ITP001 Axioms: ITP098^5.ax
%------------------------------------------------------------------------------
% File : ITP098^5 : TPTP v8.2.0. 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 ) ) ) ) ) ).
%------------------------------------------------------------------------------