ITP001 Axioms: ITP098^5.ax


%------------------------------------------------------------------------------
% File     : ITP098^5 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 set theory export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : enumeral^2.ax [Gau20]
%          : HL4098^5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  207 (   4 unt;  53 typ;   0 def)
%            Number of atoms       : 4204 ( 164 equ;   0 cnn)
%            Maximal formula atoms :  162 (  20 avg)
%            Number of connectives : 8055 (   4   ~;   8   |; 134   &;7290   @)
%                                         (  26 <=>; 593  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   58 (  14 avg;7290 nst)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   55 (  55   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  120 ( 117 usr;  66 con; 0-2 aty)
%            Number of variables   :  763 (  44   ^ 701   !;  18   ?; 763   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_ty_2Eenumeral_2Ebl,type,
    ty_2Eenumeral_2Ebl: del > del ).

thf(tp_ty_2Eenumeral_2Ebt,type,
    ty_2Eenumeral_2Ebt: del > del ).

thf(tp_c_2Eenumeral_2EBL__ACCUM,type,
    c_2Eenumeral_2EBL__ACCUM: del > $i ).

thf(mem_c_2Eenumeral_2EBL__ACCUM,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EBL__ACCUM @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( ty_2Eenumeral_2Ebl @ A_27a ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2EBL__CONS,type,
    c_2Eenumeral_2EBL__CONS: del > $i ).

thf(mem_c_2Eenumeral_2EBL__CONS,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EBL__CONS @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( ty_2Eenumeral_2Ebl @ A_27a ) ) ) ) ).

thf(tp_c_2Eenumeral_2EENUMERAL,type,
    c_2Eenumeral_2EENUMERAL: del > $i ).

thf(mem_c_2Eenumeral_2EENUMERAL,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ bool ) ) ) ) ).

thf(tp_c_2Eenumeral_2EK2,type,
    c_2Eenumeral_2EK2: del > $i ).

thf(mem_c_2Eenumeral_2EK2,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EK2 @ A_27a ) @ ( arr @ A_27a @ ty_2Enum_2Enum ) ) ).

thf(tp_c_2Eenumeral_2ELESS__ALL,type,
    c_2Eenumeral_2ELESS__ALL: del > $i ).

thf(mem_c_2Eenumeral_2ELESS__ALL,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2ELESS__ALL @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ) ).

thf(tp_c_2Eenumeral_2EOL,type,
    c_2Eenumeral_2EOL: del > $i ).

thf(mem_c_2Eenumeral_2EOL,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EOL @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) ) ) ).

thf(tp_c_2Eenumeral_2EOL__bt,type,
    c_2Eenumeral_2EOL__bt: del > $i ).

thf(mem_c_2Eenumeral_2EOL__bt,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EOL__bt @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ bool ) ) ) ).

thf(tp_c_2Eenumeral_2EOL__bt__lb,type,
    c_2Eenumeral_2EOL__bt__lb: del > $i ).

thf(mem_c_2Eenumeral_2EOL__bt__lb,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EOL__bt__lb @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ bool ) ) ) ) ).

thf(tp_c_2Eenumeral_2EOL__bt__lb__ub,type,
    c_2Eenumeral_2EOL__bt__lb__ub: del > $i ).

thf(mem_c_2Eenumeral_2EOL__bt__lb__ub,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EOL__bt__lb__ub @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ bool ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2EOL__bt__ub,type,
    c_2Eenumeral_2EOL__bt__ub: del > $i ).

thf(mem_c_2Eenumeral_2EOL__bt__ub,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EOL__bt__ub @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ bool ) ) ) ) ).

thf(tp_c_2Eenumeral_2EOL__sublists,type,
    c_2Eenumeral_2EOL__sublists: del > $i ).

thf(mem_c_2Eenumeral_2EOL__sublists,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EOL__sublists @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ bool ) ) ) ).

thf(tp_c_2Eenumeral_2EOU,type,
    c_2Eenumeral_2EOU: del > $i ).

thf(mem_c_2Eenumeral_2EOU,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EOU @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2EOWL,type,
    c_2Eenumeral_2EOWL: del > $i ).

thf(mem_c_2Eenumeral_2EOWL,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EOWL @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) ) ) ) ).

thf(tp_c_2Eenumeral_2EUO,type,
    c_2Eenumeral_2EUO: del > $i ).

thf(mem_c_2Eenumeral_2EUO,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2EUO @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebl__CASE,type,
    c_2Eenumeral_2Ebl__CASE: del > del > $i ).

thf(mem_c_2Eenumeral_2Ebl__CASE,axiom,
    ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eenumeral_2Ebl__CASE @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( arr @ A_27b @ ( arr @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ A_27b ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebl__rev,type,
    c_2Eenumeral_2Ebl__rev: del > $i ).

thf(mem_c_2Eenumeral_2Ebl__rev,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebl__rev @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebl__size,type,
    c_2Eenumeral_2Ebl__size: del > $i ).

thf(mem_c_2Eenumeral_2Ebl__size,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebl__size @ A_27a ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ty_2Enum_2Enum ) ) ) ).

thf(tp_c_2Eenumeral_2Ebl__to__bt,type,
    c_2Eenumeral_2Ebl__to__bt: del > $i ).

thf(mem_c_2Eenumeral_2Ebl__to__bt,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebl__to__bt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ).

thf(tp_c_2Eenumeral_2Ebl__to__set,type,
    c_2Eenumeral_2Ebl__to__set: del > $i ).

thf(mem_c_2Eenumeral_2Ebl__to__set,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebl__to__set @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( arr @ A_27a @ bool ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__CASE,type,
    c_2Eenumeral_2Ebt__CASE: del > del > $i ).

thf(mem_c_2Eenumeral_2Ebt__CASE,axiom,
    ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eenumeral_2Ebt__CASE @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27b @ ( arr @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ A_27b ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__rev,type,
    c_2Eenumeral_2Ebt__rev: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__rev,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__rev @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( ty_2Eenumeral_2Ebl @ A_27a ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__size,type,
    c_2Eenumeral_2Ebt__size: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__size,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__size @ A_27a ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ty_2Enum_2Enum ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__bl,type,
    c_2Eenumeral_2Ebt__to__bl: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__bl,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__bl @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( ty_2Eenumeral_2Ebl @ A_27a ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__list,type,
    c_2Eenumeral_2Ebt__to__list: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__list,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__list @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__list__ac,type,
    c_2Eenumeral_2Ebt__to__list__ac: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__list__ac,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__list__ac @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__ol,type,
    c_2Eenumeral_2Ebt__to__ol: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__ol,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__ol @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__ol__ac,type,
    c_2Eenumeral_2Ebt__to__ol__ac: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__ol__ac,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__ol__ac @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__ol__lb,type,
    c_2Eenumeral_2Ebt__to__ol__lb: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__ol__lb,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__ol__lb @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__ol__lb__ac,type,
    c_2Eenumeral_2Ebt__to__ol__lb__ac: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__ol__lb__ac,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__ol__lb__ac @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__ol__lb__ub,type,
    c_2Eenumeral_2Ebt__to__ol__lb__ub: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__ol__lb__ub,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__ol__lb__ub__ac,type,
    c_2Eenumeral_2Ebt__to__ol__lb__ub__ac: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__ol__lb__ub__ac,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__ol__ub,type,
    c_2Eenumeral_2Ebt__to__ol__ub: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__ol__ub,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__ol__ub @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__ol__ub__ac,type,
    c_2Eenumeral_2Ebt__to__ol__ub__ac: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__ol__ub__ac,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__ol__ub__ac @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__set__lb,type,
    c_2Eenumeral_2Ebt__to__set__lb: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__set__lb,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__set__lb @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ bool ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__set__lb__ub,type,
    c_2Eenumeral_2Ebt__to__set__lb__ub: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__set__lb__ub,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__set__lb__ub @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ebt__to__set__ub,type,
    c_2Eenumeral_2Ebt__to__set__ub: del > $i ).

thf(mem_c_2Eenumeral_2Ebt__to__set__ub,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ebt__to__set__ub @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Eincr__sbuild,type,
    c_2Eenumeral_2Eincr__sbuild: del > $i ).

thf(mem_c_2Eenumeral_2Eincr__sbuild,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Eincr__sbuild @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Eincr__smerge,type,
    c_2Eenumeral_2Eincr__smerge: del > $i ).

thf(mem_c_2Eenumeral_2Eincr__smerge,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Eincr__smerge @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Eincr__ssort,type,
    c_2Eenumeral_2Eincr__ssort: del > $i ).

thf(mem_c_2Eenumeral_2Eincr__ssort,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Eincr__ssort @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ).

thf(tp_c_2Eenumeral_2Elist__to__bl,type,
    c_2Eenumeral_2Elist__to__bl: del > $i ).

thf(mem_c_2Eenumeral_2Elist__to__bl,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Elist__to__bl @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Eenumeral_2Ebl @ A_27a ) ) ) ).

thf(tp_c_2Eenumeral_2Elist__to__bt,type,
    c_2Eenumeral_2Elist__to__bt: del > $i ).

thf(mem_c_2Eenumeral_2Elist__to__bt,axiom,
    ! [A_27c: del] : ( mem @ ( c_2Eenumeral_2Elist__to__bt @ A_27c ) @ ( arr @ ( ty_2Elist_2Elist @ A_27c ) @ ( ty_2Eenumeral_2Ebt @ A_27c ) ) ) ).

thf(tp_c_2Eenumeral_2Elol__set,type,
    c_2Eenumeral_2Elol__set: del > $i ).

thf(mem_c_2Eenumeral_2Elol__set,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Elol__set @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( arr @ A_27a @ bool ) ) ) ).

thf(tp_c_2Eenumeral_2Enbl,type,
    c_2Eenumeral_2Enbl: del > $i ).

thf(mem_c_2Eenumeral_2Enbl,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Enbl @ A_27a ) @ ( ty_2Eenumeral_2Ebl @ A_27a ) ) ).

thf(tp_c_2Eenumeral_2Enode,type,
    c_2Eenumeral_2Enode: del > $i ).

thf(mem_c_2Eenumeral_2Enode,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Enode @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ent,type,
    c_2Eenumeral_2Ent: del > $i ).

thf(mem_c_2Eenumeral_2Ent,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ent @ A_27a ) @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ).

thf(tp_c_2Eenumeral_2Eonebl,type,
    c_2Eenumeral_2Eonebl: del > $i ).

thf(mem_c_2Eenumeral_2Eonebl,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( ty_2Eenumeral_2Ebl @ A_27a ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Esdiff,type,
    c_2Eenumeral_2Esdiff: del > $i ).

thf(mem_c_2Eenumeral_2Esdiff,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Esdiff @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Esinter,type,
    c_2Eenumeral_2Esinter: del > $i ).

thf(mem_c_2Eenumeral_2Esinter,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Esinter @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Esmerge,type,
    c_2Eenumeral_2Esmerge: del > $i ).

thf(mem_c_2Eenumeral_2Esmerge,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Esmerge__out,type,
    c_2Eenumeral_2Esmerge__out: del > $i ).

thf(mem_c_2Eenumeral_2Esmerge__out,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Esmerge__out @ A_27a ) @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).

thf(tp_c_2Eenumeral_2Ezerbl,type,
    c_2Eenumeral_2Ezerbl: del > $i ).

thf(mem_c_2Eenumeral_2Ezerbl,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( ty_2Eenumeral_2Ebl @ A_27a ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__TY__DEF,axiom,
    ! [A_27a: del] :
    ? [V0rep: $i] :
      ( ( mem @ V0rep @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) )
      & ( p
        @ ( ap
          @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( ty_2Eind__type_2Erecspace @ A_27a ) @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
            @ ( lam @ ( ty_2Eind__type_2Erecspace @ A_27a )
              @ ^ [V1a0_27: $i] :
                  ( ap @ ( c_2Ebool_2E_21 @ ( arr @ ( ty_2Eind__type_2Erecspace @ A_27a ) @ bool ) )
                  @ ( lam @ ( arr @ ( ty_2Eind__type_2Erecspace @ A_27a ) @ bool )
                    @ ^ [V2_27bt_27: $i] :
                        ( ap
                        @ ( ap @ c_2Emin_2E_3D_3D_3E
                          @ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Eind__type_2Erecspace @ A_27a ) )
                            @ ( lam @ ( ty_2Eind__type_2Erecspace @ A_27a )
                              @ ^ [V3a0_27: $i] :
                                  ( ap
                                  @ ( ap @ c_2Emin_2E_3D_3D_3E
                                    @ ( ap
                                      @ ( ap @ c_2Ebool_2E_5C_2F
                                        @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) @ V3a0_27 )
                                          @ ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( c_2Ebool_2EARB @ A_27a ) )
                                            @ ( lam @ ty_2Enum_2Enum
                                              @ ^ [V4n: $i] : ( c_2Eind__type_2EBOTTOM @ A_27a ) ) ) ) )
                                      @ ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ A_27a ) )
                                        @ ( lam @ ( ty_2Eind__type_2Erecspace @ A_27a )
                                          @ ^ [V5a0: $i] :
                                              ( ap @ ( c_2Ebool_2E_3F @ A_27a )
                                              @ ( lam @ A_27a
                                                @ ^ [V6a1: $i] :
                                                    ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ A_27a ) )
                                                    @ ( lam @ ( ty_2Eind__type_2Erecspace @ A_27a )
                                                      @ ^ [V7a2: $i] :
                                                          ( ap
                                                          @ ( ap @ c_2Ebool_2E_2F_5C
                                                            @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) @ V3a0_27 )
                                                              @ ( ap
                                                                @ ( ap
                                                                  @ ( ap
                                                                    @ ( lam @ ( ty_2Eind__type_2Erecspace @ A_27a )
                                                                      @ ^ [V8a0: $i] :
                                                                          ( lam @ A_27a
                                                                          @ ^ [V9a1: $i] :
                                                                              ( lam @ ( ty_2Eind__type_2Erecspace @ A_27a )
                                                                              @ ^ [V10a2: $i] :
                                                                                  ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V9a1 )
                                                                                  @ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) @ V8a0 )
                                                                                    @ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) @ V10a2 )
                                                                                      @ ( lam @ ty_2Enum_2Enum
                                                                                        @ ^ [V11n: $i] : ( c_2Eind__type_2EBOTTOM @ A_27a ) ) ) ) ) ) ) )
                                                                    @ V5a0 )
                                                                  @ V6a1 )
                                                                @ V7a2 ) ) )
                                                          @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2_27bt_27 @ V5a0 ) ) @ ( ap @ V2_27bt_27 @ V7a2 ) ) ) ) ) ) ) ) ) ) )
                                  @ ( ap @ V2_27bt_27 @ V3a0_27 ) ) ) ) )
                        @ ( ap @ V2_27bt_27 @ V1a0_27 ) ) ) ) ) )
          @ V0rep ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__size__def,axiom,
    ! [A_27a: del] :
      ( ! [V0f: $i] :
          ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__size @ A_27a ) @ V0f ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) )
            = fo__c_2Enum_2E0 ) )
      & ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2a0: $i] :
              ( ( mem @ V2a0 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V3a1: $i] :
                  ( ( mem @ V3a1 @ A_27a )
                 => ! [V4a2: $i] :
                      ( ( mem @ V4a2 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                     => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__size @ A_27a ) @ V1f ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V2a0 ) @ V3a1 ) @ V4a2 ) ) )
                        = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__size @ A_27a ) @ V1f ) @ V2a0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V1f @ V3a1 ) ) @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__size @ A_27a ) @ V1f ) @ V4a2 ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Edatatype__bt,axiom,
    ! [A_27a: del,V0bt: $i] :
      ( ( mem @ V0bt @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ bool ) ) )
     => ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ bool ) @ ( ap @ ( ap @ V0bt @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ ( c_2Eenumeral_2Enode @ A_27a ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebt__nchotomy,axiom,
    ! [A_27a: del,V0bb: $i] :
      ( ( mem @ V0bb @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
     => ( ( V0bb
          = ( c_2Eenumeral_2Ent @ A_27a ) )
        | ? [V1b: $i] :
            ( ( mem @ V1b @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
            & ? [V2a: $i] :
                ( ( mem @ V2a @ A_27a )
                & ? [V3b0: $i] :
                    ( ( mem @ V3b0 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                    & ( V0bb
                      = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V1b ) @ V2a ) @ V3b0 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebt__Axiom,axiom,
    ! [A_27a: del,A_27b: del,V0f0: $i] :
      ( ( mem @ V0f0 @ A_27b )
     => ! [V1f1: $i] :
          ( ( mem @ V1f1 @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) ) ) ) )
         => ? [V2fn: $i] :
              ( ( mem @ V2fn @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) )
              & ( ( ap @ V2fn @ ( c_2Eenumeral_2Ent @ A_27a ) )
                = V0f0 )
              & ! [V3a0: $i] :
                  ( ( mem @ V3a0 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V4a1: $i] :
                      ( ( mem @ V4a1 @ A_27a )
                     => ! [V5a2: $i] :
                          ( ( mem @ V5a2 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                         => ( ( ap @ V2fn @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V3a0 ) @ V4a1 ) @ V5a2 ) )
                            = ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ V1f1 @ V4a1 ) @ V3a0 ) @ V5a2 ) @ ( ap @ V2fn @ V3a0 ) ) @ ( ap @ V2fn @ V5a2 ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebt__induction,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ bool ) )
     => ( ( ( p @ ( ap @ V0P @ ( c_2Eenumeral_2Ent @ A_27a ) ) )
          & ! [V1b: $i] :
              ( ( mem @ V1b @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V2b0: $i] :
                  ( ( mem @ V2b0 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ( ( ( p @ ( ap @ V0P @ V1b ) )
                      & ( p @ ( ap @ V0P @ V2b0 ) ) )
                   => ! [V3a: $i] :
                        ( ( mem @ V3a @ A_27a )
                       => ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V1b ) @ V3a ) @ V2b0 ) ) ) ) ) ) ) )
       => ! [V4b: $i] :
            ( ( mem @ V4b @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
           => ( p @ ( ap @ V0P @ V4b ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebt__case__cong,axiom,
    ! [A_27a: del,A_27b: del,V0v_27: $i] :
      ( ( mem @ V0v_27 @ A_27b )
     => ! [V1f_27: $i] :
          ( ( mem @ V1f_27 @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) )
         => ! [V2M: $i] :
              ( ( mem @ V2M @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V3M_27: $i] :
                  ( ( mem @ V3M_27 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V4v: $i] :
                      ( ( mem @ V4v @ A_27b )
                     => ! [V5f: $i] :
                          ( ( mem @ V5f @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) )
                         => ( ( ( V2M = V3M_27 )
                              & ( ( V3M_27
                                  = ( c_2Eenumeral_2Ent @ A_27a ) )
                               => ( V4v = V0v_27 ) )
                              & ! [V6a0: $i] :
                                  ( ( mem @ V6a0 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                                 => ! [V7a1: $i] :
                                      ( ( mem @ V7a1 @ A_27a )
                                     => ! [V8a2: $i] :
                                          ( ( mem @ V8a2 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                                         => ( ( V3M_27
                                              = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V6a0 ) @ V7a1 ) @ V8a2 ) )
                                           => ( ( ap @ ( ap @ ( ap @ V5f @ V6a0 ) @ V7a1 ) @ V8a2 )
                                              = ( ap @ ( ap @ ( ap @ V1f_27 @ V6a0 ) @ V7a1 ) @ V8a2 ) ) ) ) ) ) )
                           => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__CASE @ A_27a @ A_27b ) @ V2M ) @ V4v ) @ V5f )
                              = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__CASE @ A_27a @ A_27b ) @ V3M_27 ) @ V0v_27 ) @ V1f_27 ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebt__case__eq,axiom,
    ! [A_27a: del,A_27b: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
     => ! [V1v: $i] :
          ( ( mem @ V1v @ A_27b )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) )
             => ! [V3v_27: $i] :
                  ( ( mem @ V3v_27 @ A_27b )
                 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__CASE @ A_27a @ A_27b ) @ V0x ) @ V1v ) @ V2f )
                      = V3v_27 )
                  <=> ( ( ( V0x
                          = ( c_2Eenumeral_2Ent @ A_27a ) )
                        & ( V1v = V3v_27 ) )
                      | ? [V4b: $i] :
                          ( ( mem @ V4b @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                          & ? [V5a: $i] :
                              ( ( mem @ V5a @ A_27a )
                              & ? [V6b0: $i] :
                                  ( ( mem @ V6b0 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                                  & ( V0x
                                    = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V4b ) @ V5a ) @ V6b0 ) )
                                  & ( ( ap @ ( ap @ ( ap @ V2f @ V4b ) @ V5a ) @ V6b0 )
                                    = V3v_27 ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebl__TY__DEF,axiom,
    ! [A_27a: del] :
    ? [V0rep: $i] :
      ( ( mem @ V0rep @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ) )
      & ( p
        @ ( ap
          @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
            @ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) )
              @ ^ [V1a0_27: $i] :
                  ( ap @ ( c_2Ebool_2E_21 @ ( arr @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) @ bool ) )
                  @ ( lam @ ( arr @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) @ bool )
                    @ ^ [V2_27bl_27: $i] :
                        ( ap
                        @ ( ap @ c_2Emin_2E_3D_3D_3E
                          @ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) )
                            @ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) )
                              @ ^ [V3a0_27: $i] :
                                  ( ap
                                  @ ( ap @ c_2Emin_2E_3D_3D_3E
                                    @ ( ap
                                      @ ( ap @ c_2Ebool_2E_5C_2F
                                        @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ V3a0_27 )
                                          @ ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) @ ( c_2Ebool_2EARB @ A_27a ) ) @ ( c_2Ebool_2EARB @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) )
                                            @ ( lam @ ty_2Enum_2Enum
                                              @ ^ [V4n: $i] : ( c_2Eind__type_2EBOTTOM @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ) ) ) )
                                      @ ( ap
                                        @ ( ap @ c_2Ebool_2E_5C_2F
                                          @ ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) )
                                            @ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) )
                                              @ ^ [V5a: $i] :
                                                  ( ap
                                                  @ ( ap @ c_2Ebool_2E_2F_5C
                                                    @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ V3a0_27 )
                                                      @ ( ap
                                                        @ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) )
                                                          @ ^ [V6a: $i] :
                                                              ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) @ ( c_2Ebool_2EARB @ A_27a ) ) @ ( c_2Ebool_2EARB @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) )
                                                              @ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ V6a )
                                                                @ ( lam @ ty_2Enum_2Enum
                                                                  @ ^ [V7n: $i] : ( c_2Eind__type_2EBOTTOM @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ) ) ) )
                                                        @ V5a ) ) )
                                                  @ ( ap @ V2_27bl_27 @ V5a ) ) ) ) )
                                        @ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
                                          @ ( lam @ A_27a
                                            @ ^ [V8a0: $i] :
                                                ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                                                @ ( lam @ ( ty_2Eenumeral_2Ebt @ A_27a )
                                                  @ ^ [V9a1: $i] :
                                                      ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) )
                                                      @ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) )
                                                        @ ^ [V10a2: $i] :
                                                            ( ap
                                                            @ ( ap @ c_2Ebool_2E_2F_5C
                                                              @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ V3a0_27 )
                                                                @ ( ap
                                                                  @ ( ap
                                                                    @ ( ap
                                                                      @ ( lam @ A_27a
                                                                        @ ^ [V11a0: $i] :
                                                                            ( lam @ ( ty_2Eenumeral_2Ebt @ A_27a )
                                                                            @ ^ [V12a1: $i] :
                                                                                ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) )
                                                                                @ ^ [V13a2: $i] :
                                                                                    ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) @ V11a0 ) @ V12a1 ) )
                                                                                    @ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ V13a2 )
                                                                                      @ ( lam @ ty_2Enum_2Enum
                                                                                        @ ^ [V14n: $i] : ( c_2Eind__type_2EBOTTOM @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Eenumeral_2Ebt @ A_27a ) ) ) ) ) ) ) ) )
                                                                      @ V8a0 )
                                                                    @ V9a1 )
                                                                  @ V10a2 ) ) )
                                                            @ ( ap @ V2_27bl_27 @ V10a2 ) ) ) ) ) ) ) ) ) ) )
                                  @ ( ap @ V2_27bl_27 @ V3a0_27 ) ) ) ) )
                        @ ( ap @ V2_27bl_27 @ V1a0_27 ) ) ) ) ) )
          @ V0rep ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebl__case__def,axiom,
    ! [A_27a: del,A_27b: del] :
      ( ! [V0v: $i] :
          ( ( mem @ V0v @ A_27b )
         => ! [V1f: $i] :
              ( ( mem @ V1f @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) )
             => ! [V2f1: $i] :
                  ( ( mem @ V2f1 @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) )
                 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__CASE @ A_27a @ A_27b ) @ ( c_2Eenumeral_2Enbl @ A_27a ) ) @ V0v ) @ V1f ) @ V2f1 )
                    = V0v ) ) ) )
      & ! [V3a: $i] :
          ( ( mem @ V3a @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
         => ! [V4v: $i] :
              ( ( mem @ V4v @ A_27b )
             => ! [V5f: $i] :
                  ( ( mem @ V5f @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) )
                 => ! [V6f1: $i] :
                      ( ( mem @ V6f1 @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) )
                     => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__CASE @ A_27a @ A_27b ) @ ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V3a ) ) @ V4v ) @ V5f ) @ V6f1 )
                        = ( ap @ V5f @ V3a ) ) ) ) ) )
      & ! [V7a0: $i] :
          ( ( mem @ V7a0 @ A_27a )
         => ! [V8a1: $i] :
              ( ( mem @ V8a1 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V9a2: $i] :
                  ( ( mem @ V9a2 @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                 => ! [V10v: $i] :
                      ( ( mem @ V10v @ A_27b )
                     => ! [V11f: $i] :
                          ( ( mem @ V11f @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) )
                         => ! [V12f1: $i] :
                              ( ( mem @ V12f1 @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) )
                             => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__CASE @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V7a0 ) @ V8a1 ) @ V9a2 ) ) @ V10v ) @ V11f ) @ V12f1 )
                                = ( ap @ ( ap @ ( ap @ V12f1 @ V7a0 ) @ V8a1 ) @ V9a2 ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebl__size__def,axiom,
    ! [A_27a: del] :
      ( ! [V0f: $i] :
          ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__size @ A_27a ) @ V0f ) @ ( c_2Eenumeral_2Enbl @ A_27a ) ) )
            = fo__c_2Enum_2E0 ) )
      & ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2a: $i] :
              ( ( mem @ V2a @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
             => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__size @ A_27a ) @ V1f ) @ ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V2a ) ) )
                = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__size @ A_27a ) @ V1f ) @ V2a ) ) ) ) ) )
      & ! [V3f: $i] :
          ( ( mem @ V3f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V4a0: $i] :
              ( ( mem @ V4a0 @ A_27a )
             => ! [V5a1: $i] :
                  ( ( mem @ V5a1 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V6a2: $i] :
                      ( ( mem @ V6a2 @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                     => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__size @ A_27a ) @ V3f ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V4a0 ) @ V5a1 ) @ V6a2 ) ) )
                        = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V3f @ V4a0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__size @ A_27a ) @ V3f ) @ V5a1 ) ) @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__size @ A_27a ) @ V3f ) @ V6a2 ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Edatatype__bl,axiom,
    ! [A_27a: del,V0bl: $i] :
      ( ( mem @ V0bl @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( arr @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( ty_2Eenumeral_2Ebl @ A_27a ) ) @ ( arr @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( ty_2Eenumeral_2Ebl @ A_27a ) ) ) ) @ bool ) ) ) )
     => ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ bool ) @ ( ap @ ( ap @ ( ap @ V0bl @ ( c_2Eenumeral_2Enbl @ A_27a ) ) @ ( c_2Eenumeral_2Ezerbl @ A_27a ) ) @ ( c_2Eenumeral_2Eonebl @ A_27a ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebl__11,axiom,
    ! [A_27a: del] :
      ( ! [V0a: $i] :
          ( ( mem @ V0a @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
         => ! [V1a_27: $i] :
              ( ( mem @ V1a_27 @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
             => ( ( ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V0a )
                  = ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V1a_27 ) )
              <=> ( V0a = V1a_27 ) ) ) )
      & ! [V2a0: $i] :
          ( ( mem @ V2a0 @ A_27a )
         => ! [V3a1: $i] :
              ( ( mem @ V3a1 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V4a2: $i] :
                  ( ( mem @ V4a2 @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                 => ! [V5a0_27: $i] :
                      ( ( mem @ V5a0_27 @ A_27a )
                     => ! [V6a1_27: $i] :
                          ( ( mem @ V6a1_27 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                         => ! [V7a2_27: $i] :
                              ( ( mem @ V7a2_27 @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                             => ( ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V2a0 ) @ V3a1 ) @ V4a2 )
                                  = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V5a0_27 ) @ V6a1_27 ) @ V7a2_27 ) )
                              <=> ( ( V2a0 = V5a0_27 )
                                  & ( V3a1 = V6a1_27 )
                                  & ( V4a2 = V7a2_27 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebl__distinct,axiom,
    ! [A_27a: del] :
      ( ! [V0a: $i] :
          ( ( mem @ V0a @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
         => ( ( c_2Eenumeral_2Enbl @ A_27a )
           != ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V0a ) ) )
      & ! [V1a2: $i] :
          ( ( mem @ V1a2 @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
         => ! [V2a1: $i] :
              ( ( mem @ V2a1 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V3a0: $i] :
                  ( ( mem @ V3a0 @ A_27a )
                 => ( ( c_2Eenumeral_2Enbl @ A_27a )
                   != ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V3a0 ) @ V2a1 ) @ V1a2 ) ) ) ) )
      & ! [V4a2: $i] :
          ( ( mem @ V4a2 @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
         => ! [V5a1: $i] :
              ( ( mem @ V5a1 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V6a0: $i] :
                  ( ( mem @ V6a0 @ A_27a )
                 => ! [V7a: $i] :
                      ( ( mem @ V7a @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                     => ( ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V7a )
                       != ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V6a0 ) @ V5a1 ) @ V4a2 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebl__nchotomy,axiom,
    ! [A_27a: del,V0bb: $i] :
      ( ( mem @ V0bb @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
     => ( ( V0bb
          = ( c_2Eenumeral_2Enbl @ A_27a ) )
        | ? [V1b: $i] :
            ( ( mem @ V1b @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
            & ( V0bb
              = ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V1b ) ) )
        | ? [V2a: $i] :
            ( ( mem @ V2a @ A_27a )
            & ? [V3b0: $i] :
                ( ( mem @ V3b0 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                & ? [V4b: $i] :
                    ( ( mem @ V4b @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                    & ( V0bb
                      = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V2a ) @ V3b0 ) @ V4b ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebl__Axiom,axiom,
    ! [A_27a: del,A_27b: del,V0f0: $i] :
      ( ( mem @ V0f0 @ A_27b )
     => ! [V1f1: $i] :
          ( ( mem @ V1f1 @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( arr @ A_27b @ A_27b ) ) )
         => ! [V2f2: $i] :
              ( ( mem @ V2f2 @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ ( arr @ A_27b @ A_27b ) ) ) ) )
             => ? [V3fn: $i] :
                  ( ( mem @ V3fn @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) )
                  & ( ( ap @ V3fn @ ( c_2Eenumeral_2Enbl @ A_27a ) )
                    = V0f0 )
                  & ! [V4a: $i] :
                      ( ( mem @ V4a @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                     => ( ( ap @ V3fn @ ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V4a ) )
                        = ( ap @ ( ap @ V1f1 @ V4a ) @ ( ap @ V3fn @ V4a ) ) ) )
                  & ! [V5a0: $i] :
                      ( ( mem @ V5a0 @ A_27a )
                     => ! [V6a1: $i] :
                          ( ( mem @ V6a1 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                         => ! [V7a2: $i] :
                              ( ( mem @ V7a2 @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                             => ( ( ap @ V3fn @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V5a0 ) @ V6a1 ) @ V7a2 ) )
                                = ( ap @ ( ap @ ( ap @ ( ap @ V2f2 @ V5a0 ) @ V6a1 ) @ V7a2 ) @ ( ap @ V3fn @ V7a2 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebl__induction,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ bool ) )
     => ( ( ( p @ ( ap @ V0P @ ( c_2Eenumeral_2Enbl @ A_27a ) ) )
          & ! [V1b: $i] :
              ( ( mem @ V1b @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
             => ( ( p @ ( ap @ V0P @ V1b ) )
               => ( p @ ( ap @ V0P @ ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V1b ) ) ) ) )
          & ! [V2b: $i] :
              ( ( mem @ V2b @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
             => ( ( p @ ( ap @ V0P @ V2b ) )
               => ! [V3b0: $i] :
                    ( ( mem @ V3b0 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                   => ! [V4a: $i] :
                        ( ( mem @ V4a @ A_27a )
                       => ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V4a ) @ V3b0 ) @ V2b ) ) ) ) ) ) ) )
       => ! [V5b: $i] :
            ( ( mem @ V5b @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
           => ( p @ ( ap @ V0P @ V5b ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebl__case__cong,axiom,
    ! [A_27a: del,A_27b: del,V0v_27: $i] :
      ( ( mem @ V0v_27 @ A_27b )
     => ! [V1f_27: $i] :
          ( ( mem @ V1f_27 @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) )
         => ! [V2f1_27: $i] :
              ( ( mem @ V2f1_27 @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) )
             => ! [V3M: $i] :
                  ( ( mem @ V3M @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                 => ! [V4M_27: $i] :
                      ( ( mem @ V4M_27 @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                     => ! [V5v: $i] :
                          ( ( mem @ V5v @ A_27b )
                         => ! [V6f: $i] :
                              ( ( mem @ V6f @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) )
                             => ! [V7f1: $i] :
                                  ( ( mem @ V7f1 @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) )
                                 => ( ( ( V3M = V4M_27 )
                                      & ( ( V4M_27
                                          = ( c_2Eenumeral_2Enbl @ A_27a ) )
                                       => ( V5v = V0v_27 ) )
                                      & ! [V8a: $i] :
                                          ( ( mem @ V8a @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                                         => ( ( V4M_27
                                              = ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V8a ) )
                                           => ( ( ap @ V6f @ V8a )
                                              = ( ap @ V1f_27 @ V8a ) ) ) )
                                      & ! [V9a0: $i] :
                                          ( ( mem @ V9a0 @ A_27a )
                                         => ! [V10a1: $i] :
                                              ( ( mem @ V10a1 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                                             => ! [V11a2: $i] :
                                                  ( ( mem @ V11a2 @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                                                 => ( ( V4M_27
                                                      = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V9a0 ) @ V10a1 ) @ V11a2 ) )
                                                   => ( ( ap @ ( ap @ ( ap @ V7f1 @ V9a0 ) @ V10a1 ) @ V11a2 )
                                                      = ( ap @ ( ap @ ( ap @ V2f1_27 @ V9a0 ) @ V10a1 ) @ V11a2 ) ) ) ) ) ) )
                                   => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__CASE @ A_27a @ A_27b ) @ V3M ) @ V5v ) @ V6f ) @ V7f1 )
                                      = ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__CASE @ A_27a @ A_27b ) @ V4M_27 ) @ V0v_27 ) @ V1f_27 ) @ V2f1_27 ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebl__case__eq,axiom,
    ! [A_27a: del,A_27b: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
     => ! [V1v: $i] :
          ( ( mem @ V1v @ A_27b )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) )
             => ! [V3f1: $i] :
                  ( ( mem @ V3f1 @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) )
                 => ! [V4v_27: $i] :
                      ( ( mem @ V4v_27 @ A_27b )
                     => ( ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__CASE @ A_27a @ A_27b ) @ V0x ) @ V1v ) @ V2f ) @ V3f1 )
                          = V4v_27 )
                      <=> ( ( ( V0x
                              = ( c_2Eenumeral_2Enbl @ A_27a ) )
                            & ( V1v = V4v_27 ) )
                          | ? [V5b: $i] :
                              ( ( mem @ V5b @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                              & ( V0x
                                = ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V5b ) )
                              & ( ( ap @ V2f @ V5b )
                                = V4v_27 ) )
                          | ? [V6a: $i] :
                              ( ( mem @ V6a @ A_27a )
                              & ? [V7b0: $i] :
                                  ( ( mem @ V7b0 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                                  & ? [V8b: $i] :
                                      ( ( mem @ V8b @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                                      & ( V0x
                                        = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V6a ) @ V7b0 ) @ V8b ) )
                                      & ( ( ap @ ( ap @ ( ap @ V3f1 @ V6a ) @ V7b0 ) @ V8b )
                                        = V4v_27 ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebt__11,axiom,
    ! [A_27a: del,V0a0: $i] :
      ( ( mem @ V0a0 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
     => ! [V1a1: $i] :
          ( ( mem @ V1a1 @ A_27a )
         => ! [V2a2: $i] :
              ( ( mem @ V2a2 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V3a0_27: $i] :
                  ( ( mem @ V3a0_27 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V4a1_27: $i] :
                      ( ( mem @ V4a1_27 @ A_27a )
                     => ! [V5a2_27: $i] :
                          ( ( mem @ V5a2_27 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                         => ( ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V0a0 ) @ V1a1 ) @ V2a2 )
                              = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V3a0_27 ) @ V4a1_27 ) @ V5a2_27 ) )
                          <=> ( ( V0a0 = V3a0_27 )
                              & ( V1a1 = V4a1_27 )
                              & ( V2a2 = V5a2_27 ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebt__distinct,axiom,
    ! [A_27a: del,V0a2: $i] :
      ( ( mem @ V0a2 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
     => ! [V1a1: $i] :
          ( ( mem @ V1a1 @ A_27a )
         => ! [V2a0: $i] :
              ( ( mem @ V2a0 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ( ( c_2Eenumeral_2Ent @ A_27a )
               != ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V2a0 ) @ V1a1 ) @ V0a2 ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebt__case__def,axiom,
    ! [A_27a: del,A_27b: del] :
      ( ! [V0v: $i] :
          ( ( mem @ V0v @ A_27b )
         => ! [V1f: $i] :
              ( ( mem @ V1f @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__CASE @ A_27a @ A_27b ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ V0v ) @ V1f )
                = V0v ) ) )
      & ! [V2a0: $i] :
          ( ( mem @ V2a0 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ! [V3a1: $i] :
              ( ( mem @ V3a1 @ A_27a )
             => ! [V4a2: $i] :
                  ( ( mem @ V4a2 @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V5v: $i] :
                      ( ( mem @ V5v @ A_27b )
                     => ! [V6f: $i] :
                          ( ( mem @ V6f @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) )
                         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__CASE @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V2a0 ) @ V3a1 ) @ V4a2 ) ) @ V5v ) @ V6f )
                            = ( ap @ ( ap @ ( ap @ V6f @ V2a0 ) @ V3a1 ) @ V4a2 ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2EBL__ACCUM,axiom,
    ! [A_27a: del] :
      ( ! [V0a: $i] :
          ( ( mem @ V0a @ A_27a )
         => ! [V1ac: $i] :
              ( ( mem @ V1ac @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EBL__ACCUM @ A_27a ) @ V0a ) @ V1ac ) @ ( c_2Eenumeral_2Enbl @ A_27a ) )
                = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V0a ) @ V1ac ) @ ( c_2Eenumeral_2Enbl @ A_27a ) ) ) ) )
      & ! [V2a: $i] :
          ( ( mem @ V2a @ A_27a )
         => ! [V3ac: $i] :
              ( ( mem @ V3ac @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V4bl: $i] :
                  ( ( mem @ V4bl @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EBL__ACCUM @ A_27a ) @ V2a ) @ V3ac ) @ ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V4bl ) )
                    = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V2a ) @ V3ac ) @ V4bl ) ) ) ) )
      & ! [V5a: $i] :
          ( ( mem @ V5a @ A_27a )
         => ! [V6ac: $i] :
              ( ( mem @ V6ac @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V7r: $i] :
                  ( ( mem @ V7r @ A_27a )
                 => ! [V8rft: $i] :
                      ( ( mem @ V8rft @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                     => ! [V9bl: $i] :
                          ( ( mem @ V9bl @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EBL__ACCUM @ A_27a ) @ V5a ) @ V6ac ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V7r ) @ V8rft ) @ V9bl ) )
                            = ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EBL__ACCUM @ A_27a ) @ V5a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V6ac ) @ V7r ) @ V8rft ) ) @ V9bl ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2EBL__CONS,axiom,
    ! [A_27a: del,V0a: $i] :
      ( ( mem @ V0a @ A_27a )
     => ! [V1bl: $i] :
          ( ( mem @ V1bl @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Eenumeral_2EBL__CONS @ A_27a ) @ V0a ) @ V1bl )
            = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EBL__ACCUM @ A_27a ) @ V0a ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ V1bl ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Elist__to__bl,axiom,
    ! [A_27a: del] :
      ( ( ( ap @ ( c_2Eenumeral_2Elist__to__bl @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) )
        = ( c_2Eenumeral_2Enbl @ A_27a ) )
      & ! [V0a: $i] :
          ( ( mem @ V0a @ A_27a )
         => ! [V1l: $i] :
              ( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
             => ( ( ap @ ( c_2Eenumeral_2Elist__to__bl @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0a ) @ V1l ) )
                = ( ap @ ( ap @ ( c_2Eenumeral_2EBL__CONS @ A_27a ) @ V0a ) @ ( ap @ ( c_2Eenumeral_2Elist__to__bl @ A_27a ) @ V1l ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__list,axiom,
    ! [A_27a: del] :
      ( ( ( ap @ ( c_2Eenumeral_2Ebt__to__list @ A_27a ) @ ( c_2Eenumeral_2Ent @ A_27a ) )
        = ( c_2Elist_2ENIL @ A_27a ) )
      & ! [V0l: $i] :
          ( ( mem @ V0l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ! [V1x: $i] :
              ( ( mem @ V1x @ A_27a )
             => ! [V2r: $i] :
                  ( ( mem @ V2r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ( ( ap @ ( c_2Eenumeral_2Ebt__to__list @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V0l ) @ V1x ) @ V2r ) )
                    = ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( c_2Eenumeral_2Ebt__to__list @ A_27a ) @ V0l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) @ ( ap @ ( c_2Eenumeral_2Ebt__to__list @ A_27a ) @ V2r ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__list__ac,axiom,
    ! [A_27a: del] :
      ( ! [V0m: $i] :
          ( ( mem @ V0m @ ( ty_2Elist_2Elist @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__list__ac @ A_27a ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ V0m )
            = V0m ) )
      & ! [V1l: $i] :
          ( ( mem @ V1l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ! [V2x: $i] :
              ( ( mem @ V2x @ A_27a )
             => ! [V3r: $i] :
                  ( ( mem @ V3r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V4m: $i] :
                      ( ( mem @ V4m @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__list__ac @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V1l ) @ V2x ) @ V3r ) ) @ V4m )
                        = ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__list__ac @ A_27a ) @ V1l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__list__ac @ A_27a ) @ V3r ) @ V4m ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebt__to__list__thm,axiom,
    ! [A_27a: del,V0t: $i] :
      ( ( mem @ V0t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
     => ( ( ap @ ( c_2Eenumeral_2Ebt__to__list @ A_27a ) @ V0t )
        = ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__list__ac @ A_27a ) @ V0t ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__rev,axiom,
    ! [A_27a: del] :
      ( ! [V0bl: $i] :
          ( ( mem @ V0bl @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__rev @ A_27a ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ V0bl )
            = V0bl ) )
      & ! [V1lft: $i] :
          ( ( mem @ V1lft @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ A_27a )
             => ! [V3rft: $i] :
                  ( ( mem @ V3rft @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V4bl: $i] :
                      ( ( mem @ V4bl @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                     => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__rev @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V1lft ) @ V2r ) @ V3rft ) ) @ V4bl )
                        = ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__rev @ A_27a ) @ V1lft ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V2r ) @ V3rft ) @ V4bl ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2EK2,axiom,
    ! [A_27a: del,V0a: $i] :
      ( ( mem @ V0a @ A_27a )
     => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Eenumeral_2EK2 @ A_27a ) @ V0a ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebl__rev,axiom,
    ! [A_27a: del] :
      ( ! [V0ft: $i] :
          ( ( mem @ V0ft @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__rev @ A_27a ) @ V0ft ) @ ( c_2Eenumeral_2Enbl @ A_27a ) )
            = V0ft ) )
      & ! [V1ft: $i] :
          ( ( mem @ V1ft @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ! [V2b: $i] :
              ( ( mem @ V2b @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
             => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__rev @ A_27a ) @ V1ft ) @ ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V2b ) )
                = ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__rev @ A_27a ) @ V1ft ) @ V2b ) ) ) )
      & ! [V3ft: $i] :
          ( ( mem @ V3ft @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ! [V4a: $i] :
              ( ( mem @ V4a @ A_27a )
             => ! [V5f: $i] :
                  ( ( mem @ V5f @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V6b: $i] :
                      ( ( mem @ V6b @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                     => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__rev @ A_27a ) @ V3ft ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V4a ) @ V5f ) @ V6b ) )
                        = ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__rev @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V3ft ) @ V4a ) @ V5f ) ) @ V6b ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebl__to__bt,axiom,
    ! [A_27a: del] :
      ( ( c_2Eenumeral_2Ebl__to__bt @ A_27a )
      = ( ap @ ( c_2Eenumeral_2Ebl__rev @ A_27a ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__bl,axiom,
    ! [A_27a: del,V0t: $i] :
      ( ( mem @ V0t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
     => ( ( ap @ ( c_2Eenumeral_2Ebt__to__bl @ A_27a ) @ V0t )
        = ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__rev @ A_27a ) @ V0t ) @ ( c_2Eenumeral_2Enbl @ A_27a ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Elist__to__bt,axiom,
    ! [A_27c: del,V0l: $i] :
      ( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27c ) )
     => ( ( ap @ ( c_2Eenumeral_2Elist__to__bt @ A_27c ) @ V0l )
        = ( ap @ ( c_2Eenumeral_2Ebl__to__bt @ A_27c ) @ ( ap @ ( c_2Eenumeral_2Elist__to__bl @ A_27c ) @ V0l ) ) ) ) ).

thf(ax_thm_2Eenumeral_2EOL,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) )
          <=> $true ) )
      & ! [V1cmp: $i] :
          ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V2a: $i] :
              ( ( mem @ V2a @ A_27a )
             => ! [V3l: $i] :
                  ( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V1cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2a ) @ V3l ) ) )
                  <=> ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V1cmp ) @ V3l ) )
                      & ! [V4p: $i] :
                          ( ( mem @ V4p @ A_27a )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4p ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V3l ) ) )
                           => ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V1cmp ) @ V2a ) @ V4p ) )
                              = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Esmerge__ind,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) ) ) )
     => ( ( ! [V1cmp: $i] :
              ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V1cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
          & ! [V2cmp: $i] :
              ( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V3x: $i] :
                  ( ( mem @ V3x @ A_27a )
                 => ! [V4l: $i] :
                      ( ( mem @ V4l @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V2cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3x ) @ V4l ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) )
          & ! [V5cmp: $i] :
              ( ( mem @ V5cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V6y: $i] :
                  ( ( mem @ V6y @ A_27a )
                 => ! [V7m: $i] :
                      ( ( mem @ V7m @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V5cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V6y ) @ V7m ) ) ) ) ) )
          & ! [V8cmp: $i] :
              ( ( mem @ V8cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V9x: $i] :
                  ( ( mem @ V9x @ A_27a )
                 => ! [V10l: $i] :
                      ( ( mem @ V10l @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ! [V11y: $i] :
                          ( ( mem @ V11y @ A_27a )
                         => ! [V12m: $i] :
                              ( ( mem @ V12m @ ( ty_2Elist_2Elist @ A_27a ) )
                             => ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V8cmp ) @ V9x ) @ V11y ) )
                                      = fo__c_2EternaryComparisons_2EEQUAL )
                                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V8cmp ) @ V10l ) @ V12m ) ) )
                                  & ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V8cmp ) @ V9x ) @ V11y ) )
                                      = fo__c_2EternaryComparisons_2EGREATER )
                                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V8cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V9x ) @ V10l ) ) @ V12m ) ) )
                                  & ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V8cmp ) @ V9x ) @ V11y ) )
                                      = fo__c_2EternaryComparisons_2ELESS )
                                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V8cmp ) @ V10l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V11y ) @ V12m ) ) ) ) )
                               => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V8cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V9x ) @ V10l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V11y ) @ V12m ) ) ) ) ) ) ) ) ) )
       => ! [V13v: $i] :
            ( ( mem @ V13v @ ( ty_2Etoto_2Etoto @ A_27a ) )
           => ! [V14v1: $i] :
                ( ( mem @ V14v1 @ ( ty_2Elist_2Elist @ A_27a ) )
               => ! [V15v2: $i] :
                    ( ( mem @ V15v2 @ ( ty_2Elist_2Elist @ A_27a ) )
                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V13v ) @ V14v1 ) @ V15v2 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Esmerge,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V0cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) )
            = ( c_2Elist_2ENIL @ A_27a ) ) )
      & ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2l: $i] :
              ( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
             => ! [V3cmp: $i] :
                  ( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V3cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ V2l ) ) @ ( c_2Elist_2ENIL @ A_27a ) )
                    = ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ V2l ) ) ) ) )
      & ! [V4y: $i] :
          ( ( mem @ V4y @ A_27a )
         => ! [V5m: $i] :
              ( ( mem @ V5m @ ( ty_2Elist_2Elist @ A_27a ) )
             => ! [V6cmp: $i] :
                  ( ( mem @ V6cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V6cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4y ) @ V5m ) )
                    = ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4y ) @ V5m ) ) ) ) )
      & ! [V7y: $i] :
          ( ( mem @ V7y @ A_27a )
         => ! [V8x: $i] :
              ( ( mem @ V8x @ A_27a )
             => ! [V9m: $i] :
                  ( ( mem @ V9m @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ! [V10l: $i] :
                      ( ( mem @ V10l @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ! [V11cmp: $i] :
                          ( ( mem @ V11cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V11cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V8x ) @ V10l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V7y ) @ V9m ) )
                            = ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Eordering__CASE @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V11cmp ) @ V8x ) @ V7y ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V8x ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V11cmp ) @ V10l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V7y ) @ V9m ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V8x ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V11cmp ) @ V10l ) @ V9m ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V7y ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V11cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V8x ) @ V10l ) ) @ V9m ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Esmerge__nil,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1l: $i] :
          ( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
         => ( ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V0cmp ) @ V1l ) @ ( c_2Elist_2ENIL @ A_27a ) )
              = V1l )
            & ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V0cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V1l )
              = V1l ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Esmerge__OL,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1l: $i] :
          ( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
         => ! [V2m: $i] :
              ( ( mem @ V2m @ ( ty_2Elist_2Elist @ A_27a ) )
             => ( ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ V1l ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ V2m ) ) )
               => ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V0cmp ) @ V1l ) @ V2m ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOL__sublists__ind,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ bool ) ) )
     => ( ( ! [V1cmp: $i] :
              ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ( p @ ( ap @ ( ap @ V0P @ V1cmp ) @ ( c_2Elist_2ENIL @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) )
          & ! [V2cmp: $i] :
              ( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V3lol: $i] :
                  ( ( mem @ V3lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                 => ( ( p @ ( ap @ ( ap @ V0P @ V2cmp ) @ V3lol ) )
                   => ( p @ ( ap @ ( ap @ V0P @ V2cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ V3lol ) ) ) ) ) )
          & ! [V4cmp: $i] :
              ( ( mem @ V4cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V5m: $i] :
                  ( ( mem @ V5m @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ! [V6lol: $i] :
                      ( ( mem @ V6lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                     => ( ( p @ ( ap @ ( ap @ V0P @ V4cmp ) @ V6lol ) )
                       => ( p @ ( ap @ ( ap @ V0P @ V4cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V5m ) ) @ V6lol ) ) ) ) ) ) ) )
       => ! [V7v: $i] :
            ( ( mem @ V7v @ ( ty_2Etoto_2Etoto @ A_27a ) )
           => ! [V8v1: $i] :
                ( ( mem @ V8v1 @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
               => ( p @ ( ap @ ( ap @ V0P @ V7v ) @ V8v1 ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOL__sublists,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__sublists @ A_27a ) @ V0cmp ) @ ( c_2Elist_2ENIL @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) )
          <=> $true ) )
      & ! [V1lol: $i] :
          ( ( mem @ V1lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
         => ! [V2cmp: $i] :
              ( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__sublists @ A_27a ) @ V2cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ V1lol ) ) )
              <=> ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__sublists @ A_27a ) @ V2cmp ) @ V1lol ) ) ) ) )
      & ! [V3m: $i] :
          ( ( mem @ V3m @ ( ty_2Elist_2Elist @ A_27a ) )
         => ! [V4lol: $i] :
              ( ( mem @ V4lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
             => ! [V5cmp: $i] :
                  ( ( mem @ V5cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__sublists @ A_27a ) @ V5cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V3m ) ) @ V4lol ) ) )
                  <=> ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V5cmp ) @ V3m ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__sublists @ A_27a ) @ V5cmp ) @ V4lol ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Elol__set__primitive,axiom,
    ! [A_27a: del] :
      ( ( c_2Eenumeral_2Elol__set @ A_27a )
      = ( ap
        @ ( ap @ ( c_2Erelation_2EWFREC @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( arr @ A_27a @ bool ) )
          @ ( ap @ ( c_2Emin_2E_40 @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ bool ) ) )
            @ ( lam @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ bool ) )
              @ ^ [V0R: $i] :
                  ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Erelation_2EWF @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) @ V0R ) )
                  @ ( ap
                    @ ( ap @ c_2Ebool_2E_2F_5C
                      @ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                        @ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) )
                          @ ^ [V1lol: $i] : ( ap @ ( ap @ V0R @ V1lol ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ V1lol ) ) ) ) )
                    @ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Elist_2Elist @ A_27a ) )
                      @ ( lam @ ( ty_2Elist_2Elist @ A_27a )
                        @ ^ [V2m: $i] :
                            ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                            @ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) )
                              @ ^ [V3lol: $i] : ( ap @ ( ap @ V0R @ V3lol ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2m ) ) @ V3lol ) ) ) ) ) ) ) ) ) ) )
        @ ( lam @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( arr @ A_27a @ bool ) )
          @ ^ [V4lol__set: $i] :
              ( lam @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) )
              @ ^ [V5a: $i] :
                  ( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( arr @ A_27a @ bool ) ) @ V5a ) @ ( ap @ ( c_2Ecombin_2EI @ ( arr @ A_27a @ bool ) ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
                  @ ( lam @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) )
                    @ ^ [V6v: $i] :
                        ( lam @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) )
                        @ ^ [V7lol: $i] :
                            ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ A_27a @ bool ) ) @ V6v ) @ ( ap @ ( c_2Ecombin_2EI @ ( arr @ A_27a @ bool ) ) @ ( ap @ V4lol__set @ V7lol ) ) )
                            @ ( lam @ ( ty_2Elist_2Elist @ A_27a )
                              @ ^ [V8m: $i] : ( ap @ ( c_2Ecombin_2EI @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V8m ) ) @ ( ap @ V4lol__set @ V7lol ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Elol__set__ind,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ bool ) )
     => ( ( ( p @ ( ap @ V0P @ ( c_2Elist_2ENIL @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) )
          & ! [V1lol: $i] :
              ( ( mem @ V1lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
             => ( ( p @ ( ap @ V0P @ V1lol ) )
               => ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ V1lol ) ) ) ) )
          & ! [V2m: $i] :
              ( ( mem @ V2m @ ( ty_2Elist_2Elist @ A_27a ) )
             => ! [V3lol: $i] :
                  ( ( mem @ V3lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                 => ( ( p @ ( ap @ V0P @ V3lol ) )
                   => ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2m ) ) @ V3lol ) ) ) ) ) ) )
       => ! [V4v: $i] :
            ( ( mem @ V4v @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
           => ( p @ ( ap @ V0P @ V4v ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Elol__set,axiom,
    ! [A_27a: del] :
      ( ( ( ap @ ( c_2Eenumeral_2Elol__set @ A_27a ) @ ( c_2Elist_2ENIL @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
        = ( c_2Epred__set_2EEMPTY @ A_27a ) )
      & ! [V0lol: $i] :
          ( ( mem @ V0lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
         => ( ( ap @ ( c_2Eenumeral_2Elol__set @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ V0lol ) )
            = ( ap @ ( c_2Eenumeral_2Elol__set @ A_27a ) @ V0lol ) ) )
      & ! [V1m: $i] :
          ( ( mem @ V1m @ ( ty_2Elist_2Elist @ A_27a ) )
         => ! [V2lol: $i] :
              ( ( mem @ V2lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
             => ( ( ap @ ( c_2Eenumeral_2Elol__set @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V1m ) ) @ V2lol ) )
                = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1m ) ) @ ( ap @ ( c_2Eenumeral_2Elol__set @ A_27a ) @ V2lol ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Eincr__smerge__ind,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ bool ) ) ) )
     => ( ( ! [V1cmp: $i] :
              ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V2l: $i] :
                  ( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V1cmp ) @ V2l ) @ ( c_2Elist_2ENIL @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) )
          & ! [V3cmp: $i] :
              ( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V4l: $i] :
                  ( ( mem @ V4l @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ! [V5lol: $i] :
                      ( ( mem @ V5lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                     => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V3cmp ) @ V4l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ V5lol ) ) ) ) ) )
          & ! [V6cmp: $i] :
              ( ( mem @ V6cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V7l: $i] :
                  ( ( mem @ V7l @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ! [V8m: $i] :
                      ( ( mem @ V8m @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ! [V9lol: $i] :
                          ( ( mem @ V9lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                         => ( ( p @ ( ap @ ( ap @ ( ap @ V0P @ V6cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V6cmp ) @ V7l ) @ V8m ) ) @ V9lol ) )
                           => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V6cmp ) @ V7l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V8m ) ) @ V9lol ) ) ) ) ) ) ) ) )
       => ! [V10v: $i] :
            ( ( mem @ V10v @ ( ty_2Etoto_2Etoto @ A_27a ) )
           => ! [V11v1: $i] :
                ( ( mem @ V11v1 @ ( ty_2Elist_2Elist @ A_27a ) )
               => ! [V12v2: $i] :
                    ( ( mem @ V12v2 @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V10v ) @ V11v1 ) @ V12v2 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Eincr__smerge,axiom,
    ! [A_27a: del] :
      ( ! [V0l: $i] :
          ( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
         => ! [V1cmp: $i] :
              ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__smerge @ A_27a ) @ V1cmp ) @ V0l ) @ ( c_2Elist_2ENIL @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                = ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0l ) ) @ ( c_2Elist_2ENIL @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) )
      & ! [V2lol: $i] :
          ( ( mem @ V2lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
         => ! [V3l: $i] :
              ( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
             => ! [V4cmp: $i] :
                  ( ( mem @ V4cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__smerge @ A_27a ) @ V4cmp ) @ V3l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ V2lol ) )
                    = ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V3l ) ) @ V2lol ) ) ) ) )
      & ! [V5m: $i] :
          ( ( mem @ V5m @ ( ty_2Elist_2Elist @ A_27a ) )
         => ! [V6lol: $i] :
              ( ( mem @ V6lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
             => ! [V7l: $i] :
                  ( ( mem @ V7l @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ! [V8cmp: $i] :
                      ( ( mem @ V8cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__smerge @ A_27a ) @ V8cmp ) @ V7l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V5m ) ) @ V6lol ) )
                        = ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__smerge @ A_27a ) @ V8cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V8cmp ) @ V7l ) @ V5m ) ) @ V6lol ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Eincr__smerge__OL,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1lol: $i] :
          ( ( mem @ V1lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
         => ! [V2l: $i] :
              ( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
             => ( ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__sublists @ A_27a ) @ V0cmp ) @ V1lol ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ V2l ) ) )
               => ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__sublists @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__smerge @ A_27a ) @ V0cmp ) @ V2l ) @ V1lol ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Esmerge__out__ind,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ bool ) ) ) )
     => ( ( ! [V1cmp: $i] :
              ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V2l: $i] :
                  ( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V1cmp ) @ V2l ) @ ( c_2Elist_2ENIL @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) )
          & ! [V3cmp: $i] :
              ( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V4l: $i] :
                  ( ( mem @ V4l @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ! [V5lol: $i] :
                      ( ( mem @ V5lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                     => ( ( p @ ( ap @ ( ap @ ( ap @ V0P @ V3cmp ) @ V4l ) @ V5lol ) )
                       => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V3cmp ) @ V4l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ V5lol ) ) ) ) ) ) )
          & ! [V6cmp: $i] :
              ( ( mem @ V6cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V7l: $i] :
                  ( ( mem @ V7l @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ! [V8m: $i] :
                      ( ( mem @ V8m @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ! [V9lol: $i] :
                          ( ( mem @ V9lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                         => ( ( p @ ( ap @ ( ap @ ( ap @ V0P @ V6cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V6cmp ) @ V7l ) @ V8m ) ) @ V9lol ) )
                           => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V6cmp ) @ V7l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V8m ) ) @ V9lol ) ) ) ) ) ) ) ) )
       => ! [V10v: $i] :
            ( ( mem @ V10v @ ( ty_2Etoto_2Etoto @ A_27a ) )
           => ! [V11v1: $i] :
                ( ( mem @ V11v1 @ ( ty_2Elist_2Elist @ A_27a ) )
               => ! [V12v2: $i] :
                    ( ( mem @ V12v2 @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V10v ) @ V11v1 ) @ V12v2 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Esmerge__out,axiom,
    ! [A_27a: del] :
      ( ! [V0l: $i] :
          ( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
         => ! [V1cmp: $i] :
              ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge__out @ A_27a ) @ V1cmp ) @ V0l ) @ ( c_2Elist_2ENIL @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
                = V0l ) ) )
      & ! [V2lol: $i] :
          ( ( mem @ V2lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
         => ! [V3l: $i] :
              ( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
             => ! [V4cmp: $i] :
                  ( ( mem @ V4cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge__out @ A_27a ) @ V4cmp ) @ V3l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ V2lol ) )
                    = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge__out @ A_27a ) @ V4cmp ) @ V3l ) @ V2lol ) ) ) ) )
      & ! [V5m: $i] :
          ( ( mem @ V5m @ ( ty_2Elist_2Elist @ A_27a ) )
         => ! [V6lol: $i] :
              ( ( mem @ V6lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
             => ! [V7l: $i] :
                  ( ( mem @ V7l @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ! [V8cmp: $i] :
                      ( ( mem @ V8cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge__out @ A_27a ) @ V8cmp ) @ V7l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V5m ) ) @ V6lol ) )
                        = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge__out @ A_27a ) @ V8cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V8cmp ) @ V7l ) @ V5m ) ) @ V6lol ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Eincr__sbuild,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__sbuild @ A_27a ) @ V0cmp ) @ ( c_2Elist_2ENIL @ A_27a ) )
            = ( c_2Elist_2ENIL @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) )
      & ! [V1cmp: $i] :
          ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V2x: $i] :
              ( ( mem @ V2x @ A_27a )
             => ! [V3l: $i] :
                  ( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ( ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__sbuild @ A_27a ) @ V1cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ V3l ) )
                    = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__smerge @ A_27a ) @ V1cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__sbuild @ A_27a ) @ V1cmp ) @ V3l ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Eincr__ssort,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1l: $i] :
          ( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__ssort @ A_27a ) @ V0cmp ) @ V1l )
            = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge__out @ A_27a ) @ V0cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__sbuild @ A_27a ) @ V0cmp ) @ V1l ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__set,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ ( c_2Eenumeral_2Ent @ A_27a ) )
            = ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
      & ! [V1cmp: $i] :
          ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V2l: $i] :
              ( ( mem @ V2l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V3x: $i] :
                  ( ( mem @ V3x @ A_27a )
                 => ! [V4r: $i] :
                      ( ( mem @ V4r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                     => ( ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V1cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V2l ) @ V3x ) @ V4r ) )
                        = ( ap
                          @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a )
                            @ ( ap
                              @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a )
                                @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                                  @ ( lam @ A_27a
                                    @ ^ [V5y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V5y ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5y ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V1cmp ) @ V2l ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V1cmp ) @ V5y ) @ V3x ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) )
                              @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V3x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) )
                          @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                            @ ( lam @ A_27a
                              @ ^ [V6z: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V6z ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6z ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V1cmp ) @ V4r ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V1cmp ) @ V3x ) @ V6z ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__set__lb,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1lb: $i] :
          ( ( mem @ V1lb @ A_27a )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__set__lb @ A_27a ) @ V0cmp ) @ V1lb ) @ V2t )
                = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                  @ ( lam @ A_27a
                    @ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ V2t ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V0cmp ) @ V1lb ) @ V3x ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__set__ub,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ! [V2ub: $i] :
              ( ( mem @ V2ub @ A_27a )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__set__ub @ A_27a ) @ V0cmp ) @ V1t ) @ V2ub )
                = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                  @ ( lam @ A_27a
                    @ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ V1t ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V0cmp ) @ V3x ) @ V2ub ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__set__lb__ub,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1lb: $i] :
          ( ( mem @ V1lb @ A_27a )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V3ub: $i] :
                  ( ( mem @ V3ub @ A_27a )
                 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__set__lb__ub @ A_27a ) @ V0cmp ) @ V1lb ) @ V2t ) @ V3ub )
                    = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                      @ ( lam @ A_27a
                        @ ^ [V4x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V4x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ V2t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V0cmp ) @ V1lb ) @ V4x ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V0cmp ) @ V4x ) @ V3ub ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EIN__bt__to__set,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V1y: $i] :
              ( ( mem @ V1y @ A_27a )
             => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1y ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) ) )
              <=> $false ) ) )
      & ! [V2cmp: $i] :
          ( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V3l: $i] :
              ( ( mem @ V3l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V4x: $i] :
                  ( ( mem @ V4x @ A_27a )
                 => ! [V5r: $i] :
                      ( ( mem @ V5r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                     => ! [V6y: $i] :
                          ( ( mem @ V6y @ A_27a )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6y ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V2cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V3l ) @ V4x ) @ V5r ) ) ) )
                          <=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6y ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V2cmp ) @ V3l ) ) )
                                & ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V2cmp ) @ V6y ) @ V4x ) )
                                  = fo__c_2EternaryComparisons_2ELESS ) )
                              | ( V6y = V4x )
                              | ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6y ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V2cmp ) @ V5r ) ) )
                                & ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V2cmp ) @ V4x ) @ V6y ) )
                                  = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2ENOT__IN__nt,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ A_27a )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1y ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) ) )
          <=> $false ) ) ) ).

thf(conj_thm_2Eenumeral_2EIN__node,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2l: $i] :
              ( ( mem @ V2l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V3y: $i] :
                  ( ( mem @ V3y @ A_27a )
                 => ! [V4r: $i] :
                      ( ( mem @ V4r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V2l ) @ V3y ) @ V4r ) ) ) )
                      <=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Eordering__CASE @ bool ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V0cmp ) @ V1x ) @ V3y ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ V2l ) ) ) @ c_2Ebool_2ET ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ V4r ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__ol__lb__ub,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V1lb: $i] :
              ( ( mem @ V1lb @ A_27a )
             => ! [V2ub: $i] :
                  ( ( mem @ V2ub @ A_27a )
                 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub @ A_27a ) @ V0cmp ) @ V1lb ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ V2ub )
                    = ( c_2Elist_2ENIL @ A_27a ) ) ) ) )
      & ! [V3cmp: $i] :
          ( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V4lb: $i] :
              ( ( mem @ V4lb @ A_27a )
             => ! [V5l: $i] :
                  ( ( mem @ V5l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V6x: $i] :
                      ( ( mem @ V6x @ A_27a )
                     => ! [V7r: $i] :
                          ( ( mem @ V7r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                         => ! [V8ub: $i] :
                              ( ( mem @ V8ub @ A_27a )
                             => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub @ A_27a ) @ V3cmp ) @ V4lb ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V5l ) @ V6x ) @ V7r ) ) @ V8ub )
                                = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V3cmp ) @ V4lb ) @ V6x ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V3cmp ) @ V6x ) @ V8ub ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub @ A_27a ) @ V3cmp ) @ V4lb ) @ V5l ) @ V6x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V6x ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub @ A_27a ) @ V3cmp ) @ V6x ) @ V7r ) @ V8ub ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub @ A_27a ) @ V3cmp ) @ V4lb ) @ V5l ) @ V8ub ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub @ A_27a ) @ V3cmp ) @ V4lb ) @ V7r ) @ V8ub ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__ol__lb,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V1lb: $i] :
              ( ( mem @ V1lb @ A_27a )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb @ A_27a ) @ V0cmp ) @ V1lb ) @ ( c_2Eenumeral_2Ent @ A_27a ) )
                = ( c_2Elist_2ENIL @ A_27a ) ) ) )
      & ! [V2cmp: $i] :
          ( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V3lb: $i] :
              ( ( mem @ V3lb @ A_27a )
             => ! [V4l: $i] :
                  ( ( mem @ V4l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V5x: $i] :
                      ( ( mem @ V5x @ A_27a )
                     => ! [V6r: $i] :
                          ( ( mem @ V6r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb @ A_27a ) @ V2cmp ) @ V3lb ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V4l ) @ V5x ) @ V6r ) )
                            = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V2cmp ) @ V3lb ) @ V5x ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub @ A_27a ) @ V2cmp ) @ V3lb ) @ V4l ) @ V5x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V5x ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb @ A_27a ) @ V2cmp ) @ V5x ) @ V6r ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb @ A_27a ) @ V2cmp ) @ V3lb ) @ V6r ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__ol__ub,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V1ub: $i] :
              ( ( mem @ V1ub @ A_27a )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ub @ A_27a ) @ V0cmp ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ V1ub )
                = ( c_2Elist_2ENIL @ A_27a ) ) ) )
      & ! [V2cmp: $i] :
          ( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V3l: $i] :
              ( ( mem @ V3l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V4x: $i] :
                  ( ( mem @ V4x @ A_27a )
                 => ! [V5r: $i] :
                      ( ( mem @ V5r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                     => ! [V6ub: $i] :
                          ( ( mem @ V6ub @ A_27a )
                         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ub @ A_27a ) @ V2cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V3l ) @ V4x ) @ V5r ) ) @ V6ub )
                            = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V2cmp ) @ V4x ) @ V6ub ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ub @ A_27a ) @ V2cmp ) @ V3l ) @ V4x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4x ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub @ A_27a ) @ V2cmp ) @ V4x ) @ V5r ) @ V6ub ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ub @ A_27a ) @ V2cmp ) @ V3l ) @ V6ub ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__ol,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol @ A_27a ) @ V0cmp ) @ ( c_2Eenumeral_2Ent @ A_27a ) )
            = ( c_2Elist_2ENIL @ A_27a ) ) )
      & ! [V1cmp: $i] :
          ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V2l: $i] :
              ( ( mem @ V2l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V3x: $i] :
                  ( ( mem @ V3x @ A_27a )
                 => ! [V4r: $i] :
                      ( ( mem @ V4r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                     => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol @ A_27a ) @ V1cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V2l ) @ V3x ) @ V4r ) )
                        = ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ub @ A_27a ) @ V1cmp ) @ V2l ) @ V3x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3x ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb @ A_27a ) @ V1cmp ) @ V3x ) @ V4r ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Eol__set,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ V1t )
            = ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol @ A_27a ) @ V0cmp ) @ V1t ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOL__bt__to__ol__lb__ub,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ! [V2lb: $i] :
              ( ( mem @ V2lb @ A_27a )
             => ! [V3ub: $i] :
                  ( ( mem @ V3ub @ A_27a )
                 => ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub @ A_27a ) @ V0cmp ) @ V2lb ) @ V1t ) @ V3ub ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOL__bt__to__ol__lb,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ! [V2lb: $i] :
              ( ( mem @ V2lb @ A_27a )
             => ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb @ A_27a ) @ V0cmp ) @ V2lb ) @ V1t ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOL__bt__to__ol__ub,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ! [V2ub: $i] :
              ( ( mem @ V2ub @ A_27a )
             => ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ub @ A_27a ) @ V0cmp ) @ V1t ) @ V2ub ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOL__bt__to__ol,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol @ A_27a ) @ V0cmp ) @ V1t ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__ol__lb__ub__ac,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V1lb: $i] :
              ( ( mem @ V1lb @ A_27a )
             => ! [V2ub: $i] :
                  ( ( mem @ V2ub @ A_27a )
                 => ! [V3m: $i] :
                      ( ( mem @ V3m @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac @ A_27a ) @ V0cmp ) @ V1lb ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ V2ub ) @ V3m )
                        = V3m ) ) ) ) )
      & ! [V4cmp: $i] :
          ( ( mem @ V4cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V5lb: $i] :
              ( ( mem @ V5lb @ A_27a )
             => ! [V6l: $i] :
                  ( ( mem @ V6l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V7x: $i] :
                      ( ( mem @ V7x @ A_27a )
                     => ! [V8r: $i] :
                          ( ( mem @ V8r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                         => ! [V9ub: $i] :
                              ( ( mem @ V9ub @ A_27a )
                             => ! [V10m: $i] :
                                  ( ( mem @ V10m @ ( ty_2Elist_2Elist @ A_27a ) )
                                 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac @ A_27a ) @ V4cmp ) @ V5lb ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V6l ) @ V7x ) @ V8r ) ) @ V9ub ) @ V10m )
                                    = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V5lb ) @ V7x ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V7x ) @ V9ub ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac @ A_27a ) @ V4cmp ) @ V5lb ) @ V6l ) @ V7x ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V7x ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac @ A_27a ) @ V4cmp ) @ V7x ) @ V8r ) @ V9ub ) @ V10m ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac @ A_27a ) @ V4cmp ) @ V5lb ) @ V6l ) @ V9ub ) @ V10m ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac @ A_27a ) @ V4cmp ) @ V5lb ) @ V8r ) @ V9ub ) @ V10m ) ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__ol__lb__ac,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V1lb: $i] :
              ( ( mem @ V1lb @ A_27a )
             => ! [V2m: $i] :
                  ( ( mem @ V2m @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ac @ A_27a ) @ V0cmp ) @ V1lb ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ V2m )
                    = V2m ) ) ) )
      & ! [V3cmp: $i] :
          ( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V4lb: $i] :
              ( ( mem @ V4lb @ A_27a )
             => ! [V5l: $i] :
                  ( ( mem @ V5l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V6x: $i] :
                      ( ( mem @ V6x @ A_27a )
                     => ! [V7r: $i] :
                          ( ( mem @ V7r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                         => ! [V8m: $i] :
                              ( ( mem @ V8m @ ( ty_2Elist_2Elist @ A_27a ) )
                             => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ac @ A_27a ) @ V3cmp ) @ V4lb ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V5l ) @ V6x ) @ V7r ) ) @ V8m )
                                = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V3cmp ) @ V4lb ) @ V6x ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac @ A_27a ) @ V3cmp ) @ V4lb ) @ V5l ) @ V6x ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V6x ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ac @ A_27a ) @ V3cmp ) @ V6x ) @ V7r ) @ V8m ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ac @ A_27a ) @ V3cmp ) @ V4lb ) @ V7r ) @ V8m ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__ol__ub__ac,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V1ub: $i] :
              ( ( mem @ V1ub @ A_27a )
             => ! [V2m: $i] :
                  ( ( mem @ V2m @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ub__ac @ A_27a ) @ V0cmp ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ V1ub ) @ V2m )
                    = V2m ) ) ) )
      & ! [V3cmp: $i] :
          ( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V4l: $i] :
              ( ( mem @ V4l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V5x: $i] :
                  ( ( mem @ V5x @ A_27a )
                 => ! [V6r: $i] :
                      ( ( mem @ V6r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                     => ! [V7ub: $i] :
                          ( ( mem @ V7ub @ A_27a )
                         => ! [V8m: $i] :
                              ( ( mem @ V8m @ ( ty_2Elist_2Elist @ A_27a ) )
                             => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ub__ac @ A_27a ) @ V3cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V4l ) @ V5x ) @ V6r ) ) @ V7ub ) @ V8m )
                                = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V3cmp ) @ V5x ) @ V7ub ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ub__ac @ A_27a ) @ V3cmp ) @ V4l ) @ V5x ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V5x ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac @ A_27a ) @ V3cmp ) @ V5x ) @ V6r ) @ V7ub ) @ V8m ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ub__ac @ A_27a ) @ V3cmp ) @ V4l ) @ V7ub ) @ V8m ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebt__to__ol__ac,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V1m: $i] :
              ( ( mem @ V1m @ ( ty_2Elist_2Elist @ A_27a ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ac @ A_27a ) @ V0cmp ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ V1m )
                = V1m ) ) )
      & ! [V2cmp: $i] :
          ( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V3l: $i] :
              ( ( mem @ V3l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V4x: $i] :
                  ( ( mem @ V4x @ A_27a )
                 => ! [V5r: $i] :
                      ( ( mem @ V5r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                     => ! [V6m: $i] :
                          ( ( mem @ V6m @ ( ty_2Elist_2Elist @ A_27a ) )
                         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ac @ A_27a ) @ V2cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V3l ) @ V4x ) @ V5r ) ) @ V6m )
                            = ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ub__ac @ A_27a ) @ V2cmp ) @ V3l ) @ V4x ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4x ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__lb__ac @ A_27a ) @ V2cmp ) @ V4x ) @ V5r ) @ V6m ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2EOWL,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2l: $i] :
              ( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
             => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOWL @ A_27a ) @ V0cmp ) @ V1s ) @ V2l ) )
              <=> ( ( V1s
                    = ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2l ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ V2l ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOWL__bt__to__ol,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOWL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ V1t ) ) @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol @ A_27a ) @ V0cmp ) @ V1t ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2EOU,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
         => ! [V2u: $i] :
              ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOU @ A_27a ) @ V0cmp ) @ V1t ) @ V2u )
                = ( ap
                  @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a )
                    @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                      @ ( lam @ A_27a
                        @ ^ [V3x: $i] :
                            ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3x )
                            @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1t ) )
                              @ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
                                @ ( lam @ A_27a
                                  @ ^ [V4z: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4z ) @ V2u ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V0cmp ) @ V3x ) @ V4z ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) )
                  @ V2u ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2EUO,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EUO @ A_27a ) @ V0cmp ) @ V1s ) @ V2t )
                = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s )
                  @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                    @ ( lam @ A_27a
                      @ ^ [V3y: $i] :
                          ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3y )
                          @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V2t ) )
                            @ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
                              @ ( lam @ A_27a
                                @ ^ [V4z: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4z ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V0cmp ) @ V4z ) @ V3y ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EEMPTY__OU,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1sl: $i] :
          ( ( mem @ V1sl @ ( arr @ A_27a @ bool ) )
         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOU @ A_27a ) @ V0cmp ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V1sl )
            = V1sl ) ) ) ).

thf(conj_thm_2Eenumeral_2EOU__EMPTY,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOU @ A_27a ) @ V0cmp ) @ V1t ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
            = V1t ) ) ) ).

thf(conj_thm_2Eenumeral_2ELESS__UO__LEM,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2y: $i] :
              ( ( mem @ V2y @ A_27a )
             => ! [V3s: $i] :
                  ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
                 => ( ! [V4z: $i] :
                        ( ( mem @ V4z @ A_27a )
                       => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4z ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EUO @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V3s ) ) )
                         => ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V0cmp ) @ V2y ) @ V4z ) )
                            = fo__c_2EternaryComparisons_2ELESS ) ) )
                  <=> ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V0cmp ) @ V2y ) @ V1x ) )
                      = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2ELESS__ALL,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2ELESS__ALL @ A_27a ) @ V0cmp ) @ V1x ) @ V2s ) )
              <=> ! [V3y: $i] :
                    ( ( mem @ V3y @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V2s ) )
                     => ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V0cmp ) @ V1x ) @ V3y ) )
                        = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2ELESS__ALL__OU,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2u: $i] :
              ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
             => ! [V3v: $i] :
                  ( ( mem @ V3v @ ( arr @ A_27a @ bool ) )
                 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2ELESS__ALL @ A_27a ) @ V0cmp ) @ V1x ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOU @ A_27a ) @ V0cmp ) @ V2u ) @ V3v ) ) )
                  <=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2ELESS__ALL @ A_27a ) @ V0cmp ) @ V1x ) @ V2u ) )
                      & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2ELESS__ALL @ A_27a ) @ V0cmp ) @ V1x ) @ V3v ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOU__ASSOC,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ ( arr @ A_27a @ bool ) )
         => ! [V2b: $i] :
              ( ( mem @ V2b @ ( arr @ A_27a @ bool ) )
             => ! [V3c: $i] :
                  ( ( mem @ V3c @ ( arr @ A_27a @ bool ) )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOU @ A_27a ) @ V0cmp ) @ V1a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOU @ A_27a ) @ V0cmp ) @ V2b ) @ V3c ) )
                    = ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOU @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOU @ A_27a ) @ V0cmp ) @ V1a ) @ V2b ) ) @ V3c ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2Ebl__to__set,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__to__set @ A_27a ) @ V0cmp ) @ ( c_2Eenumeral_2Enbl @ A_27a ) )
            = ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
      & ! [V1cmp: $i] :
          ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V2b: $i] :
              ( ( mem @ V2b @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
             => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__to__set @ A_27a ) @ V1cmp ) @ ( ap @ ( c_2Eenumeral_2Ezerbl @ A_27a ) @ V2b ) )
                = ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__to__set @ A_27a ) @ V1cmp ) @ V2b ) ) ) )
      & ! [V3cmp: $i] :
          ( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V4x: $i] :
              ( ( mem @ V4x @ A_27a )
             => ! [V5t: $i] :
                  ( ( mem @ V5t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V6b: $i] :
                      ( ( mem @ V6b @ ( ty_2Eenumeral_2Ebl @ A_27a ) )
                     => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__to__set @ A_27a ) @ V3cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Eonebl @ A_27a ) @ V4x ) @ V5t ) @ V6b ) )
                        = ( ap
                          @ ( ap @ ( ap @ ( c_2Eenumeral_2EOU @ A_27a ) @ V3cmp )
                            @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V4x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
                              @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                                @ ( lam @ A_27a
                                  @ ^ [V7y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V7y ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V7y ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V3cmp ) @ V5t ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V3cmp ) @ V4x ) @ V7y ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) )
                          @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebl__to__set @ A_27a ) @ V3cmp ) @ V6b ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2ELESS__ALL__UO__LEM,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ A_27a )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2ELESS__ALL @ A_27a ) @ V0cmp ) @ V1a ) @ V2s ) )
               => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EUO @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V2s )
                  = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1a ) @ V2s ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2ELESS__ALL__OU__UO__LEM,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ A_27a )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ! [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
                 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2ELESS__ALL @ A_27a ) @ V0cmp ) @ V1a ) @ V2s ) )
                      & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2ELESS__ALL @ A_27a ) @ V0cmp ) @ V1a ) @ V3t ) ) )
                   => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOU @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EUO @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V2s ) ) @ V3t )
                      = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOU @ A_27a ) @ V0cmp ) @ V2s ) @ V3t ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebt__to__ol__ID__IMP,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1l: $i] :
          ( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ V1l ) )
           => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol @ A_27a ) @ V0cmp ) @ ( ap @ ( c_2Eenumeral_2Elist__to__bt @ A_27a ) @ V1l ) )
              = V1l ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOL__UNION__IMP,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1l: $i] :
          ( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ V1l ) )
           => ! [V2m: $i] :
                ( ( mem @ V2m @ ( ty_2Elist_2Elist @ A_27a ) )
               => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ V2m ) )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V0cmp ) @ V1l ) @ V2m ) ) )
                    & ( ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V0cmp ) @ V1l ) @ V2m ) )
                      = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2m ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Esinter__ind,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) ) ) )
     => ( ( ! [V1cmp: $i] :
              ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V1cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
          & ! [V2cmp: $i] :
              ( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V3x: $i] :
                  ( ( mem @ V3x @ A_27a )
                 => ! [V4l: $i] :
                      ( ( mem @ V4l @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V2cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3x ) @ V4l ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) )
          & ! [V5cmp: $i] :
              ( ( mem @ V5cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V6y: $i] :
                  ( ( mem @ V6y @ A_27a )
                 => ! [V7m: $i] :
                      ( ( mem @ V7m @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V5cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V6y ) @ V7m ) ) ) ) ) )
          & ! [V8cmp: $i] :
              ( ( mem @ V8cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V9x: $i] :
                  ( ( mem @ V9x @ A_27a )
                 => ! [V10l: $i] :
                      ( ( mem @ V10l @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ! [V11y: $i] :
                          ( ( mem @ V11y @ A_27a )
                         => ! [V12m: $i] :
                              ( ( mem @ V12m @ ( ty_2Elist_2Elist @ A_27a ) )
                             => ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V8cmp ) @ V9x ) @ V11y ) )
                                      = fo__c_2EternaryComparisons_2EEQUAL )
                                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V8cmp ) @ V10l ) @ V12m ) ) )
                                  & ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V8cmp ) @ V9x ) @ V11y ) )
                                      = fo__c_2EternaryComparisons_2EGREATER )
                                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V8cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V9x ) @ V10l ) ) @ V12m ) ) )
                                  & ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V8cmp ) @ V9x ) @ V11y ) )
                                      = fo__c_2EternaryComparisons_2ELESS )
                                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V8cmp ) @ V10l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V11y ) @ V12m ) ) ) ) )
                               => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V8cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V9x ) @ V10l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V11y ) @ V12m ) ) ) ) ) ) ) ) ) )
       => ! [V13v: $i] :
            ( ( mem @ V13v @ ( ty_2Etoto_2Etoto @ A_27a ) )
           => ! [V14v1: $i] :
                ( ( mem @ V14v1 @ ( ty_2Elist_2Elist @ A_27a ) )
               => ! [V15v2: $i] :
                    ( ( mem @ V15v2 @ ( ty_2Elist_2Elist @ A_27a ) )
                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V13v ) @ V14v1 ) @ V15v2 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Esinter,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esinter @ A_27a ) @ V0cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) )
            = ( c_2Elist_2ENIL @ A_27a ) ) )
      & ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2l: $i] :
              ( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
             => ! [V3cmp: $i] :
                  ( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esinter @ A_27a ) @ V3cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ V2l ) ) @ ( c_2Elist_2ENIL @ A_27a ) )
                    = ( c_2Elist_2ENIL @ A_27a ) ) ) ) )
      & ! [V4y: $i] :
          ( ( mem @ V4y @ A_27a )
         => ! [V5m: $i] :
              ( ( mem @ V5m @ ( ty_2Elist_2Elist @ A_27a ) )
             => ! [V6cmp: $i] :
                  ( ( mem @ V6cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esinter @ A_27a ) @ V6cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4y ) @ V5m ) )
                    = ( c_2Elist_2ENIL @ A_27a ) ) ) ) )
      & ! [V7y: $i] :
          ( ( mem @ V7y @ A_27a )
         => ! [V8x: $i] :
              ( ( mem @ V8x @ A_27a )
             => ! [V9m: $i] :
                  ( ( mem @ V9m @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ! [V10l: $i] :
                      ( ( mem @ V10l @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ! [V11cmp: $i] :
                          ( ( mem @ V11cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esinter @ A_27a ) @ V11cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V8x ) @ V10l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V7y ) @ V9m ) )
                            = ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Eordering__CASE @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V11cmp ) @ V8x ) @ V7y ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esinter @ A_27a ) @ V11cmp ) @ V10l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V7y ) @ V9m ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V8x ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esinter @ A_27a ) @ V11cmp ) @ V10l ) @ V9m ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esinter @ A_27a ) @ V11cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V8x ) @ V10l ) ) @ V9m ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOL__INTER__IMP,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1l: $i] :
          ( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ V1l ) )
           => ! [V2m: $i] :
                ( ( mem @ V2m @ ( ty_2Elist_2Elist @ A_27a ) )
               => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ V2m ) )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esinter @ A_27a ) @ V0cmp ) @ V1l ) @ V2m ) ) )
                    & ( ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esinter @ A_27a ) @ V0cmp ) @ V1l ) @ V2m ) )
                      = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2m ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Esdiff__ind,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) ) ) )
     => ( ( ! [V1cmp: $i] :
              ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V1cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
          & ! [V2cmp: $i] :
              ( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V3x: $i] :
                  ( ( mem @ V3x @ A_27a )
                 => ! [V4l: $i] :
                      ( ( mem @ V4l @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V2cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3x ) @ V4l ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) )
          & ! [V5cmp: $i] :
              ( ( mem @ V5cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V6y: $i] :
                  ( ( mem @ V6y @ A_27a )
                 => ! [V7m: $i] :
                      ( ( mem @ V7m @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V5cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V6y ) @ V7m ) ) ) ) ) )
          & ! [V8cmp: $i] :
              ( ( mem @ V8cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
             => ! [V9x: $i] :
                  ( ( mem @ V9x @ A_27a )
                 => ! [V10l: $i] :
                      ( ( mem @ V10l @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ! [V11y: $i] :
                          ( ( mem @ V11y @ A_27a )
                         => ! [V12m: $i] :
                              ( ( mem @ V12m @ ( ty_2Elist_2Elist @ A_27a ) )
                             => ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V8cmp ) @ V9x ) @ V11y ) )
                                      = fo__c_2EternaryComparisons_2EEQUAL )
                                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V8cmp ) @ V10l ) @ V12m ) ) )
                                  & ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V8cmp ) @ V9x ) @ V11y ) )
                                      = fo__c_2EternaryComparisons_2EGREATER )
                                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V8cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V9x ) @ V10l ) ) @ V12m ) ) )
                                  & ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V8cmp ) @ V9x ) @ V11y ) )
                                      = fo__c_2EternaryComparisons_2ELESS )
                                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V8cmp ) @ V10l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V11y ) @ V12m ) ) ) ) )
                               => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V8cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V9x ) @ V10l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V11y ) @ V12m ) ) ) ) ) ) ) ) ) )
       => ! [V13v: $i] :
            ( ( mem @ V13v @ ( ty_2Etoto_2Etoto @ A_27a ) )
           => ! [V14v1: $i] :
                ( ( mem @ V14v1 @ ( ty_2Elist_2Elist @ A_27a ) )
               => ! [V15v2: $i] :
                    ( ( mem @ V15v2 @ ( ty_2Elist_2Elist @ A_27a ) )
                   => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V13v ) @ V14v1 ) @ V15v2 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Esdiff,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esdiff @ A_27a ) @ V0cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) )
            = ( c_2Elist_2ENIL @ A_27a ) ) )
      & ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2l: $i] :
              ( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
             => ! [V3cmp: $i] :
                  ( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esdiff @ A_27a ) @ V3cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ V2l ) ) @ ( c_2Elist_2ENIL @ A_27a ) )
                    = ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ V2l ) ) ) ) )
      & ! [V4y: $i] :
          ( ( mem @ V4y @ A_27a )
         => ! [V5m: $i] :
              ( ( mem @ V5m @ ( ty_2Elist_2Elist @ A_27a ) )
             => ! [V6cmp: $i] :
                  ( ( mem @ V6cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esdiff @ A_27a ) @ V6cmp ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4y ) @ V5m ) )
                    = ( c_2Elist_2ENIL @ A_27a ) ) ) ) )
      & ! [V7y: $i] :
          ( ( mem @ V7y @ A_27a )
         => ! [V8x: $i] :
              ( ( mem @ V8x @ A_27a )
             => ! [V9m: $i] :
                  ( ( mem @ V9m @ ( ty_2Elist_2Elist @ A_27a ) )
                 => ! [V10l: $i] :
                      ( ( mem @ V10l @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ! [V11cmp: $i] :
                          ( ( mem @ V11cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
                         => ( ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esdiff @ A_27a ) @ V11cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V8x ) @ V10l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V7y ) @ V9m ) )
                            = ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Eordering__CASE @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V11cmp ) @ V8x ) @ V7y ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V8x ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esdiff @ A_27a ) @ V11cmp ) @ V10l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V7y ) @ V9m ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esdiff @ A_27a ) @ V11cmp ) @ V10l ) @ V9m ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esdiff @ A_27a ) @ V11cmp ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V8x ) @ V10l ) ) @ V9m ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOL__DIFF__IMP,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1l: $i] :
          ( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ V1l ) )
           => ! [V2m: $i] :
                ( ( mem @ V2m @ ( ty_2Elist_2Elist @ A_27a ) )
               => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ V2m ) )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esdiff @ A_27a ) @ V0cmp ) @ V1l ) @ V2m ) ) )
                    & ( ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esdiff @ A_27a ) @ V0cmp ) @ V1l ) @ V2m ) )
                      = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2m ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EENUMERAL__set,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1l: $i] :
          ( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
         => ( ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l )
            = ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ ( ap @ ( c_2Eenumeral_2Elist__to__bt @ A_27a ) @ ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__ssort @ A_27a ) @ V0cmp ) @ V1l ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOL__ENUMERAL,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1l: $i] :
          ( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL @ A_27a ) @ V0cmp ) @ V1l ) )
           => ( ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l )
              = ( ap @ ( ap @ ( c_2Eenumeral_2EENUMERAL @ A_27a ) @ V0cmp ) @ ( ap @ ( c_2Eenumeral_2Elist__to__bt @ A_27a ) @ V1l ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOWL__UNION__THM,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2l: $i] :
              ( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
             => ! [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
                 => ! [V4m: $i] :
                      ( ( mem @ V4m @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOWL @ A_27a ) @ V0cmp ) @ V1s ) @ V2l ) )
                          & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOWL @ A_27a ) @ V0cmp ) @ V3t ) @ V4m ) ) )
                       => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOWL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V3t ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esmerge @ A_27a ) @ V0cmp ) @ V2l ) @ V4m ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOWL__INTER__THM,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2l: $i] :
              ( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
             => ! [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
                 => ! [V4m: $i] :
                      ( ( mem @ V4m @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOWL @ A_27a ) @ V0cmp ) @ V1s ) @ V2l ) )
                          & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOWL @ A_27a ) @ V0cmp ) @ V3t ) @ V4m ) ) )
                       => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOWL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ V3t ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esinter @ A_27a ) @ V0cmp ) @ V2l ) @ V4m ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2EOWL__DIFF__THM,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2l: $i] :
              ( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
             => ! [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
                 => ! [V4m: $i] :
                      ( ( mem @ V4m @ ( ty_2Elist_2Elist @ A_27a ) )
                     => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOWL @ A_27a ) @ V0cmp ) @ V1s ) @ V2l ) )
                          & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOWL @ A_27a ) @ V0cmp ) @ V3t ) @ V4m ) ) )
                       => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOWL @ A_27a ) @ V0cmp ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V1s ) @ V3t ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Esdiff @ A_27a ) @ V0cmp ) @ V2l ) @ V4m ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2EOL__bt__lb__ub,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V1lb: $i] :
              ( ( mem @ V1lb @ A_27a )
             => ! [V2ub: $i] :
                  ( ( mem @ V2ub @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__lb__ub @ A_27a ) @ V0cmp ) @ V1lb ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ V2ub ) )
                  <=> ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V0cmp ) @ V1lb ) @ V2ub ) )
                      = fo__c_2EternaryComparisons_2ELESS ) ) ) ) )
      & ! [V3cmp: $i] :
          ( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V4lb: $i] :
              ( ( mem @ V4lb @ A_27a )
             => ! [V5l: $i] :
                  ( ( mem @ V5l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V6x: $i] :
                      ( ( mem @ V6x @ A_27a )
                     => ! [V7r: $i] :
                          ( ( mem @ V7r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                         => ! [V8ub: $i] :
                              ( ( mem @ V8ub @ A_27a )
                             => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__lb__ub @ A_27a ) @ V3cmp ) @ V4lb ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V5l ) @ V6x ) @ V7r ) ) @ V8ub ) )
                              <=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__lb__ub @ A_27a ) @ V3cmp ) @ V4lb ) @ V5l ) @ V6x ) )
                                  & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__lb__ub @ A_27a ) @ V3cmp ) @ V6x ) @ V7r ) @ V8ub ) ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2EOL__bt__lb,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V1lb: $i] :
              ( ( mem @ V1lb @ A_27a )
             => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__lb @ A_27a ) @ V0cmp ) @ V1lb ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) )
              <=> $true ) ) )
      & ! [V2cmp: $i] :
          ( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V3lb: $i] :
              ( ( mem @ V3lb @ A_27a )
             => ! [V4l: $i] :
                  ( ( mem @ V4l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                 => ! [V5x: $i] :
                      ( ( mem @ V5x @ A_27a )
                     => ! [V6r: $i] :
                          ( ( mem @ V6r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                         => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__lb @ A_27a ) @ V2cmp ) @ V3lb ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V4l ) @ V5x ) @ V6r ) ) )
                          <=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__lb__ub @ A_27a ) @ V2cmp ) @ V3lb ) @ V4l ) @ V5x ) )
                              & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__lb @ A_27a ) @ V2cmp ) @ V5x ) @ V6r ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2EOL__bt__ub,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V1ub: $i] :
              ( ( mem @ V1ub @ A_27a )
             => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__ub @ A_27a ) @ V0cmp ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) @ V1ub ) )
              <=> $true ) ) )
      & ! [V2cmp: $i] :
          ( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V3l: $i] :
              ( ( mem @ V3l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V4x: $i] :
                  ( ( mem @ V4x @ A_27a )
                 => ! [V5r: $i] :
                      ( ( mem @ V5r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                     => ! [V6ub: $i] :
                          ( ( mem @ V6ub @ A_27a )
                         => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__ub @ A_27a ) @ V2cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V3l ) @ V4x ) @ V5r ) ) @ V6ub ) )
                          <=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__ub @ A_27a ) @ V2cmp ) @ V3l ) @ V4x ) )
                              & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__lb__ub @ A_27a ) @ V2cmp ) @ V4x ) @ V5r ) @ V6ub ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eenumeral_2EOL__bt,axiom,
    ! [A_27a: del] :
      ( ! [V0cmp: $i] :
          ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt @ A_27a ) @ V0cmp ) @ ( c_2Eenumeral_2Ent @ A_27a ) ) )
          <=> $true ) )
      & ! [V1cmp: $i] :
          ( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
         => ! [V2l: $i] :
              ( ( mem @ V2l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
             => ! [V3x: $i] :
                  ( ( mem @ V3x @ A_27a )
                 => ! [V4r: $i] :
                      ( ( mem @ V4r @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt @ A_27a ) @ V1cmp ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Enode @ A_27a ) @ V2l ) @ V3x ) @ V4r ) ) )
                      <=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__ub @ A_27a ) @ V1cmp ) @ V2l ) @ V3x ) )
                          & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt__lb @ A_27a ) @ V1cmp ) @ V3x ) @ V4r ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Ebetter__bt__to__ol,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol @ A_27a ) @ V0cmp ) @ V1t )
            = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Eenumeral_2EOL__bt @ A_27a ) @ V0cmp ) @ V1t ) ) @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__list__ac @ A_27a ) @ V1t ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2Ebt__to__ol__ac @ A_27a ) @ V0cmp ) @ V1t ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ) ).

thf(conj_thm_2Eenumeral_2Eset__OWL__thm,axiom,
    ! [A_27a: del,V0cmp: $i] :
      ( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
     => ! [V1l: $i] :
          ( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
         => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eenumeral_2EOWL @ A_27a ) @ V0cmp ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) @ ( ap @ ( ap @ ( c_2Eenumeral_2Eincr__ssort @ A_27a ) @ V0cmp ) @ V1l ) ) ) ) ) ).

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