEL__simp,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] :
      ( ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V0n_2E0)))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2EPRE_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) )
      & ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V0n_2E0)))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V0n_2E0)))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ) ).

tff(thm_2Elist_2EEL__compute,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1n_2E0))
        <=> ( V1n_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ! [V0l_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1n_2E0))),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2EPRE_2E1(V1n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) ) ) ).

tff(thm_2Elist_2ENOT__NULL__MEM,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
    <=> ? [V1e_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) ) ).

tff(thm_2Elist_2EFILTER__COND__REWRITE,axiom,
    ! [A_27a: d,V0l_2E0: u,V1P_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V2h_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0)))))
         => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) ) )
      & ! [V3h_2E0: u] :
          ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3h_2E0)))))
         => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) ) ) ) ).

tff(thm_2Elist_2EEVERY__FILTER__IMP,axiom,
    ! [A_27a: d,V0P1_2E0: u,V1P2_2E0: u,V2l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))))) ) ).

tff(thm_2Elist_2EEVERY__FILTER,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1P2_2E0: u,V0P1_2E0: u,V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0))),s(A_27a,V3x_2E0)))))
        <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0),s(A_27a,V3x_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(A_27a,V3x_2E0))))) ) )
     => ! [V0P1_2E0: u,V1P2_2E0: u,V2l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) ) ) ).

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

tff(thm_2Elist_2EMEM,axiom,
    ! [A_27a: d] :
      ( ! [V0x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) = mono_2Ec_2Ebool_2EF_2E0 )
      & ! [V1x_2E0: u,V2h_2E0: u,V3t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))))
        <=> ( ( s(A_27a,V1x_2E0) = s(A_27a,V2h_2E0) )
            | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))))) ) ) ) ).

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

tff(thm_2Elist_2EFILTER__EQ__CONS,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u,V2h_2E0: u,V3lr_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3lr_2E0))) )
    <=> ? [V4l1_2E0: u,V5l2_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))) )
          & ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V4l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
          & ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V3lr_2E0) )
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2h_2E0))))) ) ) ).

tff(thm_2Elist_2EFILTER__NEQ__ID,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) != s(tyop_2Elist_2Elist(A_27a),V1l_2E0) )
    <=> ? [V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))
          & ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) ) ) ).

tff(thm_2Elist_2EFILTER__EQ__ID,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) )
    <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ).

tff(thm_2Elist_2EFILTER__NEQ__NIL,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
    <=> ? [V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) ) ) ).

tff(thm_2Elist_2EFILTER__EQ__NIL,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0P_2E0: u,V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2x_2E0)))))
        <=> ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) )
     => ! [V0P_2E0: u,V1l_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
        <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ) ).

tff(thm_2Elist_2ELENGTH__TL,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) = mono_2Ec_2Earithmetic_2E_2D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ) ) ).

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

tff(thm_2Elist_2EFOLDL__EQ__FOLDR,axiom,
    ! [A_27a: d,V0f_2E0: u,V1l_2E0: u,V2e_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0))))) )
     => ( s(A_27a,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) ) ) ).

tff(thm_2Elist_2ELIST__EQ,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))) )
        & ! [V2x_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2x_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))))
           => ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) ) ) )
     => ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) ) ) ).

tff(thm_2Elist_2ELIST__EQ__REWRITE,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) )
    <=> ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))) )
        & ! [V2x_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2x_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))))
           => ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) ) ) ) ) ).

tff(thm_2Elist_2EMEM__SPLIT,axiom,
    ! [A_27a: d,V0x_2E0: u,V1l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))
    <=> ? [V2l1_2E0: u,V3l2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))))) ) ) ).

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

tff(thm_2Elist_2EAPPEND__11__LENGTH,axiom,
    ! [A_27a: d] :
      ( ! [V0l1_2E0: u,V1l2_2E0: u,V2l1_27_2E0: u,V3l2_27_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l1_27_2E0)))) )
         => ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0))) )
          <=> ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l1_27_2E0) )
              & ( s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0) ) ) ) )
      & ! [V4l1_2E0: u,V5l2_2E0: u,V6l1_27_2E0: u,V7l2_27_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l2_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V7l2_27_2E0)))) )
         => ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l1_2E0),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V6l1_27_2E0),s(tyop_2Elist_2Elist(A_27a),V7l2_27_2E0))) )
          <=> ( ( s(tyop_2Elist_2Elist(A_27a),V4l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V6l1_27_2E0) )
              & ( s(tyop_2Elist_2Elist(A_27a),V5l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V7l2_27_2E0) ) ) ) ) ) ).

tff(thm_2Elist_2EAPPEND__LENGTH__EQ,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l1_27_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0)))) )
     => ! [V2l2_2E0: u,V3l2_27_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0)))) )
         => ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0))) )
          <=> ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0) )
              & ( s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0) ) ) ) ) ) ).

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

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

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

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

tff(thm_2Elist_2ECONS__ACYCLIC,axiom,
    ! [A_27a: d,V0l_2E0: u,V1x_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) )
      & ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) != s(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) ) ).

tff(thm_2Elist_2ELENGTH__EQ__NIL,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ! [V1l_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) = mono_2Ec_2Enum_2E0_2E0 )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) )
    <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) ) ).

tff(thm_2Elist_2ELENGTH__EQ__NUM__compute,axiom,
    ! [A_27a: d] :
      ( ! [V0l_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) = mono_2Ec_2Enum_2E0_2E0 )
        <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
      & ! [V1l_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V2n_2E0)) )
        <=> ? [V3h_2E0: u,V4l_27_2E0: u] :
              ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0)))) = mono_2Ec_2Earithmetic_2E_2D_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V2n_2E0)),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) )
              & ( s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0))) ) ) )
      & ! [V5l_2E0: u,V6n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l_2E0)))) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V6n_2E0)) )
        <=> ? [V7h_2E0: u,V8l_27_2E0: u] :
              ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V8l_27_2E0)))) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V6n_2E0)) )
              & ( s(tyop_2Elist_2Elist(A_27a),V5l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7h_2E0),s(tyop_2Elist_2Elist(A_27a),V8l_27_2E0))) ) ) )
      & ! [V9l_2E0: u,V10n1_2E0: mono_2Etyop_2Enum_2Enum,V11n2_2E0: mono_2Etyop_2Enum_2Enum] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V9l_2E0)))) = mono_2Ec_2Earithmetic_2E_2B_2E2(V10n1_2E0,V11n2_2E0) )
        <=> ? [V12l1_2E0: u,V13l2_2E0: u] :
              ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V12l1_2E0)))) = V10n1_2E0 )
              & ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V13l2_2E0)))) = V11n2_2E0 )
              & ( s(tyop_2Elist_2Elist(A_27a),V9l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V12l1_2E0),s(tyop_2Elist_2Elist(A_27a),V13l2_2E0))) ) ) ) ) ).

tff(thm_2Elist_2ELENGTH__EQ__NUM,axiom,
    ! [A_27a: d] :
      ( ! [V0l_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) = mono_2Ec_2Enum_2E0_2E0 )
        <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
      & ! [V1l_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) = mono_2Ec_2Enum_2ESUC_2E1(V2n_2E0) )
        <=> ? [V3h_2E0: u,V4l_27_2E0: u] :
              ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0)))) = V2n_2E0 )
              & ( s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0))) ) ) )
      & ! [V5l_2E0: u,V6n1_2E0: mono_2Etyop_2Enum_2Enum,V7n2_2E0: mono_2Etyop_2Enum_2Enum] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l_2E0)))) = mono_2Ec_2Earithmetic_2E_2B_2E2(V6n1_2E0,V7n2_2E0) )
        <=> ? [V8l1_2E0: u,V9l2_2E0: u] :
              ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V8l1_2E0)))) = V6n1_2E0 )
              & ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V9l2_2E0)))) = V7n2_2E0 )
              & ( s(tyop_2Elist_2Elist(A_27a),V5l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V8l1_2E0),s(tyop_2Elist_2Elist(A_27a),V9l2_2E0))) ) ) ) ) ).

tff(thm_2Elist_2ELENGTH__EQ__SUM,axiom,
    ! [A_27a: d,V0l_2E0: u,V1n1_2E0: mono_2Etyop_2Enum_2Enum,V2n2_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) = mono_2Ec_2Earithmetic_2E_2B_2E2(V1n1_2E0,V2n2_2E0) )
    <=> ? [V3l1_2E0: u,V4l2_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0)))) = V1n1_2E0 )
          & ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4l2_2E0)))) = V2n2_2E0 )
          & ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),V4l2_2E0))) ) ) ) ).

tff(thm_2Elist_2ELENGTH__EQ__CONS,axiom,
    ! [A_27a: d,V0P_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ! [V2l_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) = mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0) )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) )
    <=> ! [V3l_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))) = V1n_2E0 )
         => ! [V4x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))))) ) ) ).

tff(thm_2Elist_2ELENGTH__CONS,axiom,
    ! [A_27a: d,V0l_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) = mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0) )
    <=> ? [V2h_2E0: u,V3l_27_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l_27_2E0)))) = V1n_2E0 )
          & ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_27_2E0))) ) ) ) ).

tff(thm_2Elist_2ENULL__LENGTH,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
    <=> ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) = mono_2Ec_2Enum_2E0_2E0 ) ) ).

tff(thm_2Elist_2ENULL__EQ,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
    <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ).

tff(thm_2Elist_2ELENGTH__NIL__SYM,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ( mono_2Ec_2Enum_2E0_2E0 = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) )
    <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ).

tff(thm_2Elist_2ELENGTH__NIL,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) = mono_2Ec_2Enum_2E0_2E0 )
    <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ).

tff(thm_2Elist_2EMEM__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u,V1f_2E0: u,V2x_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))))
    <=> ? [V3y_2E0: u] :
          ( ( s(A_27b,V2x_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3y_2E0))) )
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) ) ) ).

tff(thm_2Elist_2ENOT__EXISTS,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
    <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ).

tff(thm_2Elist_2ENOT__EVERY,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
    <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ).

tff(thm_2Elist_2EEXISTS__APPEND,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))))
    <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))
        | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) ) ) ).

tff(thm_2Elist_2EEVERY__APPEND,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))))
    <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) ) ) ).

tff(thm_2Elist_2EFLAT__compute,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0t2_2E0: u,V1t1_2E0: u,V2t_2E0: u,V3h_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V2t_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V2t_2E0))) )
      & ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V3h_2E0),s(tyop_2Elist_2Elist(A_27c),V1t1_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),V0t2_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V3h_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27c),V1t1_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),V0t2_2E0))))))) ) ) ).

tff(thm_2Elist_2EFLAT__APPEND,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1l2_2E0))))) ) ).

tff(thm_2Elist_2EMEM__FLAT,axiom,
    ! [A_27a: d,V0x_2E0: u,V1L_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1L_2E0)))))))))
    <=> ? [V2l_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V2l_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1L_2E0)))))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))))) ) ) ).

tff(thm_2Elist_2EMEM__FILTER,axiom,
    ! [A_27a: d,V0P_2E0: u,V1L_2E0: u,V2x_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))))))))
    <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1L_2E0))))))) ) ) ).

tff(thm_2Elist_2EMEM__APPEND,axiom,
    ! [A_27a: d,V0e_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))))))
    <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))))
        | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))))) ) ) ).

tff(thm_2Elist_2EEXISTS__NOT__EVERY,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0P_2E0: u,V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2x_2E0)))))
        <=> ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) )
     => ! [V0P_2E0: u,V1l_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
        <=> ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ) ).

tff(thm_2Elist_2EEVERY__NOT__EXISTS,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0P_2E0: u,V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2x_2E0)))))
        <=> ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) )
     => ! [V0P_2E0: u,V1l_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
        <=> ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ) ).

tff(thm_2Elist_2EMONO__EXISTS,axiom,
    ! [A_27a: d,V0l_2E0: u,V1Q_2E0: u,V2P_2E0: u] :
      ( ! [V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) ) ) ).

tff(thm_2Elist_2EEXISTS__SIMP,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0c_2E0: mono_2Etyop_2Emin_2Ebool,V2x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0c_2E0)))),s(A_27a,V2x_2E0)))) = V0c_2E0 )
     => ! [V0c_2E0: mono_2Etyop_2Emin_2Ebool,V1l_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0c_2E0)))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
        <=> ( ( s(tyop_2Elist_2Elist(A_27a),V1l_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
            & p(V0c_2E0) ) ) ) ).

tff(thm_2Elist_2EEXISTS__MAP,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0P_2E0: u,V1f_2E0: u,V3x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))),s(A_27a,V3x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0)))))) )
     => ! [V0P_2E0: u,V1f_2E0: u,V2l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) ) ) ).

tff(thm_2Elist_2EEXISTS__MEM,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
    <=> ? [V2e_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2e_2E0))))) ) ) ).

tff(thm_2Elist_2EMONO__EVERY,axiom,
    ! [A_27a: d,V0l_2E0: u,V1Q_2E0: u,V2P_2E0: u] :
      ( ! [V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) ) ) ).

tff(thm_2Elist_2EEVERY__SIMP,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0c_2E0: mono_2Etyop_2Emin_2Ebool,V2x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0c_2E0)))),s(A_27a,V2x_2E0)))) = V0c_2E0 )
     => ! [V0c_2E0: mono_2Etyop_2Emin_2Ebool,V1l_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0c_2E0)))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
        <=> ( ( s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
            | p(V0c_2E0) ) ) ) ).

tff(thm_2Elist_2EEVERY__MAP,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0P_2E0: u,V1f_2E0: u,V3x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))),s(A_27a,V3x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0)))))) )
     => ! [V0P_2E0: u,V1f_2E0: u,V2l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) ) ) ).

tff(thm_2Elist_2EEVERY__MEM,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
    <=> ! [V2e_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2e_2E0))))) ) ) ).

tff(thm_2Elist_2EEVERY__CONJ,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0P_2E0: u,V1Q_2E0: u,V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(A_27a,V3x_2E0)))))
        <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) ) )
     => ! [V0P_2E0: u,V1Q_2E0: u,V2l_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))
        <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) ) ) ) ).

tff(thm_2Elist_2EEVERY__EL,axiom,
    ! [A_27a: d,V0l_2E0: u,V1P_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
    <=> ! [V2n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) ) ) ).

tff(thm_2Elist_2EMAP__TL,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u,V1f_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
     => ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) ) ) ).

tff(thm_2Elist_2EEL__APPEND__EQN,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V2n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) ) ).

tff(thm_2Elist_2EEL__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))
     => ! [V2f_2E0: u] : ( s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ) ).

tff(thm_2Elist_2EMAP__MAP__o,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) ) ).

tff(thm_2Elist_2EMAP__o,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) ) ).

tff(thm_2Elist_2EMAP__EQ__f,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2l_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) )
    <=> ! [V3e_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))
         => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(A_27a,V3e_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0),s(A_27a,V3e_2E0))) ) ) ) ).

tff(thm_2Elist_2EMAP__EQ__SING,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1l_2E0: u,V2f_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) )
    <=> ? [V3x0_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3x0_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) )
          & ( s(A_27b,V0x_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x0_2E0))) ) ) ) ).

tff(thm_2Elist_2EMAP__EQ__CONS,axiom,
    ! [A_27a: d,A_27b: d,V0t_2E0: u,V1l_2E0: u,V2h_2E0: u,V3f_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))) )
    <=> ? [V4x0_2E0: u,V5t0_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x0_2E0),s(tyop_2Elist_2Elist(A_27a),V5t0_2E0))) )
          & ( s(A_27b,V2h_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V4x0_2E0))) )
          & ( s(tyop_2Elist_2Elist(A_27b),V0t_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V5t0_2E0))) ) ) ) ).

tff(thm_2Elist_2EMAP__EQ__NIL,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u,V1f_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) )
      <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
      & ( ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) )
      <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ) ).

tff(thm_2Elist_2ELENGTH__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u,V1f_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) ) ).

tff(thm_2Elist_2EMAP__ID,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1x_2E0: u] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(A_27a,V1x_2E0))) = s(A_27a,V1x_2E0) )
     => ! [V0l_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) )
          & ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) ) ) ).

tff(thm_2Elist_2EMAP__APPEND,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1l1_2E0: u,V2l2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) ) ).

tff(thm_2Elist_2ELENGTH__APPEND,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) ) ).

tff(thm_2Elist_2EAPPEND__ASSOC,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u,V2l3_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0),s(tyop_2Elist_2Elist(A_27a),V2l3_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l3_2E0))) ) ).

tff(thm_2Elist_2EAPPEND__NIL,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) ).

tff(thm_2Elist_2ECONS,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) ) ).

tff(thm_2Elist_2EEQ__LIST,axiom,
    ! [A_27a: d,V0h1_2E0: u,V1h2_2E0: u] :
      ( ( s(A_27a,V0h1_2E0) = s(A_27a,V1h2_2E0) )
     => ! [V2l1_2E0: u,V3l2_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V3l2_2E0) )
         => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h2_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) ) ) ) ).

tff(thm_2Elist_2ENOT__EQ__LIST,axiom,
    ! [A_27a: d,V0h1_2E0: u,V1h2_2E0: u] :
      ( ( s(A_27a,V0h1_2E0) != s(A_27a,V1h2_2E0) )
     => ! [V2l1_2E0: u,V3l2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h2_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) ) ) ).

tff(thm_2Elist_2ELIST__NOT__EQ,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) != s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) )
     => ! [V2h1_2E0: u,V3h2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h2_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) ) ) ).

tff(thm_2Elist_2ENOT__CONS__NIL,axiom,
    ! [A_27a: d,V0a1_2E0: u,V1a0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1a0_2E0),s(tyop_2Elist_2Elist(A_27a),V0a1_2E0))) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ).

tff(thm_2Elist_2ENOT__NIL__CONS,axiom,
    ! [A_27a: d,V0a1_2E0: u,V1a0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1a0_2E0),s(tyop_2Elist_2Elist(A_27a),V0a1_2E0))) ) ).

tff(thm_2Elist_2ECONS__11,axiom,
    ! [A_27a: d,V0a0_2E0: u,V1a1_2E0: u,V2a0_27_2E0: u,V3a1_27_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0a0_2E0),s(tyop_2Elist_2Elist(A_27a),V1a1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a0_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_27_2E0))) )
    <=> ( ( s(A_27a,V0a0_2E0) = s(A_27a,V2a0_27_2E0) )
        & ( s(tyop_2Elist_2Elist(A_27a),V1a1_2E0) = s(tyop_2Elist_2Elist(A_27a),V3a1_27_2E0) ) ) ) ).

tff(thm_2Elist_2Elist__case__compute,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1b_2E0: u,V2l_2E0: u] : ( s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V2l_2E0),s(A_27b,V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V0f_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))),s(A_27b,V1b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V0f_2E0),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))))) ) ).

tff(thm_2Elist_2Elist__nchotomy,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      | ? [V1h_2E0: u,V2t_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))) ) ) ).

tff(thm_2Elist_2Elist__distinct,axiom,
    ! [A_27a: d,V0a1_2E0: u,V1a0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1a0_2E0),s(tyop_2Elist_2Elist(A_27a),V0a1_2E0))) ) ).

tff(thm_2Elist_2Elist__11,axiom,
    ! [A_27a: d,V0a0_2E0: u,V1a1_2E0: u,V2a0_27_2E0: u,V3a1_27_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0a0_2E0),s(tyop_2Elist_2Elist(A_27a),V1a1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a0_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_27_2E0))) )
    <=> ( ( s(A_27a,V0a0_2E0) = s(A_27a,V2a0_27_2E0) )
        & ( s(tyop_2Elist_2Elist(A_27a),V1a1_2E0) = s(tyop_2Elist_2Elist(A_27a),V3a1_27_2E0) ) ) ) ).

tff(thm_2Elist_2Edatatype__list,axiom,
    ! [A_27a: d,V0list_2E0: u] : p(mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0list_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0)))))) ).

tff(thm_2Elist_2Elist__case__cong,axiom,
    ! [A_27a: d,A_27b: d,V0v_27_2E0: u,V1f_27_2E0: u,V2M_2E0: u,V3M_27_2E0: u,V4v_2E0: u,V5f_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V2M_2E0) = s(tyop_2Elist_2Elist(A_27a),V3M_27_2E0) )
        & ( ( s(tyop_2Elist_2Elist(A_27a),V3M_27_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
         => ( s(A_27b,V4v_2E0) = s(A_27b,V0v_27_2E0) ) )
        & ! [V6a0_2E0: u,V7a1_2E0: u] :
            ( ( s(tyop_2Elist_2Elist(A_27a),V3M_27_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6a0_2E0),s(tyop_2Elist_2Elist(A_27a),V7a1_2E0))) )
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V5f_2E0),s(A_27a,V6a0_2E0))),s(tyop_2Elist_2Elist(A_27a),V7a1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V1f_27_2E0),s(A_27a,V6a0_2E0))),s(tyop_2Elist_2Elist(A_27a),V7a1_2E0))) ) ) )
     => ( s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V2M_2E0),s(A_27b,V4v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V5f_2E0))) = s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V3M_27_2E0),s(A_27b,V0v_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V1f_27_2E0))) ) ) ).

tff(thm_2Elist_2Elist__case__eq,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_27_2E0: u,V2v_2E0: u,V3f_2E0: u] :
      ( ( s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V0x_2E0),s(A_27b,V2v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V3f_2E0))) = s(A_27b,V1v_27_2E0) )
    <=> ( ( ( s(tyop_2Elist_2Elist(A_27a),V0x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
          & ( s(A_27b,V2v_2E0) = s(A_27b,V1v_27_2E0) ) )
        | ? [V4a_2E0: u,V5l_2E0: u] :
            ( ( s(tyop_2Elist_2Elist(A_27a),V0x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4a_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))) )
            & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V3f_2E0),s(A_27a,V4a_2E0))),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))) = s(A_27b,V1v_27_2E0) ) ) ) ) ).

tff(thm_2Elist_2Elist__Axiom__old,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0x_2E0: u,V1f_2E0: u,V2fn1_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool))),F0_2E0),s(A_27b,V0x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn1_2E0)))))
        <=> ( ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(A_27b,V0x_2E0) )
            & ! [V3h_2E0: u,V4t_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V4t_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),V1f_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t_2E0))))),s(A_27a,V3h_2E0))),s(tyop_2Elist_2Elist(A_27a),V4t_2E0))) ) ) )
     => ! [V0x_2E0: u,V1f_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool))),F0_2E0),s(A_27b,V0x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),V1f_2E0))))))) ) ).

tff(thm_2Elist_2ETL,axiom,
    ! [A_27a: d,V0h_2E0: u,V1t_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),V1t_2E0) ) ).

tff(thm_2Elist_2ELIST__TO__SET,axiom,
    ! [A_27a: d,A_27b: d,V0t_2E0: u,V1h_2E0: u] :
      ( ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) )
      & ( s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V1h_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) ) ) ).

tff(thm_2Elist_2EMAP2__ind,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0P_2E0: u] :
      ( ( ! [V1f_2E0: u,V2h1_2E0: u,V3t1_2E0: u,V4h2_2E0: u,V5t2_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0))),s(tyop_2Elist_2Elist(A_27b),V3t1_2E0))),s(tyop_2Elist_2Elist(A_27c),V5t2_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h1_2E0),s(tyop_2Elist_2Elist(A_27b),V3t1_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4h2_2E0),s(tyop_2Elist_2Elist(A_27c),V5t2_2E0))))))) )
        & ! [V6f_2E0: u,V7y_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V6f_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27c),V7y_2E0)))))
        & ! [V8f_2E0: u,V9v4_2E0: u,V10v5_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V8f_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V9v4_2E0),s(tyop_2Elist_2Elist(A_27b),V10v5_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))))) )
     => ! [V11v_2E0: u,V12v1_2E0: u,V13v2_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V11v_2E0))),s(tyop_2Elist_2Elist(A_27b),V12v1_2E0))),s(tyop_2Elist_2Elist(A_27c),V13v2_2E0))))) ) ).

tff(thm_2Elist_2EMAP2__DEF,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d] :
      ( ! [V0t2_2E0: u,V1t1_2E0: u,V2h2_2E0: u,V3h1_2E0: u,V4f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V4f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3h1_2E0),s(tyop_2Elist_2Elist(A_27b),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V2h2_2E0),s(tyop_2Elist_2Elist(A_27c),V0t2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V4f_2E0),s(A_27b,V3h1_2E0))),s(A_27c,V2h2_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V4f_2E0),s(tyop_2Elist_2Elist(A_27b),V1t1_2E0),s(tyop_2Elist_2Elist(A_27c),V0t2_2E0))))) )
      & ! [V5y_2E0: u,V6f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V6f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27c),V5y_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V7v5_2E0: u,V8v4_2E0: u,V9f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V9f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V8v4_2E0),s(tyop_2Elist_2Elist(A_27b),V7v5_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ).

tff(thm_2Elist_2EMAP2,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,A_27f: d] :
      ( ! [V0f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0) )
      & ! [V1f_2E0: u,V2h1_2E0: u,V3t1_2E0: u,V4h2_2E0: u,V5t2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27f),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V1f_2E0),s(tyop_2Elist_2Elist(A_27d),c_2Elist_2ECONS_2E2(s(A_27d,V2h1_2E0),s(tyop_2Elist_2Elist(A_27d),V3t1_2E0))),s(tyop_2Elist_2Elist(A_27e),c_2Elist_2ECONS_2E2(s(A_27e,V4h2_2E0),s(tyop_2Elist_2Elist(A_27e),V5t2_2E0))))) = s(tyop_2Elist_2Elist(A_27f),c_2Elist_2ECONS_2E2(s(A_27f,app_2E2(s(tyop_2Emin_2Efun(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V1f_2E0),s(A_27d,V2h1_2E0))),s(A_27e,V4h2_2E0))),s(tyop_2Elist_2Elist(A_27f),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V1f_2E0),s(tyop_2Elist_2Elist(A_27d),V3t1_2E0),s(tyop_2Elist_2Elist(A_27e),V5t2_2E0))))) ) ) ).

tff(thm_2Elist_2EMAP2__NIL,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0x_2E0: u,V1f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V0x_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ).

tff(thm_2Elist_2ELENGTH__MAP2,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1xs_2E0: u,V2ys_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0),s(tyop_2Elist_2Elist(A_27b),V2ys_2E0)))))) = mono_2Ec_2Earithmetic_2EMIN_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1xs_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2ys_2E0))))) ) ).

tff(thm_2Elist_2EEL__MAP2,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1ts_2E0: u,V2tt_2E0: u,V3n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3n_2E0,mono_2Ec_2Earithmetic_2EMIN_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ts_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2tt_2E0)))))))
     => ( s(A_27c,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ts_2E0),s(tyop_2Elist_2Elist(A_27b),V2tt_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1ts_2E0))))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27b),V2tt_2E0))))) ) ) ).

tff(thm_2Elist_2ENULL,axiom,
    ! [A_27a: d] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
      & ! [V0h_2E0: u,V1t_2E0: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))))) ) ).

tff(thm_2Elist_2Elist__INDUCT0,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
        & ! [V1t_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))
           => ! [V2h_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))))) ) )
     => ! [V3l_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))) ) ).

tff(thm_2Elist_2Elist__INDUCT,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
        & ! [V1t_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))
           => ! [V2h_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))))) ) )
     => ! [V3l_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))) ) ).

tff(thm_2Elist_2Elist__Axiom,axiom,
    ! [A_27a: d,A_27b: d,V0f0_2E0: u,V1f1_2E0: u] :
    ? [V2fn_2E0: u] :
      ( ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(A_27b,V0f0_2E0) )
      & ! [V3a0_2E0: u,V4a1_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3a0_2E0),s(tyop_2Elist_2Elist(A_27a),V4a1_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b))),V1f1_2E0),s(A_27a,V3a0_2E0))),s(tyop_2Elist_2Elist(A_27a),V4a1_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),V4a1_2E0))))) ) ) ).

tff(thm_2Elist_2Elist__induction,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
        & ! [V1t_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))
           => ! [V2h_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))))) ) )
     => ! [V3l_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))) ) ).

tff(thm_2Elist_2ELIST__REL__EL__EQN,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))
    <=> ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) )
        & ! [V3n_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))))))) ) ) ) ).

tff(thm_2Elist_2ELIST__REL__cases,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1a0_2E0: u,V2a1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1a0_2E0),s(tyop_2Elist_2Elist(A_27b),V2a1_2E0)))))
    <=> ( ( ( s(tyop_2Elist_2Elist(A_27a),V1a0_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
          & ( s(tyop_2Elist_2Elist(A_27b),V2a1_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) ) )
        | ? [V3h1_2E0: u,V4h2_2E0: u,V5t1_2E0: u,V6t2_2E0: u] :
            ( ( s(tyop_2Elist_2Elist(A_27a),V1a0_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V5t1_2E0))) )
            & ( s(tyop_2Elist_2Elist(A_27b),V2a1_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h2_2E0),s(tyop_2Elist_2Elist(A_27b),V6t2_2E0))) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3h1_2E0))),s(A_27b,V4h2_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V5t1_2E0),s(tyop_2Elist_2Elist(A_27b),V6t2_2E0))))) ) ) ) ).

tff(thm_2Elist_2ELIST__REL__strongind,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1LIST__REL_27_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))
        & ! [V2h1_2E0: u,V3h2_2E0: u,V4t1_2E0: u,V5t2_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2h1_2E0))),s(A_27b,V3h2_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3h2_2E0),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0))))))) ) )
     => ! [V6a0_2E0: u,V7a1_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0))),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0))))) ) ) ).

tff(thm_2Elist_2ELIST__REL__ind,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1LIST__REL_27_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))
        & ! [V2h1_2E0: u,V3h2_2E0: u,V4t1_2E0: u,V5t2_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2h1_2E0))),s(A_27b,V3h2_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3h2_2E0),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0))))))) ) )
     => ! [V6a0_2E0: u,V7a1_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0))),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0))))) ) ) ).

tff(thm_2Elist_2ELIST__REL__rules,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))
      & ! [V1h1_2E0: u,V2h2_2E0: u,V3t1_2E0: u,V4t2_2E0: u] :
          ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1h1_2E0))),s(A_27b,V2h2_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V3t1_2E0),s(tyop_2Elist_2Elist(A_27b),V4t2_2E0))))) )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h1_2E0),s(tyop_2Elist_2Elist(A_27a),V3t1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h2_2E0),s(tyop_2Elist_2Elist(A_27b),V4t2_2E0))))))) ) ) ).

tff(thm_2Elist_2Elist__CASES,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      | ? [V1h_2E0: u,V2t_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))) ) ) ).

tff(thm_2Elist_2EFORALL__LIST,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ! [V1l_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
    <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
        & ! [V2h_2E0: u,V3t_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))))) ) ) ).

tff(thm_2Elist_2EMEM__SPLIT__APPEND__first,axiom,
    ! [A_27a: d,V0l_2E0: u,V1e_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))
    <=> ? [V2pfx_2E0: u,V3sfx_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2pfx_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3sfx_2E0))) )
          & ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2pfx_2E0))))))) ) ) ).

tff(thm_2Elist_2EMEM__SPLIT__APPEND__last,axiom,
    ! [A_27a: d,V0l_2E0: u,V1e_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))
    <=> ? [V2pfx_2E0: u,V3sfx_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2pfx_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3sfx_2E0))) )
          & ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3sfx_2E0))))))) ) ) ).

tff(thm_2Elist_2EAPPEND__EQ__APPEND,axiom,
    ! [A_27a: d,V0m2_2E0: u,V1m1_2E0: u,V2l2_2E0: u,V3l1_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27a),V0m2_2E0))) )
    <=> ( ? [V4l_2E0: u] :
            ( ( s(tyop_2Elist_2Elist(A_27a),V3l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))) )
            & ( s(tyop_2Elist_2Elist(A_27a),V0m2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) ) )
        | ? [V5l_2E0: u] :
            ( ( s(tyop_2Elist_2Elist(A_27a),V1m1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))) )
            & ( s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V5l_2E0),s(tyop_2Elist_2Elist(A_27a),V0m2_2E0))) ) ) ) ) ).

tff(thm_2Elist_2EAPPEND__EQ__CONS,axiom,
    ! [A_27a: d,V0t_2E0: u,V1l2_2E0: u,V2l1_2E0: u,V3h_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0))) )
    <=> ( ( ( s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
          & ( s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0))) ) )
        | ? [V4lt_2E0: u] :
            ( ( s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V4lt_2E0))) )
            & ( s(tyop_2Elist_2Elist(A_27a),V0t_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4lt_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) ) ) ) ) ).

tff(thm_2Elist_2EAPPEND__EQ__APPEND__MID,axiom,
    ! [A_27a: d,V0m2_2E0: u,V1m1_2E0: u,V2l2_2E0: u,V3l1_2E0: u,V4e_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27a),V0m2_2E0))) )
    <=> ( ? [V5l_2E0: u] :
            ( ( s(tyop_2Elist_2Elist(A_27a),V1m1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))) )
            & ( s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V5l_2E0),s(tyop_2Elist_2Elist(A_27a),V0m2_2E0))) ) )
        | ? [V6l_2E0: u] :
            ( ( s(tyop_2Elist_2Elist(A_27a),V3l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27a),V6l_2E0))) )
            & ( s(tyop_2Elist_2Elist(A_27a),V0m2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V6l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) ) ) ) ) ).

tff(thm_2Elist_2ELUPDATE__NIL,axiom,
    ! [A_27a: d,V0xs_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2x_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
    <=> ( s(tyop_2Elist_2Elist(A_27a),V0xs_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ).

tff(thm_2Elist_2ELUPDATE__SEM,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
      ( ! [V6p_2E0: mono_2Etyop_2Enum_2Enum,V4n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F0_2E0,V6p_2E0),V4n_2E0))
        <=> ( V6p_2E0 = V4n_2E0 ) )
     => ( ! [V0e_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2l_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0e_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) )
        & ! [V3e_2E0: u,V4n_2E0: mono_2Etyop_2Enum_2Enum,V5l_2E0: u,V6p_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V6p_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))))
           => ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6p_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V3e_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4n_2E0)),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F0_2E0,V6p_2E0),V4n_2E0))),s(A_27a,V3e_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6p_2E0)),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))) ) ) ) ) ).

tff(thm_2Elist_2EEL__LUPDATE,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V2i_2E0: mono_2Etyop_2Enum_2Enum,V3k_2E0: mono_2Etyop_2Enum_2Enum,V0ys_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3k_2E0)))),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))
        <=> ( ( V2i_2E0 = V3k_2E0 )
            & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3k_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))) ) )
     => ! [V0ys_2E0: u,V1x_2E0: u,V2i_2E0: mono_2Etyop_2Enum_2Enum,V3k_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V1x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3k_2E0)),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3k_2E0)))),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))),s(A_27a,V1x_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))))) ) ) ).

tff(thm_2Elist_2ELENGTH__LUPDATE,axiom,
    ! [A_27a: d,V0x_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2ys_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2ys_2E0)))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2ys_2E0)))) ) ).

tff(thm_2Elist_2ELUPDATE__LENGTH,axiom,
    ! [A_27a: d,V0xs_2E0: u,V1x_2E0: u,V2y_2E0: u,V3ys_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V1x_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2y_2E0),s(tyop_2Elist_2Elist(A_27a),V3ys_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V3ys_2E0))))) ) ).

tff(thm_2Elist_2ELUPDATE__SNOC,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1k_2E0: mono_2Etyop_2Enum_2Enum,V0ys_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)))),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))
        <=> ( V1k_2E0 = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))) ) )
     => ! [V0ys_2E0: u,V1k_2E0: mono_2Etyop_2Enum_2Enum,V2x_2E0: u,V3y_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V3y_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)))),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V3y_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))))))) ) ) ).

tff(thm_2Elist_2EMEM__LUPDATE__E,axiom,
    ! [A_27a: d,V0l_2E0: u,V1x_2E0: u,V2y_2E0: u,V3i_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2y_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))))
     => ( ( s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) )
        | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) ) ) ).

tff(thm_2Elist_2EMEM__LUPDATE,axiom,
    ! [A_27a: d,V0l_2E0: u,V1x_2E0: u,V2y_2E0: u,V3i_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2y_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))))
    <=> ( ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))
          & ( s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) ) )
        | ? [V4j_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V4j_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))
            & ( V3i_2E0 != V4j_2E0 )
            & ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4j_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,V1x_2E0) ) ) ) ) ).

tff(thm_2Elist_2ELUPDATE__compute,axiom,
    ! [A_27a: d] :
      ( ! [V0e_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0e_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V2e_2E0: u,V3x_2E0: u,V4l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2e_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3x_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))) )
      & ! [V5e_2E0: u,V6n_2E0: mono_2Etyop_2Enum_2Enum,V7x_2E0: u,V8l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V5e_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V6n_2E0)))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),V8l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V5e_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V6n_2E0)),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27a),V8l_2E0))))) )
      & ! [V9e_2E0: u,V10n_2E0: mono_2Etyop_2Enum_2Enum,V11x_2E0: u,V12l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V9e_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V10n_2E0)))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V11x_2E0),s(tyop_2Elist_2Elist(A_27a),V12l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V11x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V9e_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V10n_2E0)))),s(tyop_2Elist_2Elist(A_27a),V12l_2E0))))) ) ) ).

tff(thm_2Elist_2ELUPDATE__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2l_2E0: u,V3f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELUPDATE_2E3(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V0x_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) ) ).

tff(thm_2Elist_2EsplitAtPki__APPEND,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V2P_2E0: u,V4i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)))))) )
     => ! [V0l1_2E0: u,V1l2_2E0: u,V2P_2E0: u,V3k_2E0: u] :
          ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))
            & ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))))
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))))) ) )
         => ( s(A_27b,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V3k_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V3k_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) ) ) ) ).

tff(thm_2Elist_2EsplitAtPki__EQN,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u,F1_2E0: u] :
      ( ! [V0l_2E0: u,V2P_2E0: u,V3i_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0)))),V3i_2E0))
        <=> ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V0l_2E0))))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))))))) ) )
     => ( ! [V1k_2E0: u,V0l_2E0: u,V4i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))))) )
       => ! [V0l_2E0: u,V1k_2E0: u,V2P_2E0: u] : ( s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))) = s(A_27a,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Ewhile_2EOLEAST_2E1(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0))))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))))) ) ) ) ).

tff(thm_2Elist_2ETAKE__LENGTH__TOO__LONG,axiom,
    ! [A_27a: d,V0l_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))),V1n_2E0))
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) ) ).

tff(thm_2Elist_2EDROP__LENGTH__TOO__LONG,axiom,
    ! [A_27a: d,V0l_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))),V1n_2E0))
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ).

tff(thm_2Elist_2ETAKE__splitAtPki,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Enum_2Enum(V0n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) ) ).

tff(thm_2Elist_2EDROP__splitAtPki,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Enum_2Enum(V0n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) ) ).

tff(thm_2Elist_2ELIST__BIND__THM,axiom,
    ! [A_27a: d,A_27b: d,V0t_2E0: u,V1h_2E0: u,V2f_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0),s(A_27b,V1h_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))))) ) ) ).

tff(thm_2Elist_2ELIST__BIND__ID,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1x_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1x_2E0) )
     => ! [V0l_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),F0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l_2E0))) )
          & ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l_2E0))) ) ) ) ).

tff(thm_2Elist_2ELIST__BIND__APPEND,axiom,
    ! [A_27a: d,A_27b: d,V0l2_2E0: u,V1l1_2E0: u,V2f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V1l1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0l2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))))) ) ).

tff(thm_2Elist_2ELIST__BIND__MAP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0l_2E0: u,V1g_2E0: u,V2f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V0l_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1g_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1g_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0))))) ) ).

tff(thm_2Elist_2EMAP__LIST__BIND,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0l_2E0: u,V1g_2E0: u,V2f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V1g_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V1g_2E0))))) ) ).

tff(thm_2Elist_2ELIST__BIND__LIST__BIND,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0l_2E0: u,V1g_2E0: u,V2f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V1g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V1g_2E0))))) ) ).

tff(thm_2Elist_2ESINGL__LIST__APPLY__L,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1f_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1f_2E0),s(A_27b,V0x_2E0))) ) ).

tff(thm_2Elist_2ESINGL__LIST__APPLY__R,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1x_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),F0_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) )
     => ! [V0l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),F0_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) ) ).

tff(thm_2Elist_2ESINGL__APPLY__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u,V1f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))) ) ).

tff(thm_2Elist_2ESINGL__SINGL__APPLY,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V0x_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) ) ).

tff(thm_2Elist_2ESINGL__APPLY__PERMUTE,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0x_2E0: u,V2f_2E0: u] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),F0_2E0),s(A_27b,V0x_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0),s(A_27b,V0x_2E0))) )
     => ! [V0x_2E0: u,V1fs_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),V1fs_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),F0_2E0),s(A_27b,V0x_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),V1fs_2E0))) ) ) ).

tff(thm_2Elist_2EMAP__FLAT,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u,V1f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V0l_2E0))))) ) ).

tff(thm_2Elist_2ELIST__APPLY__o,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0xs_2E0: u,V1gs_2E0: u,V2fs_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),V2fs_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),V1gs_2E0))),s(tyop_2Elist_2Elist(A_27b),V0xs_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),V2fs_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),V1gs_2E0),s(tyop_2Elist_2Elist(A_27b),V0xs_2E0))))) ) ).

tff(thm_2Elist_2ESHORTLEX__THM,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2h2_2E0: u,V3h1_2E0: u,V4R_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
      & ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
      & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))))))
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))))))
      <=> ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1t1_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0t2_2E0))))))
          | ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1t1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))) )
            & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V2h2_2E0)))))
              | ( ( s(A_27a,V3h1_2E0) = s(A_27a,V2h2_2E0) )
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0))))) ) ) ) ) ) ) ).

tff(thm_2Elist_2ESHORTLEX__MONO,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2R2_2E0: u,V3R1_2E0: u] :
      ( ! [V4x_2E0: u,V5y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R1_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0y_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0y_2E0))))) ) ) ).

tff(thm_2Elist_2ESHORTLEX__NIL2,axiom,
    ! [A_27a: d,V0l_2E0: u,V1R_2E0: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) ).

tff(thm_2Elist_2ESHORTLEX__transitive,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) ) ).

tff(thm_2Elist_2ELENGTH__LT__SHORTLEX,axiom,
    ! [A_27a: d,V0R_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) ) ).

tff(thm_2Elist_2ESHORTLEX__LENGTH__LE,axiom,
    ! [A_27a: d,V0R_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))
     => p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) ) ).

tff(thm_2Elist_2ESHORTLEX__total,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))))) ) ).

tff(thm_2Elist_2EWF__SHORTLEX__same__lengths,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))
     => ! [V1l_2E0: mono_2Etyop_2Enum_2Enum,V2s_2E0: u] :
          ( ( ! [V3d_2E0: u] :
                ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V3d_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V2s_2E0)))))
               => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3d_2E0)))) = V1l_2E0 ) )
            & ? [V4a_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V4a_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V2s_2E0))))) )
         => ? [V5b_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V5b_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V2s_2E0)))))
              & ! [V6c_2E0: u] :
                  ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V6c_2E0),s(tyop_2Elist_2Elist(A_27a),V5b_2E0)))))
                 => ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V6c_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V2s_2E0))))) ) ) ) ) ).

tff(thm_2Elist_2EWF__SHORTLEX,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) ) ).

tff(thm_2Elist_2ELLEX__THM,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2h2_2E0: u,V3h1_2E0: u,V4R_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
      & ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
      & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))))))
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))))))
      <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V2h2_2E0)))))
          | ( ( s(A_27a,V3h1_2E0) = s(A_27a,V2h2_2E0) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0))))) ) ) ) ) ).

tff(thm_2Elist_2ELLEX__MONO,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2R2_2E0: u,V3R1_2E0: u] :
      ( ! [V4x_2E0: u,V5y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R1_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0y_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0y_2E0))))) ) ) ).

tff(thm_2Elist_2ELLEX__CONG,axiom,
    ! [A_27a: d,V0R_2E0: u,V1l1_2E0: u,V2l2_2E0: u,V3R_27_2E0: u,V4l1_27_2E0: u,V5l2_27_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V4l1_27_2E0) )
        & ( s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V5l2_27_2E0) )
        & ! [V6a_2E0: u,V7b_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V4l1_27_2E0)))))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V7b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V5l2_27_2E0))))))) )
           => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6a_2E0))),s(A_27a,V7b_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_27_2E0),s(A_27a,V6a_2E0))),s(A_27a,V7b_2E0)))) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4l1_27_2E0),s(tyop_2Elist_2Elist(A_27a),V5l2_27_2E0)))) ) ) ).

tff(thm_2Elist_2ELLEX__NIL2,axiom,
    ! [A_27a: d,V0l_2E0: u,V1R_2E0: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) ).

tff(thm_2Elist_2ELLEX__transitive,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) ) ).

tff(thm_2Elist_2ELLEX__total,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))))) ) ).

tff(thm_2Elist_2ELLEX__not__WF,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( ? [V1a_2E0: u,V2b_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_2E0)))))
     => ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) ) ).

tff(thm_2Elist_2ELLEX__EL__THM,axiom,
    ! [A_27a: d,V0R_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))
    <=> ? [V3n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V3n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))))
          & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))))
          & ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) )
          & ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))))) ) ) ) ).

tff(thm_2Elist_2Enub__set,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) ) ).

tff(thm_2Elist_2Eall__distinct__nub,axiom,
    ! [A_27a: d,V0l_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) ).

tff(thm_2Elist_2Enub__append,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1l2_2E0: u,V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(A_27a,V2x_2E0)))))
        <=> ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))))) )
     => ! [V0l1_2E0: u,V1l2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) ) ) ).

tff(thm_2Elist_2Elist__to__set__diff,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0l1_2E0: u,V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(A_27a,V2x_2E0)))))
        <=> ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))))) )
     => ! [V0l1_2E0: u,V1l2_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) ) ) ).

tff(thm_2Elist_2Elength__nub__append,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0l1_2E0: u,V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(A_27a,V2x_2E0)))))
        <=> ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))))) )
     => ! [V0l1_2E0: u,V1l2_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))))))) ) ) ).

tff(thm_2Elist_2EALL__DISTINCT__DROP,axiom,
    ! [A_27a: d,V0ls_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))))) ) ).

tff(thm_2Elist_2EEXISTS__LIST__EQ__MAP,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V1f_2E0: u,V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(A_27a,V2x_2E0)))))
        <=> ? [V3y_2E0: u] : ( s(A_27a,V2x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V3y_2E0))) ) )
     => ! [V0ls_2E0: u,V1f_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))
         => ? [V4l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),V0ls_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V4l_2E0))) ) ) ) ).

tff(thm_2Elist_2ELIST__TO__SET__FLAT,axiom,
    ! [A_27a: d,V0ls_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0ls_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0ls_2E0))))))) ) ).

tff(thm_2Elist_2EMEM__APPEND__lemma,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u,V3d_2E0: u,V4x_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0a_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1b_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2c_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3d_2E0))) )
        & ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1b_2E0)))))))
        & ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0a_2E0))))))) )
     => ( ( s(tyop_2Elist_2Elist(A_27a),V0a_2E0) = s(tyop_2Elist_2Elist(A_27a),V2c_2E0) )
        & ( s(tyop_2Elist_2Elist(A_27a),V1b_2E0) = s(tyop_2Elist_2Elist(A_27a),V3d_2E0) ) ) ) ).

tff(thm_2Elist_2EEVERY2__REVERSE,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))))))) ) ).

tff(thm_2Elist_2ESUM__MAP__PLUS,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V1g_2E0: u,V3x_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0))),s(A_27a,V3x_2E0)))) = mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V3x_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(A_27a,V3x_2E0))))) )
     => ! [V0f_2E0: u,V1g_2E0: u,V2ls_2E0: u] : ( mono_2Ec_2Elist_2ESUM_2E1(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0))),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Elist_2ESUM_2E1(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0))))),mono_2Ec_2Elist_2ESUM_2E1(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0)))))) ) ) ).

tff(thm_2Elist_2ETAKE__LENGTH__ID__rwt,axiom,
    ! [A_27a: d,V0l_2E0: u,V1m_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( V1m_2E0 = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) )
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1m_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) ) ) ).

tff(thm_2Elist_2EZIP__DROP,axiom,
    ! [A_27a: d,A_27b: d,V0a_2E0: u,V1b_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0a_2E0))))))
        & ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0a_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1b_2E0)))) ) )
     => ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0a_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27b),V1b_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0a_2E0),s(tyop_2Elist_2Elist(A_27b),V1b_2E0))))))) ) ) ).

tff(thm_2Elist_2EGENLIST__EL,axiom,
    ! [A_27a: d,V0ls_2E0: u,V1f_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( ( V2n_2E0 = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) )
        & ! [V3i_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3i_2E0,V2n_2E0))
           => ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) ) ) )
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))) = s(tyop_2Elist_2Elist(A_27a),V0ls_2E0) ) ) ).

tff(thm_2Elist_2EEVERY2__trans,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( ! [V1x_2E0: u,V2y_2E0: u,V3z_2E0: u] :
          ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0))))) )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_2E0))))) )
     => ! [V4x_2E0: u,V5y_2E0: u,V6z_2E0: u] :
          ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V5y_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V5y_2E0),s(tyop_2Elist_2Elist(A_27a),V6z_2E0))))) )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V6z_2E0))))) ) ) ).

tff(thm_2Elist_2EEVERY2__sym,axiom,
    ! [A_27a: d,A_27b: d,V0R2_2E0: u,V1R1_2E0: u] :
      ( ! [V2x_2E0: u,V3y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0),s(A_27b,V3y_2E0))),s(A_27a,V2x_2E0))))) )
     => ! [V4x_2E0: u,V5y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Elist_2Elist(A_27a),V4x_2E0),s(tyop_2Elist_2Elist(A_27b),V5y_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0),s(tyop_2Elist_2Elist(A_27b),V5y_2E0),s(tyop_2Elist_2Elist(A_27a),V4x_2E0))))) ) ) ).

tff(thm_2Elist_2EEVERY2__LUPDATE__same,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1l1_2E0: u,V2l2_2E0: u,V3v1_2E0: u,V4v2_2E0: u,V5n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V3v1_2E0))),s(A_27b,V4v2_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V3v1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELUPDATE_2E3(s(A_27b,V4v2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5n_2E0)),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))))))) ) ).

tff(thm_2Elist_2EEVERY2__refl,axiom,
    ! [A_27a: d,V0ls_2E0: u,V1R_2E0: u] :
      ( ! [V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) ) ).

tff(thm_2Elist_2EEVERY2__THM,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,A_27f: d,A_27g: d,A_27h: d] :
      ( ! [V0P_2E0: u,V1ys_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),V1ys_2E0)))))
        <=> ( s(tyop_2Elist_2Elist(A_27b),V1ys_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) ) )
      & ! [V2P_2E0: u,V3yys_2E0: u,V4x_2E0: u,V5xs_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4x_2E0),s(tyop_2Elist_2Elist(A_27c),V5xs_2E0))),s(tyop_2Elist_2Elist(A_27d),V3yys_2E0)))))
        <=> ? [V6y_2E0: u,V7ys_2E0: u] :
              ( ( s(tyop_2Elist_2Elist(A_27d),V3yys_2E0) = s(tyop_2Elist_2Elist(A_27d),c_2Elist_2ECONS_2E2(s(A_27d,V6y_2E0),s(tyop_2Elist_2Elist(A_27d),V7ys_2E0))) )
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27c,V4x_2E0))),s(A_27d,V6y_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Elist_2Elist(A_27c),V5xs_2E0),s(tyop_2Elist_2Elist(A_27d),V7ys_2E0))))) ) )
      & ! [V8P_2E0: u,V9xs_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),V8P_2E0),s(tyop_2Elist_2Elist(A_27e),V9xs_2E0),s(tyop_2Elist_2Elist(A_27f),c_2Elist_2ENIL_2E0)))))
        <=> ( s(tyop_2Elist_2Elist(A_27e),V9xs_2E0) = s(tyop_2Elist_2Elist(A_27e),c_2Elist_2ENIL_2E0) ) )
      & ! [V10P_2E0: u,V11xxs_2E0: u,V12y_2E0: u,V13ys_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V10P_2E0),s(tyop_2Elist_2Elist(A_27g),V11xxs_2E0),s(tyop_2Elist_2Elist(A_27h),c_2Elist_2ECONS_2E2(s(A_27h,V12y_2E0),s(tyop_2Elist_2Elist(A_27h),V13ys_2E0)))))))
        <=> ? [V14x_2E0: u,V15xs_2E0: u] :
              ( ( s(tyop_2Elist_2Elist(A_27g),V11xxs_2E0) = s(tyop_2Elist_2Elist(A_27g),c_2Elist_2ECONS_2E2(s(A_27g,V14x_2E0),s(tyop_2Elist_2Elist(A_27g),V15xs_2E0))) )
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V10P_2E0),s(A_27g,V14x_2E0))),s(A_27h,V12y_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V10P_2E0),s(tyop_2Elist_2Elist(A_27g),V15xs_2E0),s(tyop_2Elist_2Elist(A_27h),V13ys_2E0))))) ) ) ) ).

tff(thm_2Elist_2ELIST__REL__trans,axiom,
    ! [A_27a: d,V0R_2E0: u,V1l1_2E0: u,V2l2_2E0: u,V3l3_2E0: u] :
      ( ( ! [V4n_2E0: mono_2Etyop_2Enum_2Enum] :
            ( ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V4n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4n_2E0)),s(tyop_2Elist_2Elist(A_27a),V3l3_2E0))))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4n_2E0)),s(tyop_2Elist_2Elist(A_27a),V3l3_2E0))))))) )
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0),s(tyop_2Elist_2Elist(A_27a),V3l3_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l3_2E0))))) ) ).

tff(thm_2Elist_2ESWAP__REVERSE,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) )
    <=> ( s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) ) ) ).

tff(thm_2Elist_2ESWAP__REVERSE__SYM,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) )
    <=> ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) ) ) ).

tff(thm_2Elist_2EBIGUNION__IMAGE__set__SUBSET,axiom,
    ! [A_27a: d,A_27b: d,V0s_2E0: u,V1ls_2E0: u,V2f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V1ls_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))
    <=> ! [V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V1ls_2E0)))))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0),s(A_27b,V3x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) ) ) ).

tff(thm_2Elist_2EIMAGE__EL__count__LENGTH,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V1ls_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) )
     => ! [V0f_2E0: u,V1ls_2E0: u] : ( s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2Ecount_2E1(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) ) ) ).

tff(thm_2Elist_2EGENLIST__EL__MAP,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V1ls_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) )
     => ! [V0f_2E0: u,V1ls_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) ) ) ).

tff(thm_2Elist_2ELENGTH__FILTER__LEQ__MONO,axiom,
    ! [A_27a: d,V0P_2E0: u,V1Q_2E0: u] :
      ( ! [V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0))))) )
     => ! [V3ls_2E0: u] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3ls_2E0)))))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V3ls_2E0)))))))) ) ).

tff(thm_2Elist_2ELIST__EQ__MAP__PAIR,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0))) )
        & ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0))) ) )
     => ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l1_2E0) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0) ) ) ).

tff(thm_2Elist_2ETAKE__SUM,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1m_2E0: mono_2Etyop_2Enum_2Enum,V2l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1m_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))))) ) ).

tff(thm_2Elist_2EALL__DISTINCT__FILTER__EL__IMP,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u,V2n1_2E0: mono_2Etyop_2Enum_2Enum,V3n2_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))
        & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2n1_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))
        & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3n2_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n1_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))
        & ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n1_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n2_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) ) )
     => ( V2n1_2E0 = V3n2_2E0 ) ) ).

tff(thm_2Elist_2EFLAT__EQ__NIL,axiom,
    ! [A_27a: d,V0ls_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0ls_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
    <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0ls_2E0))))) ) ).

tff(thm_2Elist_2EALL__DISTINCT__MAP__INJ,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u,V1f_2E0: u] :
      ( ( ! [V2x_2E0: u,V3y_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))))
              & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3y_2E0))) ) )
           => ( s(A_27a,V2x_2E0) = s(A_27a,V3y_2E0) ) )
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))))) ) ).

tff(thm_2Elist_2ELENGTH__o__REVERSE,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u] :
      ( ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0) )
      & ( s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EREVERSE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),V0f_2E0))) ) ) ).

tff(thm_2Elist_2EREVERSE__o__REVERSE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),V0f_2E0) ) ).

tff(thm_2Elist_2EGENLIST__PLUS__APPEND,axiom,
    ! [V0n2_2E0: mono_2Etyop_2Enum_2Enum,V1n1_2E0: mono_2Etyop_2Enum_2Enum,V2a_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E1(V2a_2E0),V1n1_2E0),mono_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E1(mono_2Ec_2Earithmetic_2E_2B_2E2(V1n1_2E0,V2a_2E0)),V0n2_2E0)) = mono_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E1(V2a_2E0),mono_2Ec_2Earithmetic_2E_2B_2E2(V1n1_2E0,V0n2_2E0)) ) ).

tff(thm_2Elist_2ELIST__TO__SET__GENLIST,axiom,
    ! [A_27a: d,V0f_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2Ecount_2E1(V1n_2E0))))) ) ).

tff(thm_2Elist_2EMEM__ZIP__MEM__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0ps_2E0: u,V1p_2E0: u] :
      ( ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0)))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0)))))) )
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0))))))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0)))))))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0))))))))) ) ) ).

tff(thm_2Elist_2EDISJOINT__GENLIST__PLUS,axiom,
    ! [V0x_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2b_2E0: mono_2Etyop_2Enum_2Enum,V3a_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum(V0x_2E0,mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E1(V1n_2E0),mono_2Ec_2Earithmetic_2E_2B_2E2(V3a_2E0,V2b_2E0)))))
     => ( p(mono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum(V0x_2E0,mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E1(V1n_2E0),V3a_2E0))))
        & p(mono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum(V0x_2E0,mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E1(mono_2Ec_2Earithmetic_2E_2B_2E2(V1n_2E0,V3a_2E0)),V2b_2E0)))) ) ) ).

tff(thm_2Elist_2EEVERY2__MAP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V4Q_2E0: u,V2g_2E0: u,V8x_2E0: u,V9y_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V4Q_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0))),s(A_27c,V8x_2E0))),s(A_27b,V9y_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V4Q_2E0),s(A_27c,V8x_2E0))),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(A_27b,V9y_2E0)))))) )
     => ( ! [V5P_2E0: u,V3f_2E0: u,V6x_2E0: u,V7y_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0))),s(A_27c,V6x_2E0))),s(A_27b,V7y_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0),s(A_27c,V6x_2E0))))),s(A_27b,V7y_2E0)))) )
       => ! [V0l2_2E0: u,V1l1_2E0: u,V2g_2E0: u,V3f_2E0: u,V4Q_2E0: u,V5P_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0))),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) )
            & ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V4Q_2E0),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0),s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V4Q_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0))),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) ) ) ) ) ).

tff(thm_2Elist_2Eexists__list__GENLIST,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ? [V1ls_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))
    <=> ? [V2n_2E0: mono_2Etyop_2Enum_2Enum,V3f_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))))))) ) ).

tff(thm_2Elist_2EEVERY__MEM__MONO,axiom,
    ! [A_27a: d,V0P_2E0: u,V1Q_2E0: u,V2l_2E0: u] :
      ( ( ! [V3x_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) )
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) ) ).

tff(thm_2Elist_2EEVERY2__MEM__MONO,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1Q_2E0: u,V2l1_2E0: u,V3l2_2E0: u] :
      ( ( ! [V4x_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V4x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0)))))))))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V4x_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V4x_2E0))))) )
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0))))) ) ).

tff(thm_2Elist_2Emem__exists__set,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u,V2l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0)))))))
     => ? [V3z_2E0: u] :
          ( ( s(A_27a,V0x_2E0) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3z_2E0))) )
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3z_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))))))) ) ) ).

tff(thm_2Elist_2Eevery__zip__snd,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V2P_2E0: u,V3x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0)))))) )
     => ! [V0l1_2E0: u,V1l2_2E0: u,V2P_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) )
         => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) ) ) ) ).

tff(thm_2Elist_2Eevery__zip__fst,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V2P_2E0: u,V3x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0)))))) )
     => ! [V0l1_2E0: u,V1l2_2E0: u,V2P_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) )
         => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) ) ) ) ).

tff(thm_2Elist_2Eel__append3,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1x_2E0: u,V2l2_2E0: u] : ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(A_27a,V1x_2E0) ) ).

tff(thm_2Elist_2Elupdate__append,axiom,
    ! [A_27a: d,V0x_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2l1_2E0: u,V3l2_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))))))
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) ) ) ).

tff(thm_2Elist_2Elupdate__append2,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u,V1l1_2E0: u,V2x_2E0: u,V3l2_2E0: u,V4l3_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0v_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) ) ).

tff(thm_2Elist_2EHD__REVERSE,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V0x_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
     => ( s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))) ) ) ).

tff(thm_2Elist_2ELAST__REVERSE,axiom,
    ! [A_27a: d,V0ls_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V0ls_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
     => ( s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) = s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) ) ) ).

tff(thm_2Elist_2ENOT__NIL__EQ__LENGTH__NOT__0,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V0x_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
    <=> p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0)))))) ) ).

tff(thm_2Elist_2Elast__drop,axiom,
    ! [A_27a: d,V0l_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))
     => ( s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) ) ) ).

tff(thm_2Elist_2EdropWhile__splitAtPki,axiom,
    ! [A_27a: d,V0P_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EdropWhile_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EsplitAtPki_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Ecombin_2EK_2E0_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Enum_2Enum)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0))))) ) ).

tff(thm_2Elist_2EdropWhile__eq__nil,axiom,
    ! [A_27a: d,V0P_2E0: u,V1ls_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
    <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) ) ).

tff(thm_2Elist_2EMEM__dropWhile__IMP,axiom,
    ! [A_27a: d,V0P_2E0: u,V1ls_2E0: u,V2x_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))) ) ).

tff(thm_2Elist_2EHD__dropWhile,axiom,
    ! [A_27a: d,V0P_2E0: u,V1ls_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))
     => ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))))) ) ).

tff(thm_2Elist_2ELENGTH__dropWhile__LESS__EQ,axiom,
    ! [A_27a: d,V0P_2E0: u,V1ls_2E0: u] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) ).

tff(thm_2Elist_2EdropWhile__APPEND__EVERY,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) ) ) ).

tff(thm_2Elist_2EdropWhile__APPEND__EXISTS,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) ) ) ).

tff(thm_2Elist_2EEL__LENGTH__dropWhile__REVERSE,axiom,
    ! [A_27a: d,V0P_2E0: u,V1ls_2E0: u,V2k_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))),V2k_2E0))
        & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2k_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))) ) ).

tff(thm_2Elist_2ELENGTH__TAKE__EQ,axiom,
    ! [A_27a: d,V0xs_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0)))))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))),V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) ) ).

tff(thm_2Elist_2EIMP__EVERY__LUPDATE,axiom,
    ! [A_27a: d,V0P_2E0: u,V1xs_2E0: u,V2h_2E0: u,V3i_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2h_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2h_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0))))))) ) ).

tff(thm_2Elist_2EMAP__APPEND__MAP__EQ,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0g2_2E0: u,V1g1_2E0: u,V2f2_2E0: u,V3f1_2E0: u,V4xs_2E0: u,V5ys_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f1_2E0),s(tyop_2Elist_2Elist(A_27a),V4xs_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g1_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f2_2E0),s(tyop_2Elist_2Elist(A_27a),V4xs_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0g2_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys_2E0))))) )
    <=> ( ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f1_2E0),s(tyop_2Elist_2Elist(A_27a),V4xs_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f2_2E0),s(tyop_2Elist_2Elist(A_27a),V4xs_2E0))) )
        & ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g1_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0g2_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys_2E0))) ) ) ) ).

tff(thm_2Elist_2ELUPDATE__SOME__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0xs_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2f_2E0: u,V3h_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2ELUPDATE_2E3(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3h_2E0))))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),V0xs_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2ELUPDATE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3h_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),V0xs_2E0))))) ) ).

tff(thm_2Elist_2EZIP__EQ__NIL,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) )
     => ( ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0) )
      <=> ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
          & ( s(tyop_2Elist_2Elist(A_27b),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) ) ) ) ) ).

tff(thm_2Elist_2ELUPDATE__SAME,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ls_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1ls_2E0) ) ) ).

tff(thm_2Elist_2EUNIQUE__FILTER,axiom,
    ! [A_27a: d,V0e_2E0: u,V1L_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EUNIQUE_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))))
    <=> ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V0e_2E0))),s(tyop_2Elist_2Elist(A_27a),V1L_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) ) ) ).

tff(thm_2Elist_2EUNIQUE__LENGTH__FILTER,axiom,
    ! [A_27a: d,V0e_2E0: u,V1L_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EUNIQUE_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))))
    <=> ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V0e_2E0))),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))))) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) ) ) ).

tff(thm_2Elist_2EOPT__MMAP__cong,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2x1_2E0: u,V3x2_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V2x1_2E0) = s(tyop_2Elist_2Elist(A_27a),V3x2_2E0) )
        & ! [V4a_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3x2_2E0)))))))
           => ( s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0f1_2E0),s(A_27a,V4a_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f2_2E0),s(A_27a,V4a_2E0))) ) ) )
     => ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0f1_2E0),s(tyop_2Elist_2Elist(A_27a),V2x1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f2_2E0),s(tyop_2Elist_2Elist(A_27a),V3x2_2E0))) ) ) ).

tff(thm_2Elist_2ELAST__compute,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0x_2E0: u] : ( s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) = s(A_27a,V0x_2E0) )
      & ! [V1h1_2E0: u,V2h2_2E0: u,V3t_2E0: u] : ( s(A_27b,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h1_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h2_2E0),s(tyop_2Elist_2Elist(A_27b),V3t_2E0))))))) = s(A_27b,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h2_2E0),s(tyop_2Elist_2Elist(A_27b),V3t_2E0))))) ) ) ).

tff(thm_2Elist_2ETAKE__compute,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d] :
      ( ! [V0l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V1n_2E0)))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) )
      & ! [V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V2n_2E0)))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) )
      & ! [V3n_2E0: mono_2Etyop_2Enum_2Enum,V4h_2E0: u,V5t_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0)))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4h_2E0),s(tyop_2Elist_2Elist(A_27c),V5t_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4h_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0)),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27c),V5t_2E0))))) )
      & ! [V6n_2E0: mono_2Etyop_2Enum_2Enum,V7h_2E0: u,V8t_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V6n_2E0)))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V7h_2E0),s(tyop_2Elist_2Elist(A_27c),V8t_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V7h_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V6n_2E0)))),s(tyop_2Elist_2Elist(A_27c),V8t_2E0))))) ) ) ).

tff(thm_2Elist_2EDROP__compute,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d] :
      ( ! [V0l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) )
      & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V1n_2E0)))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) )
      & ! [V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V2n_2E0)))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) )
      & ! [V3n_2E0: mono_2Etyop_2Enum_2Enum,V4h_2E0: u,V5t_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0)))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4h_2E0),s(tyop_2Elist_2Elist(A_27c),V5t_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0)),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27c),V5t_2E0))) )
      & ! [V6n_2E0: mono_2Etyop_2Enum_2Enum,V7h_2E0: u,V8t_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V6n_2E0)))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V7h_2E0),s(tyop_2Elist_2Elist(A_27c),V8t_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V6n_2E0)))),s(tyop_2Elist_2Elist(A_27c),V8t_2E0))) ) ) ).

tff(thm_2Elist_2EoHD__thm,axiom,
    ! [A_27a: d,A_27b: d,V0t_2E0: u,V1h_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ( s(tyop_2Eoption_2Eoption(A_27b),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1h_2E0))) ) ) ).

tff(thm_2Elist_2EoEL__THM,axiom,
    ! [A_27a: d,V0xs_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Eprim__rec_2E_3C_2E2(V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) ) ).

tff(thm_2Elist_2EoEL__EQ__EL,axiom,
    ! [A_27a: d,V0xs_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2y_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2y_2E0))) )
    <=> ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))))
        & ( s(A_27a,V2y_2E0) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) ) ) ) ).

tff(thm_2Elist_2EoEL__DROP,axiom,
    ! [A_27a: d,V0xs_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2m_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2m_2E0)),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V2m_2E0,V1n_2E0))),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) ) ).

tff(thm_2Elist_2EoEL__TAKE__E,axiom,
    ! [A_27a: d,V0xs_2E0: u,V1x_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum,V3m_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3m_2E0)),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) )
     => ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) ) ) ).

tff(thm_2Elist_2EoEL__LUPDATE,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
      ( ! [V1i_2E0: mono_2Etyop_2Enum_2Enum,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F0_2E0,V1i_2E0),V2n_2E0))
        <=> ( V1i_2E0 != V2n_2E0 ) )
     => ! [V0xs_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum,V2n_2E0: mono_2Etyop_2Enum_2Enum,V3x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V3x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F0_2E0,V1i_2E0),V2n_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Eprim__rec_2E_3C_2E2(V1i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))))) ) ) ).

tff(thm_2Elist_2Elazy__list__case__compute,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1x_27_2E0: u,V2x_27_27_2E0: u] : ( s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V0x_2E0),s(A_27b,V1x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V2x_27_27_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))),s(A_27b,V1x_27_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V2x_27_27_2E0),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))))))) ) ).

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