TPTP Problem File: ITP010^5.p

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%------------------------------------------------------------------------------
% File     : ITP010^5 : TPTP v7.4.0. Released v7.4.0.
% Domain   : Interactive Theorem Proving
% Problem  : HOL4 set theory export of thm_2Ecardinal_2ECARD__NOT__LE.p, 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    : thm_2Ecardinal_2ECARD__NOT__LE.p [Gau20]
%          : HL404501^5.p [TPAP]

% Status   : Theorem
% Rating   : 0.86 v7.4.0
% Syntax   : Number of formulae    : 8027 (   2 unit;1146 type;   0 defn)
%            Number of atoms       : 422821 (8404 equality;167054 variable)
%            Maximal formula depth :  368 (  14 average)
%            Number of connectives : 400739 (1607   ~; 457   |;18912   &;359215   @)
%                                         (3600 <=>;16948  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 1303 (1303   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1151 (1146   :;   0   =)
%            Number of variables   : 39814 ( 336 sgn;24414   !;12786   ?;2614   ^)
%                                         (39814   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments :
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001^2.ax').
include('Axioms/ITP001/ITP002^5.ax').
include('Axioms/ITP001/ITP003^5.ax').
include('Axioms/ITP001/ITP004^5.ax').
include('Axioms/ITP001/ITP007^5.ax').
include('Axioms/ITP001/ITP006^5.ax').
include('Axioms/ITP001/ITP005^5.ax').
include('Axioms/ITP001/ITP008^5.ax').
include('Axioms/ITP001/ITP009^5.ax').
include('Axioms/ITP001/ITP010^5.ax').
include('Axioms/ITP001/ITP012^5.ax').
include('Axioms/ITP001/ITP011^5.ax').
include('Axioms/ITP001/ITP013^5.ax').
include('Axioms/ITP001/ITP014^5.ax').
include('Axioms/ITP001/ITP015^5.ax').
include('Axioms/ITP001/ITP017^5.ax').
include('Axioms/ITP001/ITP016^5.ax').
include('Axioms/ITP001/ITP019^5.ax').
include('Axioms/ITP001/ITP018^5.ax').
include('Axioms/ITP001/ITP021^5.ax').
include('Axioms/ITP001/ITP022^5.ax').
include('Axioms/ITP001/ITP020^5.ax').
include('Axioms/ITP001/ITP024^5.ax').
include('Axioms/ITP001/ITP023^5.ax').
include('Axioms/ITP001/ITP025^5.ax').
include('Axioms/ITP001/ITP026^5.ax').
include('Axioms/ITP001/ITP027^5.ax').
include('Axioms/ITP001/ITP028^5.ax').
include('Axioms/ITP001/ITP031^5.ax').
include('Axioms/ITP001/ITP029^5.ax').
include('Axioms/ITP001/ITP033^5.ax').
include('Axioms/ITP001/ITP030^5.ax').
include('Axioms/ITP001/ITP032^5.ax').
include('Axioms/ITP001/ITP038^5.ax').
include('Axioms/ITP001/ITP035^5.ax').
include('Axioms/ITP001/ITP034^5.ax').
include('Axioms/ITP001/ITP036^5.ax').
include('Axioms/ITP001/ITP037^5.ax').
include('Axioms/ITP001/ITP039^5.ax').
include('Axioms/ITP001/ITP041^5.ax').
include('Axioms/ITP001/ITP042^5.ax').
include('Axioms/ITP001/ITP040^5.ax').
include('Axioms/ITP001/ITP044^5.ax').
include('Axioms/ITP001/ITP051^5.ax').
include('Axioms/ITP001/ITP045^5.ax').
include('Axioms/ITP001/ITP056^5.ax').
include('Axioms/ITP001/ITP046^5.ax').
include('Axioms/ITP001/ITP043^5.ax').
include('Axioms/ITP001/ITP052^5.ax').
include('Axioms/ITP001/ITP057^5.ax').
include('Axioms/ITP001/ITP048^5.ax').
include('Axioms/ITP001/ITP047^5.ax').
include('Axioms/ITP001/ITP055^5.ax').
include('Axioms/ITP001/ITP053^5.ax').
include('Axioms/ITP001/ITP054^5.ax').
include('Axioms/ITP001/ITP058^5.ax').
include('Axioms/ITP001/ITP049^5.ax').
include('Axioms/ITP001/ITP050^5.ax').
include('Axioms/ITP001/ITP061^5.ax').
include('Axioms/ITP001/ITP069^5.ax').
include('Axioms/ITP001/ITP062^5.ax').
include('Axioms/ITP001/ITP068^5.ax').
include('Axioms/ITP001/ITP078^5.ax').
include('Axioms/ITP001/ITP064^5.ax').
include('Axioms/ITP001/ITP060^5.ax').
include('Axioms/ITP001/ITP067^5.ax').
include('Axioms/ITP001/ITP075^5.ax').
include('Axioms/ITP001/ITP074^5.ax').
%------------------------------------------------------------------------------
thf(tp_c_2Ecardinal_2E_2B__c,type,(
    c_2Ecardinal_2E_2B__c: del > del > $i )).

thf(mem_c_2Ecardinal_2E_2B__c,axiom,(
    ! [A_27a: del,A_27b: del] :
      ( mem @ ( c_2Ecardinal_2E_2B__c @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ bool ) ) ) ) )).

thf(tp_c_2Ecardinal_2EHAS__SIZE,type,(
    c_2Ecardinal_2EHAS__SIZE: del > $i )).

thf(mem_c_2Ecardinal_2EHAS__SIZE,axiom,(
    ! [A_27a: del] :
      ( mem @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) )).

thf(tp_c_2Ecardinal_2Ebijns,type,(
    c_2Ecardinal_2Ebijns: del > $i )).

thf(mem_c_2Ecardinal_2Ebijns,axiom,(
    ! [A_27a: del] :
      ( mem @ ( c_2Ecardinal_2Ebijns @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ bool ) ) ) )).

thf(tp_c_2Ecardinal_2Ecardeq,type,(
    c_2Ecardinal_2Ecardeq: del > del > $i )).

thf(mem_c_2Ecardinal_2Ecardeq,axiom,(
    ! [A_27a: del,A_27b: del] :
      ( mem @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) ) ) )).

thf(tp_c_2Ecardinal_2Ecardgeq,type,(
    c_2Ecardinal_2Ecardgeq: del > del > $i )).

thf(mem_c_2Ecardinal_2Ecardgeq,axiom,(
    ! [A_27a: del,A_27b: del] :
      ( mem @ ( c_2Ecardinal_2Ecardgeq @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) ) ) )).

thf(tp_c_2Ecardinal_2Ecardgt,type,(
    c_2Ecardinal_2Ecardgt: del > del > $i )).

thf(mem_c_2Ecardinal_2Ecardgt,axiom,(
    ! [A_27a: del,A_27b: del] :
      ( mem @ ( c_2Ecardinal_2Ecardgt @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) ) ) )).

thf(tp_c_2Ecardinal_2Ecardleq,type,(
    c_2Ecardinal_2Ecardleq: del > del > $i )).

thf(mem_c_2Ecardinal_2Ecardleq,axiom,(
    ! [A_27a: del,A_27b: del] :
      ( mem @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) ) ) )).

thf(tp_c_2Ecardinal_2Elist,type,(
    c_2Ecardinal_2Elist: del > $i )).

thf(mem_c_2Ecardinal_2Elist,axiom,(
    ! [A_27a: del] :
      ( mem @ ( c_2Ecardinal_2Elist @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) ) ) )).

thf(tp_c_2Ecardinal_2Eset__exp,type,(
    c_2Ecardinal_2Eset__exp: del > del > $i )).

thf(mem_c_2Ecardinal_2Eset__exp,axiom,(
    ! [A_27a: del,A_27b: del] :
      ( mem @ ( c_2Ecardinal_2Eset__exp @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ bool ) ) ) ) )).

thf(ax_thm_2Ecardinal_2Ecardeq__def,axiom,(
    ! [A_27a: del,A_27b: del,V0s1: $i] :
      ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
     => ! [V1s2: $i] :
          ( ( mem @ V1s2 @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s1 ) @ V1s2 ) )
          <=> ? [V2f: $i] :
                ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
                & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V2f ) @ V0s1 ) @ V1s2 ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardeq__REFL,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27a ) @ V0s ) @ V0s ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardeq__SYM,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
          <=> ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27b @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardeq__TRANS,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ! [V2u: $i] :
              ( ( mem @ V2u @ ( arr @ A_27c @ bool ) )
             => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27b @ A_27c ) @ V1t ) @ V2u ) ) )
               => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27c ) @ V0s ) @ V2u ) ) ) ) ) ) )).

thf(ax_thm_2Ecardinal_2Ecardleq__def,axiom,(
    ! [A_27a: del,A_27b: del,V0s1: $i] :
      ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
     => ! [V1s2: $i] :
          ( ( mem @ V1s2 @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s1 ) @ V1s2 ) )
          <=> ? [V2f: $i] :
                ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
                & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V2f ) @ V0s1 ) @ V1s2 ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardleq__REFL,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27a ) @ V0s ) @ V0s ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardleq__TRANS,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ! [V2u: $i] :
              ( ( mem @ V2u @ ( arr @ A_27c @ bool ) )
             => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27c ) @ V1t ) @ V2u ) ) )
               => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27c ) @ V0s ) @ V2u ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardleq__ANTISYM,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
              & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) ) )
           => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARDEQ__FINITE,axiom,(
    ! [A_27a: del,A_27b: del,V0s1: $i] :
      ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
     => ! [V1s2: $i] :
          ( ( mem @ V1s2 @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s1 ) @ V1s2 ) )
           => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s1 ) )
            <=> ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1s2 ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARDEQ__CARD,axiom,(
    ! [A_27a: del,A_27b: del,V0s1: $i] :
      ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
     => ! [V1s2: $i] :
          ( ( mem @ V1s2 @ ( arr @ A_27b @ bool ) )
         => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s1 ) @ V1s2 ) )
              & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s1 ) ) )
           => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s1 ) )
              = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V1s2 ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARDEQ__0,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0x: $i] :
      ( ( mem @ V0x @ ( arr @ A_27a @ bool ) )
     => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) )
        <=> ( V0x
            = ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
        & ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27c @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27c ) ) @ V0x ) )
        <=> ( V0x
            = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardeq__INSERT,axiom,(
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) @ V1s ) )
          <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) )
              | ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARDEQ__INSERT__RWT,axiom,(
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
           => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) @ V1s ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EEMPTY__CARDLEQ,axiom,(
    ! [A_27a: del,A_27b: del,V0t: $i] :
      ( ( mem @ V0t @ ( arr @ A_27b @ bool ) )
     => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V0t ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__CLE__INFINITE,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
              & ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1t ) ) )
           => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARDEQ__CROSS,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0s1: $i] :
      ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
     => ! [V1s2: $i] :
          ( ( mem @ V1s2 @ ( arr @ A_27b @ bool ) )
         => ! [V2t1: $i] :
              ( ( mem @ V2t1 @ ( arr @ A_27c @ bool ) )
             => ! [V3t2: $i] :
                  ( ( mem @ V3t2 @ ( arr @ A_27d @ bool ) )
                 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s1 ) @ V1s2 ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27c @ A_27d ) @ V2t1 ) @ V3t2 ) ) )
                   => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( ty_2Epair_2Eprod @ A_27a @ A_27c ) @ ( ty_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27c ) @ V0s1 ) @ V2t1 ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27b @ A_27d ) @ V1s2 ) @ V3t2 ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARDEQ__CROSS__SYM,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27b @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARDEQ__SUBSET__CARDLEQ,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
           => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARDEQ__CARDLEQ,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0s1: $i] :
      ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
     => ! [V1s2: $i] :
          ( ( mem @ V1s2 @ ( arr @ A_27b @ bool ) )
         => ! [V2t1: $i] :
              ( ( mem @ V2t1 @ ( arr @ A_27c @ bool ) )
             => ! [V3t2: $i] :
                  ( ( mem @ V3t2 @ ( arr @ A_27d @ bool ) )
                 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s1 ) @ V1s2 ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27c @ A_27d ) @ V2t1 ) @ V3t2 ) ) )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27c ) @ V0s1 ) @ V2t1 ) )
                    <=> ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27d ) @ V1s2 ) @ V3t2 ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARDLEQ__FINITE,axiom,(
    ! [A_27a: del,A_27b: del,V0s1: $i] :
      ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
     => ! [V1s2: $i] :
          ( ( mem @ V1s2 @ ( arr @ A_27b @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1s2 ) )
              & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s1 ) @ V1s2 ) ) )
           => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s1 ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EINFINITE__UNIV__INF,axiom,(
    ! [A_27a: del] :
      ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ A_27a ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ A_27a ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EIMAGE__cardleq,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) @ V1s ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARDLEQ__CROSS__CONG,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0x1: $i] :
      ( ( mem @ V0x1 @ ( arr @ A_27a @ bool ) )
     => ! [V1x2: $i] :
          ( ( mem @ V1x2 @ ( arr @ A_27b @ bool ) )
         => ! [V2y1: $i] :
              ( ( mem @ V2y1 @ ( arr @ A_27c @ bool ) )
             => ! [V3y2: $i] :
                  ( ( mem @ V3y2 @ ( arr @ A_27d @ bool ) )
                 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0x1 ) @ V1x2 ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27c @ A_27d ) @ V2y1 ) @ V3y2 ) ) )
                   => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ ( ty_2Epair_2Eprod @ A_27a @ A_27c ) @ ( ty_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27c ) @ V0x1 ) @ V2y1 ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27b @ A_27d ) @ V1x2 ) @ V3y2 ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESUBSET__CARDLEQ,axiom,(
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( arr @ A_27a @ bool ) )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ ( arr @ A_27a @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0x ) @ V1y ) )
           => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27a ) @ V0x ) @ V1y ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EIMAGE__cardleq__rwt,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27c ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
             => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V1s ) @ V2t ) )
               => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27c @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27c ) @ V0f ) @ V1s ) ) @ V2t ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecountable__thm,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) )
      <=> ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ ty_2Enum_2Enum ) @ V0s ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecountable__cardeq,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
           => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) )
            <=> ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27b ) @ V1t ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardleq__dichotomy,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
            | ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardleq__lteq,axiom,(
    ! [A_27a: del,A_27b: del,V0s1: $i] :
      ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
     => ! [V1s2: $i] :
          ( ( mem @ V1s2 @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s1 ) @ V1s2 ) )
          <=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1s2 ) @ V0s1 ) )
              | ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s1 ) @ V1s2 ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardlt__REFL,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ~ ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27a ) @ V0s ) @ V0s ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardlt__lenoteq,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) )
          <=> ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
              & ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardlt__TRANS,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27b @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27c @ bool ) )
         => ! [V2u: $i] :
              ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
             => ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27c @ A_27b ) @ V1t ) @ V0s ) )
                  & ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27c ) @ V2u ) @ V1t ) ) )
               => ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V2u ) @ V0s ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardlt__leq__trans,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0r: $i] :
      ( ( mem @ V0r @ ( arr @ A_27a @ bool ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27c @ bool ) )
             => ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1s ) @ V0r ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27c ) @ V1s ) @ V2t ) ) )
               => ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27c @ A_27a ) @ V2t ) @ V0r ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardleq__lt__trans,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0r: $i] :
      ( ( mem @ V0r @ ( arr @ A_27a @ bool ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27c @ bool ) )
             => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0r ) @ V1s ) )
                  & ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27c @ A_27b ) @ V2t ) @ V1s ) ) )
               => ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27c @ A_27a ) @ V2t ) @ V0r ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardleq__empty,axiom,(
    ! [A_27a: del,A_27b: del,V0x: $i] :
      ( ( mem @ V0x @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) )
      <=> ( V0x
          = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Eset__binomial2,axiom,(
    ! [A_27a: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ! [V1B: $i] :
          ( ( mem @ V1B @ ( arr @ A_27a @ bool ) )
         => ( ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0A ) @ V1B ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0A ) @ V1B ) )
            = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27a ) @ V0A ) @ V0A ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27a ) @ V0A ) @ V1B ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27a ) @ V1B ) @ V0A ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27a ) @ V1B ) @ V1B ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESET__SQUARED__CARDEQ__SET,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
       => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27a ) @ V0s ) @ V0s ) ) @ V0s ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESET__SUM__CARDEQ__SET,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
       => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ ( ty_2Epair_2Eprod @ bool @ A_27a ) ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ bool @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ bool ) @ c_2Ebool_2ET ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ bool ) @ c_2Ebool_2EF ) @ ( c_2Epred__set_2EEMPTY @ bool ) ) ) ) @ V0s ) ) )
          & ! [V1A: $i] :
              ( ( mem @ V1A @ ( arr @ A_27b @ bool ) )
             => ! [V2B: $i] :
                  ( ( mem @ V2B @ ( arr @ A_27b @ bool ) )
                 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27b ) @ V1A ) @ V2B ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27b @ A_27a ) @ V1A ) @ V0s ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27b @ A_27a ) @ V2B ) @ V0s ) ) )
                   => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27b @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27b ) @ V1A ) @ V2B ) ) @ V0s ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__BIGUNION,axiom,(
    ! [A_27a: del,A_27b: del,V0k: $i] :
      ( ( mem @ V0k @ ( arr @ A_27a @ bool ) )
     => ! [V1s1: $i] :
          ( ( mem @ V1s1 @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) )
         => ( ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0k ) )
              & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ ( arr @ A_27b @ bool ) @ A_27a ) @ V1s1 ) @ V0k ) )
              & ! [V2e: $i] :
                  ( ( mem @ V2e @ ( arr @ A_27b @ bool ) )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27b @ bool ) ) @ V2e ) @ V1s1 ) )
                   => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V2e ) @ V0k ) ) ) ) )
           => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27b ) @ V1s1 ) ) @ V0k ) ) ) ) ) )).

thf(ax_thm_2Ecardinal_2Eset__exp__def,axiom,(
    ! [A_27a: del,A_27b: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27b @ bool ) )
     => ! [V1B: $i] :
          ( ( mem @ V1B @ ( arr @ A_27a @ bool ) )
         => ( ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27a @ A_27b ) @ V0A ) @ V1B )
            = ( ap @ ( c_2Epred__set_2EGSPEC @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
              @ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) )
                @ ^ [V2f: $i] :
                    ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ bool ) @ V2f )
                    @ ( ap
                      @ ( ap @ c_2Ebool_2E_2F_5C
                        @ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
                          @ ( lam @ A_27a
                            @ ^ [V3b: $i] :
                                ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3b ) @ V1B ) )
                                @ ( ap @ ( c_2Ebool_2E_3F @ A_27b )
                                  @ ( lam @ A_27b
                                    @ ^ [V4a: $i] :
                                        ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4a ) @ V0A ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V2f @ V3b ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V4a ) ) ) ) ) ) ) ) )
                      @ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
                        @ ( lam @ A_27a
                          @ ^ [V5b: $i] :
                              ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5b ) @ V1B ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V2f @ V5b ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EBIJ__functions__agree,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ! [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
                 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V2s ) @ V3t ) )
                      & ! [V4x: $i] :
                          ( ( mem @ V4x @ A_27a )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) )
                           => ( ( ap @ V0f @ V4x )
                              = ( ap @ V1g @ V4x ) ) ) ) )
                   => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V1g ) @ V2s ) @ V3t ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__CARDEQ__I,axiom,(
    ! [A_27a: del,A_27b: del,V0s1: $i] :
      ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
     => ! [V1s2: $i] :
          ( ( mem @ V1s2 @ ( arr @ A_27b @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s1 ) )
              & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1s2 ) )
              & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s1 ) )
                = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V1s2 ) ) ) )
           => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s1 ) @ V1s2 ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARDEQ__CARD__EQN,axiom,(
    ! [A_27a: del,A_27b: del,V0s1: $i] :
      ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
     => ! [V1s2: $i] :
          ( ( mem @ V1s2 @ ( arr @ A_27b @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s1 ) )
              & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1s2 ) ) )
           => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s1 ) @ V1s2 ) )
            <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s1 ) )
                = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V1s2 ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARDLEQ__CARD,axiom,(
    ! [A_27a: del,A_27b: del,V0s1: $i] :
      ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
     => ! [V1s2: $i] :
          ( ( mem @ V1s2 @ ( arr @ A_27b @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s1 ) )
              & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1s2 ) ) )
           => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s1 ) @ V1s2 ) )
            <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s1 ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V1s2 ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EEMPTY__set__exp,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27b @ bool ) )
     => ! [V1B: $i] :
          ( ( mem @ V1B @ ( arr @ A_27c @ bool ) )
         => ( ( ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27a @ A_27b ) @ V0A ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
              = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ ( c_2Ecombin_2EK @ ( ty_2Eoption_2Eoption @ A_27b ) @ A_27a ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) @ ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) )
            & ( ( V1B
               != ( c_2Epred__set_2EEMPTY @ A_27c ) )
             => ( ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27c @ A_27d ) @ ( c_2Epred__set_2EEMPTY @ A_27d ) ) @ V1B )
                = ( c_2Epred__set_2EEMPTY @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27d ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EEMPTY__set__exp__CARD,axiom,(
    ! [A_27a: del,A_27b: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27b @ bool ) )
     => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27a @ A_27b ) @ V0A ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ ( ap @ c_2Epred__set_2Ecount @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESING__set__exp,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0x: $i] :
      ( ( mem @ V0x @ A_27b )
     => ! [V1B: $i] :
          ( ( mem @ V1B @ ( arr @ A_27a @ bool ) )
         => ! [V2A: $i] :
              ( ( mem @ V2A @ ( arr @ A_27c @ bool ) )
             => ( ( ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) @ V1B )
                  = ( ap
                    @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
                      @ ( lam @ A_27a
                        @ ^ [V3b: $i] :
                            ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3b ) @ V1B ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V0x ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) )
                    @ ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) )
                & ( ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27b @ A_27c ) @ V2A ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) )
                  = ( ap @ ( c_2Epred__set_2EGSPEC @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) @ A_27c )
                    @ ( lam @ A_27c
                      @ ^ [V4a: $i] :
                          ( ap
                          @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) @ bool )
                            @ ( lam @ A_27b
                              @ ^ [V5b: $i] :
                                  ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27c ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V5b ) @ V0x ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V4a ) ) @ ( c_2Eoption_2ENONE @ A_27c ) ) ) )
                          @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27c ) @ V4a ) @ V2A ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESING__set__exp__CARD,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0x: $i] :
      ( ( mem @ V0x @ A_27b )
     => ! [V1B: $i] :
          ( ( mem @ V1B @ ( arr @ A_27a @ bool ) )
         => ! [V2A: $i] :
              ( ( mem @ V2A @ ( arr @ A_27c @ bool ) )
             => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) @ V1B ) ) @ ( ap @ c_2Epred__set_2Ecount @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
                & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) @ A_27c ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27b @ A_27c ) @ V2A ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) ) @ V2A ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EPOW__TWO__set__exp,axiom,(
    ! [A_27a: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V0A ) ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27a @ ty_2Enum_2Enum ) @ ( ap @ c_2Epred__set_2Ecount @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V0A ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Eset__exp__count,axiom,(
    ! [A_27a: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ! [V1n: tp__ty_2Enum_2Enum] :
          ( p
          @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ ty_2Enum_2Enum @ A_27a ) @ V0A ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
            @ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) )
              @ ( lam @ ( ty_2Elist_2Elist @ A_27a )
                @ ^ [V2l: $i] :
                    ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) @ V2l )
                    @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
                      @ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
                        @ ( lam @ A_27a
                          @ ^ [V3e: $i] :
                              ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3e ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2l ) ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3e ) @ V0A ) ) ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Eset__exp__card__cong,axiom,(
    ! [A_27a1: del,A_27a2: del,A_27b1: del,A_27b2: del,V0a1: $i] :
      ( ( mem @ V0a1 @ ( arr @ A_27a1 @ bool ) )
     => ! [V1a2: $i] :
          ( ( mem @ V1a2 @ ( arr @ A_27a2 @ bool ) )
         => ! [V2b1: $i] :
              ( ( mem @ V2b1 @ ( arr @ A_27b1 @ bool ) )
             => ! [V3b2: $i] :
                  ( ( mem @ V3b2 @ ( arr @ A_27b2 @ bool ) )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a1 @ A_27a2 ) @ V0a1 ) @ V1a2 ) )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27b1 @ A_27b2 ) @ V2b1 ) @ V3b2 ) )
                     => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( arr @ A_27b1 @ ( ty_2Eoption_2Eoption @ A_27a1 ) ) @ ( arr @ A_27b2 @ ( ty_2Eoption_2Eoption @ A_27a2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27b1 @ A_27a1 ) @ V0a1 ) @ V2b1 ) ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27b2 @ A_27a2 ) @ V1a2 ) @ V3b2 ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Eset__exp__cardle__cong,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0b: $i] :
      ( ( mem @ V0b @ ( arr @ A_27a @ bool ) )
     => ! [V1d: $i] :
          ( ( mem @ V1d @ ( arr @ A_27b @ bool ) )
         => ! [V2a: $i] :
              ( ( mem @ V2a @ ( arr @ A_27c @ bool ) )
             => ! [V3c: $i] :
                  ( ( mem @ V3c @ ( arr @ A_27d @ bool ) )
                 => ( ( ( V0b
                        = ( c_2Epred__set_2EEMPTY @ A_27a ) )
                     => ( V1d
                        = ( c_2Epred__set_2EEMPTY @ A_27b ) ) )
                   => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27c @ A_27a ) @ V2a ) @ V0b ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27d @ A_27b ) @ V3c ) @ V1d ) ) )
                     => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ ( arr @ A_27d @ ( ty_2Eoption_2Eoption @ A_27c ) ) @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27d @ A_27c ) @ V2a ) @ V3c ) ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27b @ A_27a ) @ V0b ) @ V1d ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Eexp__INSERT__cardeq,axiom,(
    ! [A_27a: del,A_27b: del,V0e: $i] :
      ( ( mem @ V0e @ A_27a )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2A: $i] :
              ( ( mem @ V2A @ ( arr @ A_27b @ bool ) )
             => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0e ) @ V1s ) )
               => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ty_2Epair_2Eprod @ A_27b @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27a @ A_27b ) @ V2A ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0e ) @ V1s ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27b @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V2A ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27a @ A_27b ) @ V2A ) @ V1s ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Eexp__count__cardeq,axiom,(
    ! [A_27a: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ! [V1n: tp__ty_2Enum_2Enum] :
          ( ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0A ) )
            & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
         => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ ty_2Enum_2Enum @ A_27a ) @ V0A ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ V0A ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EINFINITE__Unum,axiom,(
    ! [A_27a: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0A ) )
      <=> ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ ty_2Enum_2Enum @ A_27a ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ V0A ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardleq__SURJ,axiom,(
    ! [A_27a: del,A_27b: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ! [V1B: $i] :
          ( ( mem @ V1B @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0A ) @ V1B ) )
          <=> ( ? [V2f: $i] :
                  ( ( mem @ V2f @ ( arr @ A_27b @ A_27a ) )
                  & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27b @ A_27a ) @ V2f ) @ V1B ) @ V0A ) ) )
              | ( V0A
                = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EINFINITE__cardleq__INSERT,axiom,(
    ! [A_27a: del,A_27b: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27b )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
             => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0A ) )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V1x ) @ V2s ) ) @ V0A ) )
                <=> ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V2s ) @ V0A ) ) ) ) ) ) ) )).

thf(ax_thm_2Ecardinal_2Elist__def,axiom,(
    ! [A_27a: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ( ( ap @ ( c_2Ecardinal_2Elist @ A_27a ) @ V0A )
        = ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) )
          @ ( lam @ ( ty_2Elist_2Elist @ A_27a )
            @ ^ [V1l: $i] :
                ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) @ V1l )
                @ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
                  @ ( lam @ A_27a
                    @ ^ [V2e: $i] :
                        ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2e ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2e ) @ V0A ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Elist__EMPTY,axiom,(
    ! [A_27a: del] :
      ( ( ap @ ( c_2Ecardinal_2Elist @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
      = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Elist__SING,axiom,(
    ! [A_27a: del,V0e: $i] :
      ( ( mem @ V0e @ A_27a )
     => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( ty_2Elist_2Elist @ A_27a ) @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Ecardinal_2Elist @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0e ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EUNIV__list,axiom,(
    ! [A_27a: del] :
      ( ( c_2Epred__set_2EUNIV @ ( ty_2Elist_2Elist @ A_27a ) )
      = ( ap @ ( c_2Ecardinal_2Elist @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) ) )).

thf(conj_thm_2Ecardinal_2Elist__BIGUNION__EXP,axiom,(
    ! [A_27a: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ( p
        @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ ( ap @ ( c_2Ecardinal_2Elist @ A_27a ) @ V0A ) )
          @ ( ap @ ( c_2Epred__set_2EBIGUNION @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
            @ ( ap
              @ ( ap @ ( c_2Epred__set_2EIMAGE @ ty_2Enum_2Enum @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ bool ) )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V1n: $i] :
                      ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ ty_2Enum_2Enum @ A_27a ) @ V0A ) @ ( ap @ c_2Epred__set_2Ecount @ V1n ) ) ) )
              @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EINFINITE__A__list__BIJ__A,axiom,(
    ! [A_27a: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0A ) )
       => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ ( ap @ ( c_2Ecardinal_2Elist @ A_27a ) @ V0A ) ) @ V0A ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Efinite__subsets__bijection,axiom,(
    ! [A_27a: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0A ) )
       => ( p
          @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ ( arr @ A_27a @ bool ) ) @ V0A )
            @ ( ap @ ( c_2Epred__set_2EGSPEC @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) )
              @ ( lam @ ( arr @ A_27a @ bool )
                @ ^ [V1s: $i] :
                    ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ bool ) @ V1s ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ V0A ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__IMAGE__INJ_27,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
         => ( ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ! [V3y: $i] :
                    ( ( mem @ V3y @ A_27a )
                   => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V0s ) ) )
                     => ( ( ( ap @ V1f @ V2x )
                          = ( ap @ V1f @ V3y ) )
                      <=> ( V2x = V3y ) ) ) ) )
           => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V1f ) @ V0s ) ) )
            <=> ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecountable__decomposition,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
       => ? [V1A: $i] :
            ( ( mem @ V1A @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
            & ( ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1A )
              = V0s )
            & ! [V2a: $i] :
                ( ( mem @ V2a @ ( arr @ A_27a @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2a ) @ V1A ) )
                 => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2a ) )
                    & ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V2a ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Edisjoint__countable__decomposition,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
       => ? [V1A: $i] :
            ( ( mem @ V1A @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
            & ( ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1A )
              = V0s )
            & ! [V2a: $i] :
                ( ( mem @ V2a @ ( arr @ A_27a @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2a ) @ V1A ) )
                 => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2a ) )
                    & ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V2a ) ) ) ) )
            & ! [V3a1: $i] :
                ( ( mem @ V3a1 @ ( arr @ A_27a @ bool ) )
               => ! [V4a2: $i] :
                    ( ( mem @ V4a2 @ ( arr @ A_27a @ bool ) )
                   => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V3a1 ) @ V1A ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V4a2 ) @ V1A ) )
                        & ( V3a1 != V4a2 ) )
                     => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V3a1 ) @ V4a2 ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecount__cardle,axiom,(
    ! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1A: $i] :
      ( ( mem @ V1A @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ ty_2Enum_2Enum @ A_27a ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1A ) )
      <=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1A ) )
         => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1A ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECANTOR,axiom,(
    ! [A_27a: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ ( arr @ A_27a @ bool ) @ A_27a ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V0A ) ) @ V0A ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardlt__cardle,axiom,(
    ! [A_27a: del,A_27b: del,V0B: $i] :
      ( ( mem @ V0B @ ( arr @ A_27b @ bool ) )
     => ! [V1A: $i] :
          ( ( mem @ V1A @ ( arr @ A_27a @ bool ) )
         => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V0B ) @ V1A ) )
           => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V1A ) @ V0B ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Eset__exp__product,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27c @ bool ) )
     => ! [V1B1: $i] :
          ( ( mem @ V1B1 @ ( arr @ A_27b @ bool ) )
         => ! [V2B2: $i] :
              ( ( mem @ V2B2 @ ( arr @ A_27a @ bool ) )
             => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27a @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27b @ A_27c ) @ V0A ) @ V1B1 ) ) @ V2B2 ) ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27c ) @ V0A ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27b @ A_27a ) @ V1B1 ) @ V2B2 ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECOUNT__EQ__EMPTY,axiom,(
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( ( ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V0n ) )
        = ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) )
    <=> ( V0n = fo__c_2Enum_2E0 ) ) )).

thf(conj_thm_2Ecardinal_2EPOW__EQ__X__EXP__X,axiom,(
    ! [A_27a: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0A ) )
       => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V0A ) ) @ ( ap @ ( ap @ ( c_2Ecardinal_2Eset__exp @ A_27a @ A_27a ) @ V0A ) @ V0A ) ) ) ) ) )).

thf(ax_thm_2Ecardinal_2Ebijns__def,axiom,(
    ! [A_27a: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ( ( ap @ ( c_2Ecardinal_2Ebijns @ A_27a ) @ V0A )
        = ( ap @ ( c_2Epred__set_2EGSPEC @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
          @ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) )
            @ ^ [V1f: $i] :
                ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ bool ) @ V1f )
                @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Eoption_2ETHE @ A_27a ) ) @ V1f ) ) @ V0A ) @ V0A ) )
                  @ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
                    @ ( lam @ A_27a
                      @ ^ [V2a: $i] :
                          ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2a ) @ V0A ) )
                          @ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
                            @ ( lam @ A_27a
                              @ ^ [V3b: $i] :
                                  ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ V1f @ V2a ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3b ) ) ) ) ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ecardeq__bijns__cong,axiom,(
    ! [A_27a: del,A_27b: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
     => ! [V1B: $i] :
          ( ( mem @ V1B @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0A ) @ V1B ) )
           => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ ( c_2Ecardinal_2Ebijns @ A_27a ) @ V0A ) ) @ ( ap @ ( c_2Ecardinal_2Ebijns @ A_27b ) @ V1B ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ebijections__cardeq,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
       => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( c_2Ecardinal_2Ebijns @ A_27a ) @ V0s ) ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V0s ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ELEFT__IMP__EXISTS__THM,axiom,(
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
     => ! [V1Q: $i] :
          ( ( mem @ V1Q @ bool )
         => ( ( ? [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                  & ( p @ ( ap @ V0P @ V2x ) ) )
             => ( p @ V1Q ) )
          <=> ! [V3x: $i] :
                ( ( mem @ V3x @ A_27a )
               => ( ( p @ ( ap @ V0P @ V3x ) )
                 => ( p @ V1Q ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ELEFT__IMP__FORALL__THM,axiom,(
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
     => ! [V1Q: $i] :
          ( ( mem @ V1Q @ bool )
         => ( ( ! [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                 => ( p @ ( ap @ V0P @ V2x ) ) )
             => ( p @ V1Q ) )
          <=> ? [V3x: $i] :
                ( ( mem @ V3x @ A_27a )
                & ( ( p @ ( ap @ V0P @ V3x ) )
                 => ( p @ V1Q ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ERIGHT__IMP__EXISTS__THM,axiom,(
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ bool )
     => ! [V1Q: $i] :
          ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
         => ( ( ( p @ V0P )
             => ? [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                  & ( p @ ( ap @ V1Q @ V2x ) ) ) )
          <=> ? [V3x: $i] :
                ( ( mem @ V3x @ A_27a )
                & ( ( p @ V0P )
                 => ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ERIGHT__IMP__FORALL__THM,axiom,(
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ bool )
     => ! [V1Q: $i] :
          ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
         => ( ( ( p @ V0P )
             => ! [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                 => ( p @ ( ap @ V1Q @ V2x ) ) ) )
          <=> ! [V3x: $i] :
                ( ( mem @ V3x @ A_27a )
               => ( ( p @ V0P )
                 => ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__FINITE__BIGUNIONS,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( arr @ A_27a @ bool ) ) @ V0s ) )
       => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V0s ) ) )
        <=> ! [V1t: $i] :
              ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
             => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V1t ) @ V0s ) )
               => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECONJ__EQ__IMP,axiom,(
    ! [V0r: $i] :
      ( ( mem @ V0r @ bool )
     => ! [V1p: $i] :
          ( ( mem @ V1p @ bool )
         => ! [V2q: $i] :
              ( ( mem @ V2q @ bool )
             => ( ( ( ( p @ V1p )
                    & ( p @ V2q ) )
                 => ( p @ V0r ) )
              <=> ( ( p @ V1p )
                 => ( ( p @ V2q )
                   => ( p @ V0r ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EIMP__CONJ__ALT,axiom,(
    ! [V0r: $i] :
      ( ( mem @ V0r @ bool )
     => ! [V1p: $i] :
          ( ( mem @ V1p @ bool )
         => ! [V2q: $i] :
              ( ( mem @ V2q @ bool )
             => ( ( ( ( p @ V1p )
                    & ( p @ V2q ) )
                 => ( p @ V0r ) )
              <=> ( ( p @ V2q )
                 => ( ( p @ V1p )
                   => ( p @ V0r ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ELT__SUC__LE,axiom,(
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESURJECTIVE__ON__RIGHT__INVERSE,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
             => ( ! [V3y: $i] :
                    ( ( mem @ V3y @ A_27b )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3y ) @ V2t ) )
                     => ? [V4x: $i] :
                          ( ( mem @ V4x @ A_27a )
                          & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V0s ) )
                          & ( ( ap @ V1f @ V4x )
                            = V3y ) ) ) )
              <=> ? [V5g: $i] :
                    ( ( mem @ V5g @ ( arr @ A_27b @ A_27a ) )
                    & ! [V6y: $i] :
                        ( ( mem @ V6y @ A_27b )
                       => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V6y ) @ V2t ) )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V5g @ V6y ) ) @ V0s ) )
                            & ( ( ap @ V1f @ ( ap @ V5g @ V6y ) )
                              = V6y ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESURJECTIVE__RIGHT__INVERSE,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27b @ A_27a ) )
     => ( ! [V1y: $i] :
            ( ( mem @ V1y @ A_27a )
           => ? [V2x: $i] :
                ( ( mem @ V2x @ A_27b )
                & ( ( ap @ V0f @ V2x )
                  = V1y ) ) )
      <=> ? [V3g: $i] :
            ( ( mem @ V3g @ ( arr @ A_27a @ A_27b ) )
            & ! [V4y: $i] :
                ( ( mem @ V4y @ A_27a )
               => ( ( ap @ V0f @ ( ap @ V3g @ V4y ) )
                  = V4y ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__IMAGE__INJ__GENERAL,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1A: $i] :
          ( ( mem @ V1A @ ( arr @ A_27b @ bool ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ! [V4y: $i] :
                          ( ( mem @ V4y @ A_27a )
                         => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                              & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4y ) @ V2s ) )
                              & ( ( ap @ V0f @ V3x )
                                = ( ap @ V0f @ V4y ) ) )
                           => ( V3x = V4y ) ) ) )
                  & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1A ) ) )
               => ( p
                  @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
                    @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                      @ ( lam @ A_27a
                        @ ^ [V5x: $i] :
                            ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V5x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V2s ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V5x ) ) @ V1A ) ) ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__IMAGE__INJ,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1A: $i] :
          ( ( mem @ V1A @ ( arr @ A_27b @ bool ) )
         => ( ( ! [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                 => ! [V3y: $i] :
                      ( ( mem @ V3y @ A_27a )
                     => ( ( ( ap @ V0f @ V2x )
                          = ( ap @ V0f @ V3y ) )
                       => ( V2x = V3y ) ) ) )
              & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1A ) ) )
           => ( p
              @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
                @ ( 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_2EIN @ A_27b ) @ ( ap @ V0f @ V4x ) ) @ V1A ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__IMAGE__INJ__EQ,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ! [V3y: $i] :
                    ( ( mem @ V3y @ A_27a )
                   => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V1s ) )
                        & ( ( ap @ V0f @ V2x )
                          = ( ap @ V0f @ V3y ) ) )
                     => ( V2x = V3y ) ) ) )
           => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) )
            <=> ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EINFINITE__IMAGE__INJ,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ( ! [V1x: $i] :
            ( ( mem @ V1x @ A_27a )
           => ! [V2y: $i] :
                ( ( mem @ V2y @ A_27a )
               => ( ( ( ap @ V0f @ V1x )
                    = ( ap @ V0f @ V2y ) )
                 => ( V1x = V2y ) ) ) )
       => ! [V3s: $i] :
            ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
           => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3s ) )
             => ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V3s ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EINFINITE__NONEMPTY,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
       => ( V0s
         != ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__PRODUCT__DEPENDENT,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
                       => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ V2t @ V3x ) ) ) ) ) )
               => ( p
                  @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27c )
                    @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27c @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
                      @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ ( ty_2Epair_2Eprod @ A_27c @ bool ) )
                        @ ( lam @ A_27a
                          @ ^ [V4x: $i] :
                              ( lam @ A_27b
                              @ ^ [V5y: $i] :
                                  ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27c @ bool ) @ ( ap @ ( ap @ V0f @ V4x ) @ V5y ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V5y ) @ ( ap @ V2t @ V4x ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__PRODUCT,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
              & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1t ) ) )
           => ( p
              @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
                @ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
                  @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
                    @ ( lam @ A_27a
                      @ ^ [V2x: $i] :
                          ( lam @ A_27b
                          @ ^ [V3y: $i] :
                              ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2x ) @ V3y ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3y ) @ V1t ) ) ) ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESURJECTIVE__IMAGE__THM,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ( ! [V1y: $i] :
            ( ( mem @ V1y @ A_27b )
           => ? [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
                & ( ( ap @ V0f @ V2x )
                  = V1y ) ) )
      <=> ! [V3P: $i] :
            ( ( mem @ V3P @ ( arr @ A_27b @ bool ) )
           => ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f )
                @ ( 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 @ V3P @ ( ap @ V0f @ V4x ) ) ) ) ) )
              = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27b )
                @ ( lam @ A_27b
                  @ ^ [V5x: $i] :
                      ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ V5x ) @ ( ap @ V3P @ V5x ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESURJECTIVE__ON__IMAGE,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1u: $i] :
          ( ( mem @ V1u @ ( arr @ A_27a @ bool ) )
         => ! [V2v: $i] :
              ( ( mem @ V2v @ ( arr @ A_27b @ bool ) )
             => ( ! [V3t: $i] :
                    ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ V3t ) @ V2v ) )
                     => ? [V4s: $i] :
                          ( ( mem @ V4s @ ( arr @ A_27a @ bool ) )
                          & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V4s ) @ V1u ) )
                          & ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V4s )
                            = V3t ) ) ) )
              <=> ! [V5y: $i] :
                    ( ( mem @ V5y @ A_27b )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V5y ) @ V2v ) )
                     => ? [V6x: $i] :
                          ( ( mem @ V6x @ A_27a )
                          & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V1u ) )
                          & ( ( ap @ V0f @ V6x )
                            = V5y ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESURJECTIVE__IMAGE,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ( ! [V1t: $i] :
            ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
           => ? [V2s: $i] :
                ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
                & ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s )
                  = V1t ) ) )
      <=> ! [V3y: $i] :
            ( ( mem @ V3y @ A_27b )
           => ? [V4x: $i] :
                ( ( mem @ V4x @ A_27a )
                & ( ( ap @ V0f @ V4x )
                  = V3y ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LE__INJ,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
              & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1t ) )
              & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V1t ) ) ) )
           => ? [V2f: $i] :
                ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
                & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V2f ) @ V0s ) ) @ V1t ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ! [V4y: $i] :
                        ( ( mem @ V4y @ A_27a )
                       => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                            & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4y ) @ V0s ) )
                            & ( ( ap @ V2f @ V3x )
                              = ( ap @ V2f @ V4y ) ) )
                         => ( V3x = V4y ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__IMAGE__INJ,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( ! [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                 => ! [V3y: $i] :
                      ( ( mem @ V3y @ A_27a )
                     => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
                          & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V1s ) )
                          & ( ( ap @ V0f @ V2x )
                            = ( ap @ V0f @ V3y ) ) )
                       => ( V2x = V3y ) ) ) )
              & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) )
           => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) )
              = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__IMAGE__LE,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
           => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESURJECTIVE__IFF__INJECTIVE__GEN,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                  & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1t ) )
                  & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) )
                    = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V1t ) ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V2f ) @ V0s ) ) @ V1t ) ) )
               => ( ! [V3y: $i] :
                      ( ( mem @ V3y @ A_27b )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3y ) @ V1t ) )
                       => ? [V4x: $i] :
                            ( ( mem @ V4x @ A_27a )
                            & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V0s ) )
                            & ( ( ap @ V2f @ V4x )
                              = V3y ) ) ) )
                <=> ! [V5x: $i] :
                      ( ( mem @ V5x @ A_27a )
                     => ! [V6y: $i] :
                          ( ( mem @ V6y @ A_27a )
                         => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V0s ) )
                              & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6y ) @ V0s ) )
                              & ( ( ap @ V2f @ V5x )
                                = ( ap @ V2f @ V6y ) ) )
                           => ( V5x = V6y ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESURJECTIVE__IFF__INJECTIVE,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
              & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27a ) @ V1f ) @ V0s ) ) @ V0s ) ) )
           => ( ! [V2y: $i] :
                  ( ( mem @ V2y @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2y ) @ V0s ) )
                   => ? [V3x: $i] :
                        ( ( mem @ V3x @ A_27a )
                        & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                        & ( ( ap @ V1f @ V3x )
                          = V2y ) ) ) )
            <=> ! [V4x: $i] :
                  ( ( mem @ V4x @ A_27a )
                 => ! [V5y: $i] :
                      ( ( mem @ V5y @ A_27a )
                     => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V0s ) )
                          & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5y ) @ V0s ) )
                          & ( ( ap @ V1f @ V4x )
                            = ( ap @ V1f @ V5y ) ) )
                       => ( V4x = V5y ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__EQ__BIJECTION,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
              & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1t ) )
              & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) )
                = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V1t ) ) ) )
           => ? [V2f: $i] :
                ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V2f @ V3x ) ) @ V1t ) ) ) )
                & ! [V4y: $i] :
                    ( ( mem @ V4y @ A_27b )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4y ) @ V1t ) )
                     => ? [V5x: $i] :
                          ( ( mem @ V5x @ A_27a )
                          & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V0s ) )
                          & ( ( ap @ V2f @ V5x )
                            = V4y ) ) ) )
                & ! [V6x: $i] :
                    ( ( mem @ V6x @ A_27a )
                   => ! [V7y: $i] :
                        ( ( mem @ V7y @ A_27a )
                       => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V0s ) )
                            & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V7y ) @ V0s ) )
                            & ( ( ap @ V2f @ V6x )
                              = ( ap @ V2f @ V7y ) ) )
                         => ( V6x = V7y ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__EQ__BIJECTIONS,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
              & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1t ) )
              & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) )
                = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V1t ) ) ) )
           => ? [V2f: $i] :
                ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
                & ? [V3g: $i] :
                    ( ( mem @ V3g @ ( arr @ A_27b @ A_27a ) )
                    & ! [V4x: $i] :
                        ( ( mem @ V4x @ A_27a )
                       => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V0s ) )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V2f @ V4x ) ) @ V1t ) )
                            & ( ( ap @ V3g @ ( ap @ V2f @ V4x ) )
                              = V4x ) ) ) )
                    & ! [V5y: $i] :
                        ( ( mem @ V5y @ A_27b )
                       => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V5y ) @ V1t ) )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V3g @ V5y ) ) @ V0s ) )
                            & ( ( ap @ V2f @ ( ap @ V3g @ V5y ) )
                              = V5y ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ESING__SUBSET,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V0s ) )
          <=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EINJECTIVE__ON__IMAGE,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1u: $i] :
          ( ( mem @ V1u @ ( arr @ A_27a @ bool ) )
         => ( ! [V2s: $i] :
                ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
               => ! [V3t: $i] :
                    ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
                   => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2s ) @ V1u ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V3t ) @ V1u ) )
                        & ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s )
                          = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V3t ) ) )
                     => ( V2s = V3t ) ) ) )
          <=> ! [V4x: $i] :
                ( ( mem @ V4x @ A_27a )
               => ! [V5y: $i] :
                    ( ( mem @ V5y @ A_27a )
                   => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V1u ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5y ) @ V1u ) )
                        & ( ( ap @ V0f @ V4x )
                          = ( ap @ V0f @ V5y ) ) )
                     => ( V4x = V5y ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EINJECTIVE__IMAGE,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ( ! [V1s: $i] :
            ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
           => ! [V2t: $i] :
                ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
               => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s )
                    = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2t ) )
                 => ( V1s = V2t ) ) ) )
      <=> ! [V3x: $i] :
            ( ( mem @ V3x @ A_27a )
           => ! [V4y: $i] :
                ( ( mem @ V4y @ A_27a )
               => ( ( ( ap @ V0f @ V3x )
                    = ( ap @ V0f @ V4y ) )
                 => ( V3x = V4y ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__FINITE__BIGUNION,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( arr @ A_27a @ bool ) ) @ V0s ) )
       => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V0s ) ) )
        <=> ! [V1t: $i] :
              ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
             => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V1t ) @ V0s ) )
               => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Enum__FINITE,axiom,(
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V0s ) )
      <=> ? [V1a: tp__ty_2Enum_2Enum] :
          ! [V2x: tp__ty_2Enum_2Enum] :
            ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ V0s ) )
           => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Enum__FINITE__AVOID,axiom,(
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V0s ) )
       => ? [V1a: tp__ty_2Enum_2Enum] :
            ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ V0s ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Enum__INFINITE,axiom,(
    ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) )).

thf(ax_thm_2Ecardinal_2EHAS__SIZE,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1n: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V0s ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
        <=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
            & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) )
              = V1n ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EHAS__SIZE__CARD,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1n: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V0s ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) )
            = V1n ) ) ) )).

thf(conj_thm_2Ecardinal_2EHAS__SIZE__0,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V0s ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
      <=> ( V0s
          = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EHAS__SIZE__SUC,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1n: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V0s ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
        <=> ( ( V0s
             != ( c_2Epred__set_2EEMPTY @ A_27a ) )
            & ! [V2a: $i] :
                ( ( mem @ V2a @ A_27a )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2a ) @ V0s ) )
                 => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__HAS__SIZE,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
      <=> ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V0s ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EHAS__SIZE__CLAUSES,axiom,(
    ! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1s: $i] :
      ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
     => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V1s ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
        <=> ( V1s
            = ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
        & ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V1s ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
        <=> ? [V2a: $i] :
              ( ( mem @ V2a @ A_27a )
              & ? [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V3t ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
                  & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2a ) @ V3t ) )
                  & ( V1s
                    = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2a ) @ V3t ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__SUBSET__EQ,axiom,(
    ! [A_27a: del,V0a: $i] :
      ( ( mem @ V0a @ ( arr @ A_27a @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ A_27a @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1b ) )
              & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0a ) @ V1b ) )
              & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0a ) )
                = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1b ) ) ) )
           => ( V0a = V1b ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EHAS__SIZE__INDEX,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1n: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V0s ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
         => ? [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
              & ! [V3m: tp__ty_2Enum_2Enum] :
                  ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
                 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V2f @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) @ V0s ) ) )
              & ! [V4x: $i] :
                  ( ( mem @ V4x @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V0s ) )
                   => ( p
                      @ ( ap @ ( c_2Ebool_2E_3F_21 @ ty_2Enum_2Enum )
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V5m: $i] :
                              ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V5m ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V2f @ V5m ) ) @ V4x ) ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__BIGUNION__LE,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
         => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
              ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V0s ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) )
                & ! [V4x: $i] :
                    ( ( mem @ V4x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V0s ) )
                     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ V1t @ V4x ) ) )
                        & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ ( ap @ V1t @ V4x ) ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) )
             => ( p
                @ ( ap
                  @ ( ap @ c_2Earithmetic_2E_3C_3D
                    @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b )
                      @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27b )
                        @ ( ap @ ( c_2Epred__set_2EGSPEC @ ( arr @ A_27b @ bool ) @ A_27a )
                          @ ( lam @ A_27a
                            @ ^ [V5x: $i] :
                                ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27b @ bool ) @ bool ) @ ( ap @ V1t @ V5x ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V0s ) ) ) ) ) ) )
                  @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EHAS__SIZE__BOOL,axiom,(
    p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ bool ) @ ( c_2Epred__set_2EUNIV @ bool ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__BOOL,axiom,
    ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ bool ) @ ( c_2Epred__set_2EUNIV @ bool ) ) )
    = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__BOOL,axiom,(
    p @ ( ap @ ( c_2Epred__set_2EFINITE @ bool ) @ ( c_2Epred__set_2EUNIV @ bool ) ) )).

thf(conj_thm_2Ecardinal_2EHAS__SIZE__CART__UNIV,axiom,(
    ! [A_27a: del,V0m: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
     => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__CART__UNIV,axiom,(
    ! [A_27a: del] :
      ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
     => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__CART__UNIV,axiom,(
    ! [A_27a: del] :
      ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
     => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EHAS__SIZE__NUMSEG__LT,axiom,(
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( p
      @ ( ap
        @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ ty_2Enum_2Enum )
          @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
            @ ( lam @ ty_2Enum_2Enum
              @ ^ [V1m: $i] :
                  ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ bool ) @ V1m ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V1m ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) )
        @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__NUMSEG__LT,axiom,(
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( p
      @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum )
        @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
          @ ( lam @ ty_2Enum_2Enum
            @ ^ [V1m: $i] :
                ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ bool ) @ V1m ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V1m ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EHAS__SIZE__NUMSEG__LE,axiom,(
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( p
      @ ( ap
        @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ ty_2Enum_2Enum )
          @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
            @ ( lam @ ty_2Enum_2Enum
              @ ^ [V1m: $i] :
                  ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ bool ) @ V1m ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ V1m ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) )
        @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EFINITE__NUMSEG__LE,axiom,(
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( p
      @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum )
        @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
          @ ( lam @ ty_2Enum_2Enum
            @ ^ [V1m: $i] :
                ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ bool ) @ V1m ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ V1m ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EINFINITE__DIFF__FINITE,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
         => ( ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
              & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) )
           => ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ELE__CASES,axiom,(
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
      | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ELT__CASES,axiom,(
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
      | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
      | ( V0m = V1n ) ) )).

thf(conj_thm_2Ecardinal_2ELT,axiom,
    ( ! [V0m: tp__ty_2Enum_2Enum] :
        ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
      <=> $false )
    & ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
        ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
      <=> ( ( V1m = V2n )
          | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ELT__LE,axiom,(
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
    <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
        & ( V0m != V1n ) ) ) )).

thf(conj_thm_2Ecardinal_2EGE,axiom,(
    ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ELE__SUC__LT,axiom,(
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EINJECTIVE__ON__LEFT__INVERSE,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ! [V3y: $i] :
                    ( ( mem @ V3y @ A_27a )
                   => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V1s ) )
                        & ( ( ap @ V0f @ V2x )
                          = ( ap @ V0f @ V3y ) ) )
                     => ( V2x = V3y ) ) ) )
          <=> ? [V4g: $i] :
                ( ( mem @ V4g @ ( arr @ A_27b @ A_27a ) )
                & ! [V5x: $i] :
                    ( ( mem @ V5x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V1s ) )
                     => ( ( ap @ V4g @ ( ap @ V0f @ V5x ) )
                        = V5x ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EINJECTIVE__LEFT__INVERSE,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ( ! [V1x: $i] :
            ( ( mem @ V1x @ A_27a )
           => ! [V2y: $i] :
                ( ( mem @ V2y @ A_27a )
               => ( ( ( ap @ V0f @ V1x )
                    = ( ap @ V0f @ V2y ) )
                 => ( V1x = V2y ) ) ) )
      <=> ? [V3g: $i] :
            ( ( mem @ V3g @ ( arr @ A_27b @ A_27a ) )
            & ! [V4x: $i] :
                ( ( mem @ V4x @ A_27a )
               => ( ( ap @ V3g @ ( ap @ V0f @ V4x ) )
                  = V4x ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EINTER__ACI,axiom,(
    ! [A_27a: del,V0r: $i] :
      ( ( mem @ V0r @ ( arr @ A_27a @ bool ) )
     => ! [V1p: $i] :
          ( ( mem @ V1p @ ( arr @ A_27a @ bool ) )
         => ! [V2q: $i] :
              ( ( mem @ V2q @ ( arr @ A_27a @ bool ) )
             => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1p ) @ V2q )
                  = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V2q ) @ V1p ) )
                & ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1p ) @ V2q ) ) @ V0r )
                  = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1p ) @ V2q ) ) @ V0r ) )
                & ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1p ) @ V2q ) ) @ V0r )
                  = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V2q ) @ V1p ) ) @ V0r ) )
                & ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1p ) @ V1p )
                  = V1p )
                & ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1p ) @ V1p ) ) @ V2q )
                  = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1p ) @ V2q ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECONJ__ACI,axiom,(
    ! [V0r: $i] :
      ( ( mem @ V0r @ bool )
     => ! [V1p: $i] :
          ( ( mem @ V1p @ bool )
         => ! [V2q: $i] :
              ( ( mem @ V2q @ bool )
             => ( ( ( ( p @ V1p )
                    & ( p @ V2q ) )
                <=> ( ( p @ V2q )
                    & ( p @ V1p ) ) )
                & ( ( ( p @ V1p )
                    & ( p @ V2q )
                    & ( p @ V0r ) )
                <=> ( ( p @ V1p )
                    & ( p @ V2q )
                    & ( p @ V0r ) ) )
                & ( ( ( p @ V1p )
                    & ( p @ V2q )
                    & ( p @ V0r ) )
                <=> ( ( p @ V2q )
                    & ( p @ V1p )
                    & ( p @ V0r ) ) )
                & ( ( ( p @ V1p )
                    & ( p @ V1p ) )
                <=> ( p @ V1p ) )
                & ( ( ( p @ V1p )
                    & ( p @ V1p )
                    & ( p @ V2q ) )
                <=> ( ( p @ V1p )
                    & ( p @ V2q ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EUNION__ACI,axiom,(
    ! [A_27a: del,V0r: $i] :
      ( ( mem @ V0r @ ( arr @ A_27a @ bool ) )
     => ! [V1p: $i] :
          ( ( mem @ V1p @ ( arr @ A_27a @ bool ) )
         => ! [V2q: $i] :
              ( ( mem @ V2q @ ( arr @ A_27a @ bool ) )
             => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1p ) @ V2q )
                  = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V2q ) @ V1p ) )
                & ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1p ) @ V2q ) ) @ V0r )
                  = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1p ) @ V2q ) ) @ V0r ) )
                & ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1p ) @ V2q ) ) @ V0r )
                  = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V2q ) @ V1p ) ) @ V0r ) )
                & ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1p ) @ V1p )
                  = V1p )
                & ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1p ) @ V1p ) ) @ V2q )
                  = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1p ) @ V2q ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ELT__NZ,axiom,(
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
    <=> ( V0n != fo__c_2Enum_2E0 ) ) )).

thf(conj_thm_2Ecardinal_2ELE__1,axiom,
    ( ! [V0n: tp__ty_2Enum_2Enum] :
        ( ( V0n != fo__c_2Enum_2E0 )
       => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
    & ! [V1n: tp__ty_2Enum_2Enum] :
        ( ( V1n != fo__c_2Enum_2E0 )
       => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
    & ! [V2n: tp__ty_2Enum_2Enum] :
        ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
       => ( V2n != fo__c_2Enum_2E0 ) )
    & ! [V3n: tp__ty_2Enum_2Enum] :
        ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
       => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
    & ! [V4n: tp__ty_2Enum_2Enum] :
        ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) )
       => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
    & ! [V5n: tp__ty_2Enum_2Enum] :
        ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V5n ) ) )
       => ( V5n != fo__c_2Enum_2E0 ) ) )).

thf(conj_thm_2Ecardinal_2EOR__EXISTS__THM,axiom,(
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
     => ! [V1Q: $i] :
          ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
         => ( ( ? [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                  & ( p @ ( ap @ V0P @ V2x ) ) )
              | ? [V3x: $i] :
                  ( ( mem @ V3x @ A_27a )
                  & ( p @ ( ap @ V1Q @ V3x ) ) ) )
          <=> ? [V4x: $i] :
                ( ( mem @ V4x @ A_27a )
                & ( ( p @ ( ap @ V0P @ V4x ) )
                  | ( p @ ( ap @ V1Q @ V4x ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EBIJECTIVE__INJECTIVE__SURJECTIVE,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
             => ( ( ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
                       => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V3x ) ) @ V2t ) ) ) )
                  & ! [V4y: $i] :
                      ( ( mem @ V4y @ A_27b )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4y ) @ V2t ) )
                       => ( p
                          @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
                            @ ( lam @ A_27a
                              @ ^ [V5x: $i] :
                                  ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V0f @ V5x ) ) @ V4y ) ) ) ) ) ) ) )
              <=> ( ! [V6x: $i] :
                      ( ( mem @ V6x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V1s ) )
                       => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V6x ) ) @ V2t ) ) ) )
                  & ! [V7x: $i] :
                      ( ( mem @ V7x @ A_27a )
                     => ! [V8y: $i] :
                          ( ( mem @ V8y @ A_27a )
                         => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V7x ) @ V1s ) )
                              & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V8y ) @ V1s ) )
                              & ( ( ap @ V0f @ V7x )
                                = ( ap @ V0f @ V8y ) ) )
                           => ( V7x = V8y ) ) ) )
                  & ! [V9y: $i] :
                      ( ( mem @ V9y @ A_27b )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V9y ) @ V2t ) )
                       => ? [V10x: $i] :
                            ( ( mem @ V10x @ A_27a )
                            & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V10x ) @ V1s ) )
                            & ( ( ap @ V0f @ V10x )
                              = V9y ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EBIJECTIVE__INVERSES,axiom,(
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
             => ( ( ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
                       => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V3x ) ) @ V2t ) ) ) )
                  & ! [V4y: $i] :
                      ( ( mem @ V4y @ A_27b )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4y ) @ V2t ) )
                       => ( p
                          @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
                            @ ( lam @ A_27a
                              @ ^ [V5x: $i] :
                                  ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V0f @ V5x ) ) @ V4y ) ) ) ) ) ) ) )
              <=> ( ! [V6x: $i] :
                      ( ( mem @ V6x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V1s ) )
                       => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V6x ) ) @ V2t ) ) ) )
                  & ? [V7g: $i] :
                      ( ( mem @ V7g @ ( arr @ A_27b @ A_27a ) )
                      & ! [V8y: $i] :
                          ( ( mem @ V8y @ A_27b )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V8y ) @ V2t ) )
                           => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V7g @ V8y ) ) @ V1s ) ) ) )
                      & ! [V9y: $i] :
                          ( ( mem @ V9y @ A_27b )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V9y ) @ V2t ) )
                           => ( ( ap @ V0f @ ( ap @ V7g @ V9y ) )
                              = V9y ) ) )
                      & ! [V10x: $i] :
                          ( ( mem @ V10x @ A_27a )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V10x ) @ V1s ) )
                           => ( ( ap @ V7g @ ( ap @ V0f @ V10x ) )
                              = V10x ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ele__c,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
          <=> ? [V2f: $i] :
                ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V2f @ V3x ) ) @ V1t ) ) ) )
                & ! [V4x: $i] :
                    ( ( mem @ V4x @ A_27a )
                   => ! [V5y: $i] :
                        ( ( mem @ V5y @ A_27a )
                       => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V0s ) )
                            & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5y ) @ V0s ) )
                            & ( ( ap @ V2f @ V4x )
                              = ( ap @ V2f @ V5y ) ) )
                         => ( V4x = V5y ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Elt__c,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) )
          <=> ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
              & ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Eeq__c,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
          <=> ? [V2f: $i] :
                ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V2f @ V3x ) ) @ V1t ) ) ) )
                & ! [V4y: $i] :
                    ( ( mem @ V4y @ A_27b )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4y ) @ V1t ) )
                     => ( p
                        @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
                          @ ( lam @ A_27a
                            @ ^ [V5x: $i] :
                                ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V0s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V2f @ V5x ) ) @ V4y ) ) ) ) ) ) ) ) ) ) ) )).

thf(ax_thm_2Ecardinal_2Ecardgeq__def,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardgeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
          <=> ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Ege__c,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardgeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
          <=> ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) )).

thf(ax_thm_2Ecardinal_2Ecardgt__def,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardgt @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
          <=> ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2Egt__c,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardgt @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
          <=> ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ELE__C,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
          <=> ? [V2g: $i] :
                ( ( mem @ V2g @ ( arr @ A_27b @ A_27a ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ? [V4y: $i] :
                          ( ( mem @ V4y @ A_27b )
                          & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4y ) @ V1t ) )
                          & ( ( ap @ V2g @ V4y )
                            = V3x ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EGE__C,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardgeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
          <=> ? [V2f: $i] :
                ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
                & ! [V3y: $i] :
                    ( ( mem @ V3y @ A_27b )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3y ) @ V1t ) )
                     => ? [V4x: $i] :
                          ( ( mem @ V4x @ A_27a )
                          & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V0s ) )
                          & ( V3y
                            = ( ap @ V2f @ V4x ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECOUNTABLE,axiom,(
    ! [A_27a: del,V0t: $i] :
      ( ( mem @ V0t @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0t ) )
      <=> ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardgeq @ ty_2Enum_2Enum @ A_27a ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ V0t ) ) ) ) )).

thf(conj_thm_2Ecardinal_2EEQ__C,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
          <=> ? [V2R: $i] :
                ( ( mem @ V2R @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ! [V4y: $i] :
                        ( ( mem @ V4y @ A_27b )
                       => ( ( p @ ( ap @ V2R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V3x ) @ V4y ) ) )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                            & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4y ) @ V1t ) ) ) ) ) )
                & ! [V5x: $i] :
                    ( ( mem @ V5x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V0s ) )
                     => ( p
                        @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27b )
                          @ ( lam @ A_27b
                            @ ^ [V6y: $i] :
                                ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V6y ) @ V1t ) ) @ ( ap @ V2R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V5x ) @ V6y ) ) ) ) ) ) ) )
                & ! [V7y: $i] :
                    ( ( mem @ V7y @ A_27b )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V7y ) @ V1t ) )
                     => ( p
                        @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
                          @ ( lam @ A_27a
                            @ ^ [V8x: $i] :
                                ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V8x ) @ V0s ) ) @ ( ap @ V2R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V8x ) @ V7y ) ) ) ) ) ) ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LE__REFL,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27a ) @ V0s ) @ V0s ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LE__TRANS,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ! [V2u: $i] :
              ( ( mem @ V2u @ ( arr @ A_27c @ bool ) )
             => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27c ) @ V1t ) @ V2u ) ) )
               => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27c ) @ V0s ) @ V2u ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LT__REFL,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ~ ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27a ) @ V0s ) @ V0s ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LET__TRANS,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ! [V2u: $i] :
              ( ( mem @ V2u @ ( arr @ A_27c @ bool ) )
             => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
                  & ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27c @ A_27b ) @ V2u ) @ V1t ) ) )
               => ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27c @ A_27a ) @ V2u ) @ V0s ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LTE__TRANS,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ! [V2u: $i] :
              ( ( mem @ V2u @ ( arr @ A_27c @ bool ) )
             => ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27c ) @ V1t ) @ V2u ) ) )
               => ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27c @ A_27a ) @ V2u ) @ V0s ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LT__TRANS,axiom,(
    ! [A_27a: del,A_27b: del,A_27c: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ! [V2u: $i] :
              ( ( mem @ V2u @ ( arr @ A_27c @ bool ) )
             => ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) )
                  & ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27c @ A_27b ) @ V2u ) @ V1t ) ) )
               => ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27c @ A_27a ) @ V2u ) @ V0s ) ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__EQ__REFL,axiom,(
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27a ) @ V0s ) @ V0s ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__EQ__SYM,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
          <=> ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27b @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__EQ__IMP__LE,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
           => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LT__IMP__LE,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) )
           => ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LE__RELATIONAL,axiom,(
    ! [A_27a: del,A_27b: del,V0R: $i] :
      ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ! [V3y: $i] :
                    ( ( mem @ V3y @ A_27b )
                   => ! [V4y_27: $i] :
                        ( ( mem @ V4y_27 @ A_27b )
                       => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
                            & ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
                            & ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V4y_27 ) ) )
                         => ( V3y = V4y_27 ) ) ) ) )
           => ( p
              @ ( ap
                @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a )
                  @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27b )
                    @ ( lam @ A_27b
                      @ ^ [V5y: $i] :
                          ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ V5y )
                          @ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
                            @ ( lam @ A_27a
                              @ ^ [V6x: $i] :
                                  ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V1s ) ) @ ( ap @ ( ap @ V0R @ V6x ) @ V5y ) ) ) ) ) ) ) )
                @ V1s ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LE__EMPTY,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) )
      <=> ( V0s
          = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__EQ__EMPTY,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) )
      <=> ( V0s
          = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LE__ANTISYM,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
              & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) ) )
          <=> ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LE__TOTAL,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
            | ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LET__TOTAL,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
            | ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LTE__TOTAL,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) )
            | ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__LT__TOTAL,axiom,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardeq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
            | ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) )
            | ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) )).

thf(conj_thm_2Ecardinal_2ECARD__NOT__LE,conjecture,(
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
         => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
          <=> ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) )).

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